WORKING PAPERS

ADVERTISING INTENSITY MARKET SHARE CONCENTRATION AND

DEGREE OF COOPERATION

William F Long

Working Paper No 65

June 1982

nc Bureau rl Ecooomics working papers are preJiminary materials circulated to stimulate discussioa and critical commenL AD data cootained in them are in the pabk domain Dis indodes informatioa obtaiaed by the Ccmmiioo which has become part of pablic record The IDd coodnsions set forth are those rl tile authors aod do ad middot reflect tflt 1im of other members rl the Bureau of Economics other Commissioo staff or the Commission itseJC Uponrequest agle copies rl the paper will be provided References in pobUcatioos to FfC Bureau of Ecooomks working papers by FfC ecoooomts (other than adalowiedgemeot by a mer that be b access to such aupublished materials) should be cleared with the author to protect tbe tentative dlaracter of these papers

BUREAU OF ECONOMICS FEDERAL TRADE COMJrflSSION

WASillNGTON DC 20580

ADVERTISING INTENSITY MARKET SHARE CONCENTRATION

AND DEGREE OF COOPERATION

William F Long

The represen ta t ions and conclus ions presented herein are those of the

author and have no t been adopted in whole or in part by the Federal Trade

Commission or its Bureau of Economics The Assis tant D irector o f the Bureau

of Economics for Financial Sta tistics has certif ied tha t he has

approved the discl osure avoidance proc edures used by the staff of the

Bus iness Program to ensure tha t the data included in this pap r do

indiv idual company line of bus iness data

reviewed and

Line of

no t1 id entify

ith

ADVERTI SING INTENSITY ARKET SHARE

CONCENTRATI6 a n d DEGREE of COO ERATION

Wi l lia m F L o n g

The purpo ses of this study are to assess the role that advertising

plays in several explicit models of industrial organizationl and to formushy

late procedures for testing hypotheses which that asse ssment ge nerates

In addition a technique for the explicit introduction of the degree of coshy

operation in such models is used and the impact of cooperation is explored

I bull THE GENERAL SETTING

I assume a static industry with N firms By industry I mean a group

of firms that pro duce goods which are perceived as substitutes The goods

may be perfect substitutes but nee d not be Other goods outside the group

in questio n are assumed to be irrelevant

thUsing pi q and a for price quantity and advertising for the 1--i i

firm respectively the price of the goo d is assumed to be a function of all

quantities and advertising outlays ie

(1)

where bars under letters indicate vectors I define y as the elasticity ofij

the j goo ds price with respect to the goods advertising i e

thLetting c bull c (q ) be total production cost for the i-- firm i i i

and ll its pro fit i

(2)

-De fining some additional variab les let si

v bull a s be adve rtising intensity Define S bull rs as industry sales i i i i

ith

Page 2

A bull tai as industry adverti sing and zi bull siS as the market share of the

firm

II TWO POLAR CASE OLIGOPOLY MODELS

Cournot Let each firm maximize its profit independently of all other

firms That is

(3)

- 1

si- -- - 1 - 0yii ai

This implies that

-(4) v bull yiii

Let r bull (yij) Further let Ad be a diagonal matrix with the same diagonal

as the matrix A Then the N equations in (4) may be written compactly as

(5) v bull rd l

where is a vector of ones Since rd is a diagonal matrix (5) may be reshy

written as

(6 )

where if is a vector

z on the diagonal7

Chamberlin

3

v bull

d is a diagonal matrix containing the elements of z

4 At the other extreme let each firm maximize total profit

for all firms Letting IT trribull

an

Page 3

( 7 )

- 0

This implies that

(8)

(9)

-

v bull bull

bull

bull

zl [ Y21 Y22 bull bull Y2N J

-1zl 0

-1z2 r z

0 1

Page 4

Writ ing (8) compactly gives

the matrix in the two equationsA comparison of (6) and (9) shows that

differs only in that all the elasticities are present in (9) but only the

awn-elasticities are present in ( 6 ) Since advertising expense mus t be I non-negat ive the first-order requirements are that v be the maximum of t

i

the amount shown in 6) or (9) and zero

III A SIMPLIFIED DEMAND STRUCTURE

So far the demand equation system is comple tely general I will now

move to a particular demand structure which is charac terized by an industry

elasticity of price with respect to advertising a general brand-swi tching

elas ticity and a dependence of the firm-specific elas ticity on its relative

size I make the expli cit assumpt ion that

n pound

)l

0 AA

Consider the identification of y as an elasticity of industry price

Page 5

(10)

where y is an

- (y- a)

industry demand elasticity a is a brand-swi tching

el astici ty and z1 is the market share In matrix no tation

(11) r bull ai + (y- a) t

wi th respe ct to advertising 0

le t ting S denote dS observe that

0(12) SS bull

-

-1 0s t s - -1 0S t d - 9- -

apl apl aplaa1 aa2 a 0 a

middot( a Pl

( 13)

-

-0 a bull 0

a

) 0 X s

-1 0dAA bull then d

a bull

J 0

(JA) middot and

Let the sc alar (SS)(AA) be denoted by y so ya zft

If

1

d

-

I

I

(11)

--

y

I -f

l J- a)

a) l zt

Substitutin g into (13) gives

i [ ai + (y(14) -I- bull S A

bull az + (y -

Pa ge6

I I II

bull

since l bull 1

Under these assumpt ons then y is the elasticity of industry sales

(and average industry p ice) with respect to industry advertisin g Note

that if y bull 0 so that there is no industry sales effect there will still

be positive advertising if there are brand-switching effects

Turning now to the brand-switching ef fect observe that

(15)

Noting that

-1 deg -1d z -z -

-

0 a

Page 7

(15) may be written as

0 (AA)

lx 2x 1x

ith

1y

i

First assume no

that if there are

will be no changes in market shares

- 0a bull

Page 8

Equation (17) is a general statement of the relation betbulleen changes in

advertising levels and changes in market shares which would acompany them It

may be used to make some general observations about brand-switching effects

industry effect eg y bull r t bull 0 and assume further

equal percentage changes in all advertising le =ls then there

Under these further assumptions

0l and dz -1 bull (iA) ltr assumption the second term on the right hand side of this expression is

- By

zero

necessary for rt bull 0Consequently for market shares to be unaffected it is

when y bull r l bull 0 This requirement is satisfied by equation (11)

Secondly consider effects on market shares if one firm inc ases its abull ar-

tising and others do not As a general assumption we require smiddot ch a change o

lead to a decrease in the shares of all the other firms hat is let

0 0aiai gt 0 and a a bull 0 for j + i For any matrix X with N rows and its trans-j j

pose X let X

row of X

bull middotmiddotmiddot where is a column vector which contains the

elements of the Under the assumptions about the iis given just

d-1 0 0above it follows that r becomes (aiai) iimiddot ehFor jzj lt 0 under these conditions then it follows that the j- element

N of (I- l ) lt 0 so middotij - il lt 0 or yij - yik lt 0 If this

kbulll N condition holds for all Y ij where j + i then it follows that yii - z

k Y gta

k- 1 ik since the th firms share must increase to offset the decreases in all other

shares

ei ith

1v ( ) h i

7urning

where is the

leads to z

to the r matrix given in (11) we note that 1 = cr + (y - cr) i i zi elementary vector with 1 in the position and 0 elsewhere This

bull cr + (y - cr) zi Since bull required is thatcr at- zY wYij (y - cr)zi - cr + (y - cr) zilt 0 or cr gt 0

These observations may be summarized by substituting (11) into (17) bull

giving

(18)

i s

d -1 zz -

-

-

+ (y - cr) tz

d -1 0cr(I - l ) a a bull

cr 1 z - (y - cr) 0 a

o

If ai increases and the other a s are const t cr must be positive to havej

a positive effect on zi A positive cr also bull plies a negative ffect of aJ

f all a s in-on zi other a s (including a ) fixed j

eluding a1 change by the same percentage zi remains unchanged Finally k i

if cr bull 0 there is no brand-switching effect

For a to have no effect on p requires yij bull 0 From (10) thisj i

amounts to y bull cr that is the industry demand elasticity and the brandshyswitching elasticity are equal If y gt cr gt 0 the industry elasticity yij doninates If y lt cr y lt 0 the brand-switching elasticity dominates ij

making

Page 10

Substituting ( 1 1) now in (6) the Cournot case and in (9) the

Chamberlin ease gives

-(19) Cournot vO a + (y - a) z

Chamberli n vl - y lmiddot th

The 1- element is then

-(20) Cournot vO a+ (y - a) zi i

-Chamberlin vl yi

In (19) and (20) the superscript 0 is used to denote total

independence of decision and the superscript l is used to denote

total interdependence of decision making

The relation between v and vf depends solely on t relation between

y and a f y gt a so that the industry effect dominat 3 vf v with

equality in the trirlal case of z bull 1 Cooperative irms would have ai

higher advertising intensity than non-cooperative fi

If there is equality between the industry elasticity and the

y Whe therbrand-switching elasticity or y bull there is cooperation among the firms has no effect on advertising inten-sity And if brand-switching is more important with y lt a e get

vi lt v cooperative firms will have a lower advertising intensity than

non-cooperative firms The three situations are depicted in Figure L

Given the results for the firm level variables calculation of the

corresponding re sults for the industry is s-traightforward Let

B bull t zf bull z z be the Herfindahl index of concen tration and notethat

z - bull l z bull 1 and that V bull A S bull a i 5 bull (siIS) (asi)i

bull middot Then for the general case from (6) and (9)

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

ADVERTISING INTENSITY MARKET SHARE CONCENTRATION

AND DEGREE OF COOPERATION

William F Long

The represen ta t ions and conclus ions presented herein are those of the

author and have no t been adopted in whole or in part by the Federal Trade

Commission or its Bureau of Economics The Assis tant D irector o f the Bureau

of Economics for Financial Sta tistics has certif ied tha t he has

approved the discl osure avoidance proc edures used by the staff of the

Bus iness Program to ensure tha t the data included in this pap r do

indiv idual company line of bus iness data

reviewed and

Line of

no t1 id entify

ith

ADVERTI SING INTENSITY ARKET SHARE

CONCENTRATI6 a n d DEGREE of COO ERATION

Wi l lia m F L o n g

The purpo ses of this study are to assess the role that advertising

plays in several explicit models of industrial organizationl and to formushy

late procedures for testing hypotheses which that asse ssment ge nerates

In addition a technique for the explicit introduction of the degree of coshy

operation in such models is used and the impact of cooperation is explored

I bull THE GENERAL SETTING

I assume a static industry with N firms By industry I mean a group

of firms that pro duce goods which are perceived as substitutes The goods

may be perfect substitutes but nee d not be Other goods outside the group

in questio n are assumed to be irrelevant

thUsing pi q and a for price quantity and advertising for the 1--i i

firm respectively the price of the goo d is assumed to be a function of all

quantities and advertising outlays ie

(1)

where bars under letters indicate vectors I define y as the elasticity ofij

the j goo ds price with respect to the goods advertising i e

thLetting c bull c (q ) be total production cost for the i-- firm i i i

and ll its pro fit i

(2)

-De fining some additional variab les let si

v bull a s be adve rtising intensity Define S bull rs as industry sales i i i i

ith

Page 2

A bull tai as industry adverti sing and zi bull siS as the market share of the

firm

II TWO POLAR CASE OLIGOPOLY MODELS

Cournot Let each firm maximize its profit independently of all other

firms That is

(3)

- 1

si- -- - 1 - 0yii ai

This implies that

-(4) v bull yiii

Let r bull (yij) Further let Ad be a diagonal matrix with the same diagonal

as the matrix A Then the N equations in (4) may be written compactly as

(5) v bull rd l

where is a vector of ones Since rd is a diagonal matrix (5) may be reshy

written as

(6 )

where if is a vector

z on the diagonal7

Chamberlin

3

v bull

d is a diagonal matrix containing the elements of z

4 At the other extreme let each firm maximize total profit

for all firms Letting IT trribull

an

Page 3

( 7 )

- 0

This implies that

(8)

(9)

-

v bull bull

bull

bull

zl [ Y21 Y22 bull bull Y2N J

-1zl 0

-1z2 r z

0 1

Page 4

Writ ing (8) compactly gives

the matrix in the two equationsA comparison of (6) and (9) shows that

differs only in that all the elasticities are present in (9) but only the

awn-elasticities are present in ( 6 ) Since advertising expense mus t be I non-negat ive the first-order requirements are that v be the maximum of t

i

the amount shown in 6) or (9) and zero

III A SIMPLIFIED DEMAND STRUCTURE

So far the demand equation system is comple tely general I will now

move to a particular demand structure which is charac terized by an industry

elasticity of price with respect to advertising a general brand-swi tching

elas ticity and a dependence of the firm-specific elas ticity on its relative

size I make the expli cit assumpt ion that

n pound

)l

0 AA

Consider the identification of y as an elasticity of industry price

Page 5

(10)

where y is an

- (y- a)

industry demand elasticity a is a brand-swi tching

el astici ty and z1 is the market share In matrix no tation

(11) r bull ai + (y- a) t

wi th respe ct to advertising 0

le t ting S denote dS observe that

0(12) SS bull

-

-1 0s t s - -1 0S t d - 9- -

apl apl aplaa1 aa2 a 0 a

middot( a Pl

( 13)

-

-0 a bull 0

a

) 0 X s

-1 0dAA bull then d

a bull

J 0

(JA) middot and

Let the sc alar (SS)(AA) be denoted by y so ya zft

If

1

d

-

I

I

(11)

--

y

I -f

l J- a)

a) l zt

Substitutin g into (13) gives

i [ ai + (y(14) -I- bull S A

bull az + (y -

Pa ge6

I I II

bull

since l bull 1

Under these assumpt ons then y is the elasticity of industry sales

(and average industry p ice) with respect to industry advertisin g Note

that if y bull 0 so that there is no industry sales effect there will still

be positive advertising if there are brand-switching effects

Turning now to the brand-switching ef fect observe that

(15)

Noting that

-1 deg -1d z -z -

-

0 a

Page 7

(15) may be written as

0 (AA)

lx 2x 1x

ith

1y

i

First assume no

that if there are

will be no changes in market shares

- 0a bull

Page 8

Equation (17) is a general statement of the relation betbulleen changes in

advertising levels and changes in market shares which would acompany them It

may be used to make some general observations about brand-switching effects

industry effect eg y bull r t bull 0 and assume further

equal percentage changes in all advertising le =ls then there

Under these further assumptions

0l and dz -1 bull (iA) ltr assumption the second term on the right hand side of this expression is

- By

zero

necessary for rt bull 0Consequently for market shares to be unaffected it is

when y bull r l bull 0 This requirement is satisfied by equation (11)

Secondly consider effects on market shares if one firm inc ases its abull ar-

tising and others do not As a general assumption we require smiddot ch a change o

lead to a decrease in the shares of all the other firms hat is let

0 0aiai gt 0 and a a bull 0 for j + i For any matrix X with N rows and its trans-j j

pose X let X

row of X

bull middotmiddotmiddot where is a column vector which contains the

elements of the Under the assumptions about the iis given just

d-1 0 0above it follows that r becomes (aiai) iimiddot ehFor jzj lt 0 under these conditions then it follows that the j- element

N of (I- l ) lt 0 so middotij - il lt 0 or yij - yik lt 0 If this

kbulll N condition holds for all Y ij where j + i then it follows that yii - z

k Y gta

k- 1 ik since the th firms share must increase to offset the decreases in all other

shares

ei ith

1v ( ) h i

7urning

where is the

leads to z

to the r matrix given in (11) we note that 1 = cr + (y - cr) i i zi elementary vector with 1 in the position and 0 elsewhere This

bull cr + (y - cr) zi Since bull required is thatcr at- zY wYij (y - cr)zi - cr + (y - cr) zilt 0 or cr gt 0

These observations may be summarized by substituting (11) into (17) bull

giving

(18)

i s

d -1 zz -

-

-

+ (y - cr) tz

d -1 0cr(I - l ) a a bull

cr 1 z - (y - cr) 0 a

o

If ai increases and the other a s are const t cr must be positive to havej

a positive effect on zi A positive cr also bull plies a negative ffect of aJ

f all a s in-on zi other a s (including a ) fixed j

eluding a1 change by the same percentage zi remains unchanged Finally k i

if cr bull 0 there is no brand-switching effect

For a to have no effect on p requires yij bull 0 From (10) thisj i

amounts to y bull cr that is the industry demand elasticity and the brandshyswitching elasticity are equal If y gt cr gt 0 the industry elasticity yij doninates If y lt cr y lt 0 the brand-switching elasticity dominates ij

making

Page 10

Substituting ( 1 1) now in (6) the Cournot case and in (9) the

Chamberlin ease gives

-(19) Cournot vO a + (y - a) z

Chamberli n vl - y lmiddot th

The 1- element is then

-(20) Cournot vO a+ (y - a) zi i

-Chamberlin vl yi

In (19) and (20) the superscript 0 is used to denote total

independence of decision and the superscript l is used to denote

total interdependence of decision making

The relation between v and vf depends solely on t relation between

y and a f y gt a so that the industry effect dominat 3 vf v with

equality in the trirlal case of z bull 1 Cooperative irms would have ai

higher advertising intensity than non-cooperative fi

If there is equality between the industry elasticity and the

y Whe therbrand-switching elasticity or y bull there is cooperation among the firms has no effect on advertising inten-sity And if brand-switching is more important with y lt a e get

vi lt v cooperative firms will have a lower advertising intensity than

non-cooperative firms The three situations are depicted in Figure L

Given the results for the firm level variables calculation of the

corresponding re sults for the industry is s-traightforward Let

B bull t zf bull z z be the Herfindahl index of concen tration and notethat

z - bull l z bull 1 and that V bull A S bull a i 5 bull (siIS) (asi)i

bull middot Then for the general case from (6) and (9)

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

ith

ADVERTI SING INTENSITY ARKET SHARE

CONCENTRATI6 a n d DEGREE of COO ERATION

Wi l lia m F L o n g

The purpo ses of this study are to assess the role that advertising

plays in several explicit models of industrial organizationl and to formushy

late procedures for testing hypotheses which that asse ssment ge nerates

In addition a technique for the explicit introduction of the degree of coshy

operation in such models is used and the impact of cooperation is explored

I bull THE GENERAL SETTING

I assume a static industry with N firms By industry I mean a group

of firms that pro duce goods which are perceived as substitutes The goods

may be perfect substitutes but nee d not be Other goods outside the group

in questio n are assumed to be irrelevant

thUsing pi q and a for price quantity and advertising for the 1--i i

firm respectively the price of the goo d is assumed to be a function of all

quantities and advertising outlays ie

(1)

where bars under letters indicate vectors I define y as the elasticity ofij

the j goo ds price with respect to the goods advertising i e

thLetting c bull c (q ) be total production cost for the i-- firm i i i

and ll its pro fit i

(2)

-De fining some additional variab les let si

v bull a s be adve rtising intensity Define S bull rs as industry sales i i i i

ith

Page 2

A bull tai as industry adverti sing and zi bull siS as the market share of the

firm

II TWO POLAR CASE OLIGOPOLY MODELS

Cournot Let each firm maximize its profit independently of all other

firms That is

(3)

- 1

si- -- - 1 - 0yii ai

This implies that

-(4) v bull yiii

Let r bull (yij) Further let Ad be a diagonal matrix with the same diagonal

as the matrix A Then the N equations in (4) may be written compactly as

(5) v bull rd l

where is a vector of ones Since rd is a diagonal matrix (5) may be reshy

written as

(6 )

where if is a vector

z on the diagonal7

Chamberlin

3

v bull

d is a diagonal matrix containing the elements of z

4 At the other extreme let each firm maximize total profit

for all firms Letting IT trribull

an

Page 3

( 7 )

- 0

This implies that

(8)

(9)

-

v bull bull

bull

bull

zl [ Y21 Y22 bull bull Y2N J

-1zl 0

-1z2 r z

0 1

Page 4

Writ ing (8) compactly gives

the matrix in the two equationsA comparison of (6) and (9) shows that

differs only in that all the elasticities are present in (9) but only the

awn-elasticities are present in ( 6 ) Since advertising expense mus t be I non-negat ive the first-order requirements are that v be the maximum of t

i

the amount shown in 6) or (9) and zero

III A SIMPLIFIED DEMAND STRUCTURE

So far the demand equation system is comple tely general I will now

move to a particular demand structure which is charac terized by an industry

elasticity of price with respect to advertising a general brand-swi tching

elas ticity and a dependence of the firm-specific elas ticity on its relative

size I make the expli cit assumpt ion that

n pound

)l

0 AA

Consider the identification of y as an elasticity of industry price

Page 5

(10)

where y is an

- (y- a)

industry demand elasticity a is a brand-swi tching

el astici ty and z1 is the market share In matrix no tation

(11) r bull ai + (y- a) t

wi th respe ct to advertising 0

le t ting S denote dS observe that

0(12) SS bull

-

-1 0s t s - -1 0S t d - 9- -

apl apl aplaa1 aa2 a 0 a

middot( a Pl

( 13)

-

-0 a bull 0

a

) 0 X s

-1 0dAA bull then d

a bull

J 0

(JA) middot and

Let the sc alar (SS)(AA) be denoted by y so ya zft

If

1

d

-

I

I

(11)

--

y

I -f

l J- a)

a) l zt

Substitutin g into (13) gives

i [ ai + (y(14) -I- bull S A

bull az + (y -

Pa ge6

I I II

bull

since l bull 1

Under these assumpt ons then y is the elasticity of industry sales

(and average industry p ice) with respect to industry advertisin g Note

that if y bull 0 so that there is no industry sales effect there will still

be positive advertising if there are brand-switching effects

Turning now to the brand-switching ef fect observe that

(15)

Noting that

-1 deg -1d z -z -

-

0 a

Page 7

(15) may be written as

0 (AA)

lx 2x 1x

ith

1y

i

First assume no

that if there are

will be no changes in market shares

- 0a bull

Page 8

Equation (17) is a general statement of the relation betbulleen changes in

advertising levels and changes in market shares which would acompany them It

may be used to make some general observations about brand-switching effects

industry effect eg y bull r t bull 0 and assume further

equal percentage changes in all advertising le =ls then there

Under these further assumptions

0l and dz -1 bull (iA) ltr assumption the second term on the right hand side of this expression is

- By

zero

necessary for rt bull 0Consequently for market shares to be unaffected it is

when y bull r l bull 0 This requirement is satisfied by equation (11)

Secondly consider effects on market shares if one firm inc ases its abull ar-

tising and others do not As a general assumption we require smiddot ch a change o

lead to a decrease in the shares of all the other firms hat is let

0 0aiai gt 0 and a a bull 0 for j + i For any matrix X with N rows and its trans-j j

pose X let X

row of X

bull middotmiddotmiddot where is a column vector which contains the

elements of the Under the assumptions about the iis given just

d-1 0 0above it follows that r becomes (aiai) iimiddot ehFor jzj lt 0 under these conditions then it follows that the j- element

N of (I- l ) lt 0 so middotij - il lt 0 or yij - yik lt 0 If this

kbulll N condition holds for all Y ij where j + i then it follows that yii - z

k Y gta

k- 1 ik since the th firms share must increase to offset the decreases in all other

shares

ei ith

1v ( ) h i

7urning

where is the

leads to z

to the r matrix given in (11) we note that 1 = cr + (y - cr) i i zi elementary vector with 1 in the position and 0 elsewhere This

bull cr + (y - cr) zi Since bull required is thatcr at- zY wYij (y - cr)zi - cr + (y - cr) zilt 0 or cr gt 0

These observations may be summarized by substituting (11) into (17) bull

giving

(18)

i s

d -1 zz -

-

-

+ (y - cr) tz

d -1 0cr(I - l ) a a bull

cr 1 z - (y - cr) 0 a

o

If ai increases and the other a s are const t cr must be positive to havej

a positive effect on zi A positive cr also bull plies a negative ffect of aJ

f all a s in-on zi other a s (including a ) fixed j

eluding a1 change by the same percentage zi remains unchanged Finally k i

if cr bull 0 there is no brand-switching effect

For a to have no effect on p requires yij bull 0 From (10) thisj i

amounts to y bull cr that is the industry demand elasticity and the brandshyswitching elasticity are equal If y gt cr gt 0 the industry elasticity yij doninates If y lt cr y lt 0 the brand-switching elasticity dominates ij

making

Page 10

Substituting ( 1 1) now in (6) the Cournot case and in (9) the

Chamberlin ease gives

-(19) Cournot vO a + (y - a) z

Chamberli n vl - y lmiddot th

The 1- element is then

-(20) Cournot vO a+ (y - a) zi i

-Chamberlin vl yi

In (19) and (20) the superscript 0 is used to denote total

independence of decision and the superscript l is used to denote

total interdependence of decision making

The relation between v and vf depends solely on t relation between

y and a f y gt a so that the industry effect dominat 3 vf v with

equality in the trirlal case of z bull 1 Cooperative irms would have ai

higher advertising intensity than non-cooperative fi

If there is equality between the industry elasticity and the

y Whe therbrand-switching elasticity or y bull there is cooperation among the firms has no effect on advertising inten-sity And if brand-switching is more important with y lt a e get

vi lt v cooperative firms will have a lower advertising intensity than

non-cooperative firms The three situations are depicted in Figure L

Given the results for the firm level variables calculation of the

corresponding re sults for the industry is s-traightforward Let

B bull t zf bull z z be the Herfindahl index of concen tration and notethat

z - bull l z bull 1 and that V bull A S bull a i 5 bull (siIS) (asi)i

bull middot Then for the general case from (6) and (9)

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

ith

Page 2

A bull tai as industry adverti sing and zi bull siS as the market share of the

firm

II TWO POLAR CASE OLIGOPOLY MODELS

Cournot Let each firm maximize its profit independently of all other

firms That is

(3)

- 1

si- -- - 1 - 0yii ai

This implies that

-(4) v bull yiii

Let r bull (yij) Further let Ad be a diagonal matrix with the same diagonal

as the matrix A Then the N equations in (4) may be written compactly as

(5) v bull rd l

where is a vector of ones Since rd is a diagonal matrix (5) may be reshy

written as

(6 )

where if is a vector

z on the diagonal7

Chamberlin

3

v bull

d is a diagonal matrix containing the elements of z

4 At the other extreme let each firm maximize total profit

for all firms Letting IT trribull

an

Page 3

( 7 )

- 0

This implies that

(8)

(9)

-

v bull bull

bull

bull

zl [ Y21 Y22 bull bull Y2N J

-1zl 0

-1z2 r z

0 1

Page 4

Writ ing (8) compactly gives

the matrix in the two equationsA comparison of (6) and (9) shows that

differs only in that all the elasticities are present in (9) but only the

awn-elasticities are present in ( 6 ) Since advertising expense mus t be I non-negat ive the first-order requirements are that v be the maximum of t

i

the amount shown in 6) or (9) and zero

III A SIMPLIFIED DEMAND STRUCTURE

So far the demand equation system is comple tely general I will now

move to a particular demand structure which is charac terized by an industry

elasticity of price with respect to advertising a general brand-swi tching

elas ticity and a dependence of the firm-specific elas ticity on its relative

size I make the expli cit assumpt ion that

n pound

)l

0 AA

Consider the identification of y as an elasticity of industry price

Page 5

(10)

where y is an

- (y- a)

industry demand elasticity a is a brand-swi tching

el astici ty and z1 is the market share In matrix no tation

(11) r bull ai + (y- a) t

wi th respe ct to advertising 0

le t ting S denote dS observe that

0(12) SS bull

-

-1 0s t s - -1 0S t d - 9- -

apl apl aplaa1 aa2 a 0 a

middot( a Pl

( 13)

-

-0 a bull 0

a

) 0 X s

-1 0dAA bull then d

a bull

J 0

(JA) middot and

Let the sc alar (SS)(AA) be denoted by y so ya zft

If

1

d

-

I

I

(11)

--

y

I -f

l J- a)

a) l zt

Substitutin g into (13) gives

i [ ai + (y(14) -I- bull S A

bull az + (y -

Pa ge6

I I II

bull

since l bull 1

Under these assumpt ons then y is the elasticity of industry sales

(and average industry p ice) with respect to industry advertisin g Note

that if y bull 0 so that there is no industry sales effect there will still

be positive advertising if there are brand-switching effects

Turning now to the brand-switching ef fect observe that

(15)

Noting that

-1 deg -1d z -z -

-

0 a

Page 7

(15) may be written as

0 (AA)

lx 2x 1x

ith

1y

i

First assume no

that if there are

will be no changes in market shares

- 0a bull

Page 8

Equation (17) is a general statement of the relation betbulleen changes in

advertising levels and changes in market shares which would acompany them It

may be used to make some general observations about brand-switching effects

industry effect eg y bull r t bull 0 and assume further

equal percentage changes in all advertising le =ls then there

Under these further assumptions

0l and dz -1 bull (iA) ltr assumption the second term on the right hand side of this expression is

- By

zero

necessary for rt bull 0Consequently for market shares to be unaffected it is

when y bull r l bull 0 This requirement is satisfied by equation (11)

Secondly consider effects on market shares if one firm inc ases its abull ar-

tising and others do not As a general assumption we require smiddot ch a change o

lead to a decrease in the shares of all the other firms hat is let

0 0aiai gt 0 and a a bull 0 for j + i For any matrix X with N rows and its trans-j j

pose X let X

row of X

bull middotmiddotmiddot where is a column vector which contains the

elements of the Under the assumptions about the iis given just

d-1 0 0above it follows that r becomes (aiai) iimiddot ehFor jzj lt 0 under these conditions then it follows that the j- element

N of (I- l ) lt 0 so middotij - il lt 0 or yij - yik lt 0 If this

kbulll N condition holds for all Y ij where j + i then it follows that yii - z

k Y gta

k- 1 ik since the th firms share must increase to offset the decreases in all other

shares

ei ith

1v ( ) h i

7urning

where is the

leads to z

to the r matrix given in (11) we note that 1 = cr + (y - cr) i i zi elementary vector with 1 in the position and 0 elsewhere This

bull cr + (y - cr) zi Since bull required is thatcr at- zY wYij (y - cr)zi - cr + (y - cr) zilt 0 or cr gt 0

These observations may be summarized by substituting (11) into (17) bull

giving

(18)

i s

d -1 zz -

-

-

+ (y - cr) tz

d -1 0cr(I - l ) a a bull

cr 1 z - (y - cr) 0 a

o

If ai increases and the other a s are const t cr must be positive to havej

a positive effect on zi A positive cr also bull plies a negative ffect of aJ

f all a s in-on zi other a s (including a ) fixed j

eluding a1 change by the same percentage zi remains unchanged Finally k i

if cr bull 0 there is no brand-switching effect

For a to have no effect on p requires yij bull 0 From (10) thisj i

amounts to y bull cr that is the industry demand elasticity and the brandshyswitching elasticity are equal If y gt cr gt 0 the industry elasticity yij doninates If y lt cr y lt 0 the brand-switching elasticity dominates ij

making

Page 10

Substituting ( 1 1) now in (6) the Cournot case and in (9) the

Chamberlin ease gives

-(19) Cournot vO a + (y - a) z

Chamberli n vl - y lmiddot th

The 1- element is then

-(20) Cournot vO a+ (y - a) zi i

-Chamberlin vl yi

In (19) and (20) the superscript 0 is used to denote total

independence of decision and the superscript l is used to denote

total interdependence of decision making

The relation between v and vf depends solely on t relation between

y and a f y gt a so that the industry effect dominat 3 vf v with

equality in the trirlal case of z bull 1 Cooperative irms would have ai

higher advertising intensity than non-cooperative fi

If there is equality between the industry elasticity and the

y Whe therbrand-switching elasticity or y bull there is cooperation among the firms has no effect on advertising inten-sity And if brand-switching is more important with y lt a e get

vi lt v cooperative firms will have a lower advertising intensity than

non-cooperative firms The three situations are depicted in Figure L

Given the results for the firm level variables calculation of the

corresponding re sults for the industry is s-traightforward Let

B bull t zf bull z z be the Herfindahl index of concen tration and notethat

z - bull l z bull 1 and that V bull A S bull a i 5 bull (siIS) (asi)i

bull middot Then for the general case from (6) and (9)

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

an

Page 3

( 7 )

- 0

This implies that

(8)

(9)

-

v bull bull

bull

bull

zl [ Y21 Y22 bull bull Y2N J

-1zl 0

-1z2 r z

0 1

Page 4

Writ ing (8) compactly gives

the matrix in the two equationsA comparison of (6) and (9) shows that

differs only in that all the elasticities are present in (9) but only the

awn-elasticities are present in ( 6 ) Since advertising expense mus t be I non-negat ive the first-order requirements are that v be the maximum of t

i

the amount shown in 6) or (9) and zero

III A SIMPLIFIED DEMAND STRUCTURE

So far the demand equation system is comple tely general I will now

move to a particular demand structure which is charac terized by an industry

elasticity of price with respect to advertising a general brand-swi tching

elas ticity and a dependence of the firm-specific elas ticity on its relative

size I make the expli cit assumpt ion that

n pound

)l

0 AA

Consider the identification of y as an elasticity of industry price

Page 5

(10)

where y is an

- (y- a)

industry demand elasticity a is a brand-swi tching

el astici ty and z1 is the market share In matrix no tation

(11) r bull ai + (y- a) t

wi th respe ct to advertising 0

le t ting S denote dS observe that

0(12) SS bull

-

-1 0s t s - -1 0S t d - 9- -

apl apl aplaa1 aa2 a 0 a

middot( a Pl

( 13)

-

-0 a bull 0

a

) 0 X s

-1 0dAA bull then d

a bull

J 0

(JA) middot and

Let the sc alar (SS)(AA) be denoted by y so ya zft

If

1

d

-

I

I

(11)

--

y

I -f

l J- a)

a) l zt

Substitutin g into (13) gives

i [ ai + (y(14) -I- bull S A

bull az + (y -

Pa ge6

I I II

bull

since l bull 1

Under these assumpt ons then y is the elasticity of industry sales

(and average industry p ice) with respect to industry advertisin g Note

that if y bull 0 so that there is no industry sales effect there will still

be positive advertising if there are brand-switching effects

Turning now to the brand-switching ef fect observe that

(15)

Noting that

-1 deg -1d z -z -

-

0 a

Page 7

(15) may be written as

0 (AA)

lx 2x 1x

ith

1y

i

First assume no

that if there are

will be no changes in market shares

- 0a bull

Page 8

Equation (17) is a general statement of the relation betbulleen changes in

advertising levels and changes in market shares which would acompany them It

may be used to make some general observations about brand-switching effects

industry effect eg y bull r t bull 0 and assume further

equal percentage changes in all advertising le =ls then there

Under these further assumptions

0l and dz -1 bull (iA) ltr assumption the second term on the right hand side of this expression is

- By

zero

necessary for rt bull 0Consequently for market shares to be unaffected it is

when y bull r l bull 0 This requirement is satisfied by equation (11)

Secondly consider effects on market shares if one firm inc ases its abull ar-

tising and others do not As a general assumption we require smiddot ch a change o

lead to a decrease in the shares of all the other firms hat is let

0 0aiai gt 0 and a a bull 0 for j + i For any matrix X with N rows and its trans-j j

pose X let X

row of X

bull middotmiddotmiddot where is a column vector which contains the

elements of the Under the assumptions about the iis given just

d-1 0 0above it follows that r becomes (aiai) iimiddot ehFor jzj lt 0 under these conditions then it follows that the j- element

N of (I- l ) lt 0 so middotij - il lt 0 or yij - yik lt 0 If this

kbulll N condition holds for all Y ij where j + i then it follows that yii - z

k Y gta

k- 1 ik since the th firms share must increase to offset the decreases in all other

shares

ei ith

1v ( ) h i

7urning

where is the

leads to z

to the r matrix given in (11) we note that 1 = cr + (y - cr) i i zi elementary vector with 1 in the position and 0 elsewhere This

bull cr + (y - cr) zi Since bull required is thatcr at- zY wYij (y - cr)zi - cr + (y - cr) zilt 0 or cr gt 0

These observations may be summarized by substituting (11) into (17) bull

giving

(18)

i s

d -1 zz -

-

-

+ (y - cr) tz

d -1 0cr(I - l ) a a bull

cr 1 z - (y - cr) 0 a

o

If ai increases and the other a s are const t cr must be positive to havej

a positive effect on zi A positive cr also bull plies a negative ffect of aJ

f all a s in-on zi other a s (including a ) fixed j

eluding a1 change by the same percentage zi remains unchanged Finally k i

if cr bull 0 there is no brand-switching effect

For a to have no effect on p requires yij bull 0 From (10) thisj i

amounts to y bull cr that is the industry demand elasticity and the brandshyswitching elasticity are equal If y gt cr gt 0 the industry elasticity yij doninates If y lt cr y lt 0 the brand-switching elasticity dominates ij

making

Page 10

Substituting ( 1 1) now in (6) the Cournot case and in (9) the

Chamberlin ease gives

-(19) Cournot vO a + (y - a) z

Chamberli n vl - y lmiddot th

The 1- element is then

-(20) Cournot vO a+ (y - a) zi i

-Chamberlin vl yi

In (19) and (20) the superscript 0 is used to denote total

independence of decision and the superscript l is used to denote

total interdependence of decision making

The relation between v and vf depends solely on t relation between

y and a f y gt a so that the industry effect dominat 3 vf v with

equality in the trirlal case of z bull 1 Cooperative irms would have ai

higher advertising intensity than non-cooperative fi

If there is equality between the industry elasticity and the

y Whe therbrand-switching elasticity or y bull there is cooperation among the firms has no effect on advertising inten-sity And if brand-switching is more important with y lt a e get

vi lt v cooperative firms will have a lower advertising intensity than

non-cooperative firms The three situations are depicted in Figure L

Given the results for the firm level variables calculation of the

corresponding re sults for the industry is s-traightforward Let

B bull t zf bull z z be the Herfindahl index of concen tration and notethat

z - bull l z bull 1 and that V bull A S bull a i 5 bull (siIS) (asi)i

bull middot Then for the general case from (6) and (9)

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

(9)

-

v bull bull

bull

bull

zl [ Y21 Y22 bull bull Y2N J

-1zl 0

-1z2 r z

0 1

Page 4

Writ ing (8) compactly gives

the matrix in the two equationsA comparison of (6) and (9) shows that

differs only in that all the elasticities are present in (9) but only the

awn-elasticities are present in ( 6 ) Since advertising expense mus t be I non-negat ive the first-order requirements are that v be the maximum of t

i

the amount shown in 6) or (9) and zero

III A SIMPLIFIED DEMAND STRUCTURE

So far the demand equation system is comple tely general I will now

move to a particular demand structure which is charac terized by an industry

elasticity of price with respect to advertising a general brand-swi tching

elas ticity and a dependence of the firm-specific elas ticity on its relative

size I make the expli cit assumpt ion that

n pound

)l

0 AA

Consider the identification of y as an elasticity of industry price

Page 5

(10)

where y is an

- (y- a)

industry demand elasticity a is a brand-swi tching

el astici ty and z1 is the market share In matrix no tation

(11) r bull ai + (y- a) t

wi th respe ct to advertising 0

le t ting S denote dS observe that

0(12) SS bull

-

-1 0s t s - -1 0S t d - 9- -

apl apl aplaa1 aa2 a 0 a

middot( a Pl

( 13)

-

-0 a bull 0

a

) 0 X s

-1 0dAA bull then d

a bull

J 0

(JA) middot and

Let the sc alar (SS)(AA) be denoted by y so ya zft

If

1

d

-

I

I

(11)

--

y

I -f

l J- a)

a) l zt

Substitutin g into (13) gives

i [ ai + (y(14) -I- bull S A

bull az + (y -

Pa ge6

I I II

bull

since l bull 1

Under these assumpt ons then y is the elasticity of industry sales

(and average industry p ice) with respect to industry advertisin g Note

that if y bull 0 so that there is no industry sales effect there will still

be positive advertising if there are brand-switching effects

Turning now to the brand-switching ef fect observe that

(15)

Noting that

-1 deg -1d z -z -

-

0 a

Page 7

(15) may be written as

0 (AA)

lx 2x 1x

ith

1y

i

First assume no

that if there are

will be no changes in market shares

- 0a bull

Page 8

Equation (17) is a general statement of the relation betbulleen changes in

advertising levels and changes in market shares which would acompany them It

may be used to make some general observations about brand-switching effects

industry effect eg y bull r t bull 0 and assume further

equal percentage changes in all advertising le =ls then there

Under these further assumptions

0l and dz -1 bull (iA) ltr assumption the second term on the right hand side of this expression is

- By

zero

necessary for rt bull 0Consequently for market shares to be unaffected it is

when y bull r l bull 0 This requirement is satisfied by equation (11)

Secondly consider effects on market shares if one firm inc ases its abull ar-

tising and others do not As a general assumption we require smiddot ch a change o

lead to a decrease in the shares of all the other firms hat is let

0 0aiai gt 0 and a a bull 0 for j + i For any matrix X with N rows and its trans-j j

pose X let X

row of X

bull middotmiddotmiddot where is a column vector which contains the

elements of the Under the assumptions about the iis given just

d-1 0 0above it follows that r becomes (aiai) iimiddot ehFor jzj lt 0 under these conditions then it follows that the j- element

N of (I- l ) lt 0 so middotij - il lt 0 or yij - yik lt 0 If this

kbulll N condition holds for all Y ij where j + i then it follows that yii - z

k Y gta

k- 1 ik since the th firms share must increase to offset the decreases in all other

shares

ei ith

1v ( ) h i

7urning

where is the

leads to z

to the r matrix given in (11) we note that 1 = cr + (y - cr) i i zi elementary vector with 1 in the position and 0 elsewhere This

bull cr + (y - cr) zi Since bull required is thatcr at- zY wYij (y - cr)zi - cr + (y - cr) zilt 0 or cr gt 0

These observations may be summarized by substituting (11) into (17) bull

giving

(18)

i s

d -1 zz -

-

-

+ (y - cr) tz

d -1 0cr(I - l ) a a bull

cr 1 z - (y - cr) 0 a

o

If ai increases and the other a s are const t cr must be positive to havej

a positive effect on zi A positive cr also bull plies a negative ffect of aJ

f all a s in-on zi other a s (including a ) fixed j

eluding a1 change by the same percentage zi remains unchanged Finally k i

if cr bull 0 there is no brand-switching effect

For a to have no effect on p requires yij bull 0 From (10) thisj i

amounts to y bull cr that is the industry demand elasticity and the brandshyswitching elasticity are equal If y gt cr gt 0 the industry elasticity yij doninates If y lt cr y lt 0 the brand-switching elasticity dominates ij

making

Page 10

Substituting ( 1 1) now in (6) the Cournot case and in (9) the

Chamberlin ease gives

-(19) Cournot vO a + (y - a) z

Chamberli n vl - y lmiddot th

The 1- element is then

-(20) Cournot vO a+ (y - a) zi i

-Chamberlin vl yi

In (19) and (20) the superscript 0 is used to denote total

independence of decision and the superscript l is used to denote

total interdependence of decision making

The relation between v and vf depends solely on t relation between

y and a f y gt a so that the industry effect dominat 3 vf v with

equality in the trirlal case of z bull 1 Cooperative irms would have ai

higher advertising intensity than non-cooperative fi

If there is equality between the industry elasticity and the

y Whe therbrand-switching elasticity or y bull there is cooperation among the firms has no effect on advertising inten-sity And if brand-switching is more important with y lt a e get

vi lt v cooperative firms will have a lower advertising intensity than

non-cooperative firms The three situations are depicted in Figure L

Given the results for the firm level variables calculation of the

corresponding re sults for the industry is s-traightforward Let

B bull t zf bull z z be the Herfindahl index of concen tration and notethat

z - bull l z bull 1 and that V bull A S bull a i 5 bull (siIS) (asi)i

bull middot Then for the general case from (6) and (9)

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

n pound

)l

0 AA

Consider the identification of y as an elasticity of industry price

Page 5

(10)

where y is an

- (y- a)

industry demand elasticity a is a brand-swi tching

el astici ty and z1 is the market share In matrix no tation

(11) r bull ai + (y- a) t

wi th respe ct to advertising 0

le t ting S denote dS observe that

0(12) SS bull

-

-1 0s t s - -1 0S t d - 9- -

apl apl aplaa1 aa2 a 0 a

middot( a Pl

( 13)

-

-0 a bull 0

a

) 0 X s

-1 0dAA bull then d

a bull

J 0

(JA) middot and

Let the sc alar (SS)(AA) be denoted by y so ya zft

If

1

d

-

I

I

(11)

--

y

I -f

l J- a)

a) l zt

Substitutin g into (13) gives

i [ ai + (y(14) -I- bull S A

bull az + (y -

Pa ge6

I I II

bull

since l bull 1

Under these assumpt ons then y is the elasticity of industry sales

(and average industry p ice) with respect to industry advertisin g Note

that if y bull 0 so that there is no industry sales effect there will still

be positive advertising if there are brand-switching effects

Turning now to the brand-switching ef fect observe that

(15)

Noting that

-1 deg -1d z -z -

-

0 a

Page 7

(15) may be written as

0 (AA)

lx 2x 1x

ith

1y

i

First assume no

that if there are

will be no changes in market shares

- 0a bull

Page 8

Equation (17) is a general statement of the relation betbulleen changes in

advertising levels and changes in market shares which would acompany them It

may be used to make some general observations about brand-switching effects

industry effect eg y bull r t bull 0 and assume further

equal percentage changes in all advertising le =ls then there

Under these further assumptions

0l and dz -1 bull (iA) ltr assumption the second term on the right hand side of this expression is

- By

zero

necessary for rt bull 0Consequently for market shares to be unaffected it is

when y bull r l bull 0 This requirement is satisfied by equation (11)

Secondly consider effects on market shares if one firm inc ases its abull ar-

tising and others do not As a general assumption we require smiddot ch a change o

lead to a decrease in the shares of all the other firms hat is let

0 0aiai gt 0 and a a bull 0 for j + i For any matrix X with N rows and its trans-j j

pose X let X

row of X

bull middotmiddotmiddot where is a column vector which contains the

elements of the Under the assumptions about the iis given just

d-1 0 0above it follows that r becomes (aiai) iimiddot ehFor jzj lt 0 under these conditions then it follows that the j- element

N of (I- l ) lt 0 so middotij - il lt 0 or yij - yik lt 0 If this

kbulll N condition holds for all Y ij where j + i then it follows that yii - z

k Y gta

k- 1 ik since the th firms share must increase to offset the decreases in all other

shares

ei ith

1v ( ) h i

7urning

where is the

leads to z

to the r matrix given in (11) we note that 1 = cr + (y - cr) i i zi elementary vector with 1 in the position and 0 elsewhere This

bull cr + (y - cr) zi Since bull required is thatcr at- zY wYij (y - cr)zi - cr + (y - cr) zilt 0 or cr gt 0

These observations may be summarized by substituting (11) into (17) bull

giving

(18)

i s

d -1 zz -

-

-

+ (y - cr) tz

d -1 0cr(I - l ) a a bull

cr 1 z - (y - cr) 0 a

o

If ai increases and the other a s are const t cr must be positive to havej

a positive effect on zi A positive cr also bull plies a negative ffect of aJ

f all a s in-on zi other a s (including a ) fixed j

eluding a1 change by the same percentage zi remains unchanged Finally k i

if cr bull 0 there is no brand-switching effect

For a to have no effect on p requires yij bull 0 From (10) thisj i

amounts to y bull cr that is the industry demand elasticity and the brandshyswitching elasticity are equal If y gt cr gt 0 the industry elasticity yij doninates If y lt cr y lt 0 the brand-switching elasticity dominates ij

making

Page 10

Substituting ( 1 1) now in (6) the Cournot case and in (9) the

Chamberlin ease gives

-(19) Cournot vO a + (y - a) z

Chamberli n vl - y lmiddot th

The 1- element is then

-(20) Cournot vO a+ (y - a) zi i

-Chamberlin vl yi

In (19) and (20) the superscript 0 is used to denote total

independence of decision and the superscript l is used to denote

total interdependence of decision making

The relation between v and vf depends solely on t relation between

y and a f y gt a so that the industry effect dominat 3 vf v with

equality in the trirlal case of z bull 1 Cooperative irms would have ai

higher advertising intensity than non-cooperative fi

If there is equality between the industry elasticity and the

y Whe therbrand-switching elasticity or y bull there is cooperation among the firms has no effect on advertising inten-sity And if brand-switching is more important with y lt a e get

vi lt v cooperative firms will have a lower advertising intensity than

non-cooperative firms The three situations are depicted in Figure L

Given the results for the firm level variables calculation of the

corresponding re sults for the industry is s-traightforward Let

B bull t zf bull z z be the Herfindahl index of concen tration and notethat

z - bull l z bull 1 and that V bull A S bull a i 5 bull (siIS) (asi)i

bull middot Then for the general case from (6) and (9)

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

1

d

-

I

I

(11)

--

y

I -f

l J- a)

a) l zt

Substitutin g into (13) gives

i [ ai + (y(14) -I- bull S A

bull az + (y -

Pa ge6

I I II

bull

since l bull 1

Under these assumpt ons then y is the elasticity of industry sales

(and average industry p ice) with respect to industry advertisin g Note

that if y bull 0 so that there is no industry sales effect there will still

be positive advertising if there are brand-switching effects

Turning now to the brand-switching ef fect observe that

(15)

Noting that

-1 deg -1d z -z -

-

0 a

Page 7

(15) may be written as

0 (AA)

lx 2x 1x

ith

1y

i

First assume no

that if there are

will be no changes in market shares

- 0a bull

Page 8

Equation (17) is a general statement of the relation betbulleen changes in

advertising levels and changes in market shares which would acompany them It

may be used to make some general observations about brand-switching effects

industry effect eg y bull r t bull 0 and assume further

equal percentage changes in all advertising le =ls then there

Under these further assumptions

0l and dz -1 bull (iA) ltr assumption the second term on the right hand side of this expression is

- By

zero

necessary for rt bull 0Consequently for market shares to be unaffected it is

when y bull r l bull 0 This requirement is satisfied by equation (11)

Secondly consider effects on market shares if one firm inc ases its abull ar-

tising and others do not As a general assumption we require smiddot ch a change o

lead to a decrease in the shares of all the other firms hat is let

0 0aiai gt 0 and a a bull 0 for j + i For any matrix X with N rows and its trans-j j

pose X let X

row of X

bull middotmiddotmiddot where is a column vector which contains the

elements of the Under the assumptions about the iis given just

d-1 0 0above it follows that r becomes (aiai) iimiddot ehFor jzj lt 0 under these conditions then it follows that the j- element

N of (I- l ) lt 0 so middotij - il lt 0 or yij - yik lt 0 If this

kbulll N condition holds for all Y ij where j + i then it follows that yii - z

k Y gta

k- 1 ik since the th firms share must increase to offset the decreases in all other

shares

ei ith

1v ( ) h i

7urning

where is the

leads to z

to the r matrix given in (11) we note that 1 = cr + (y - cr) i i zi elementary vector with 1 in the position and 0 elsewhere This

bull cr + (y - cr) zi Since bull required is thatcr at- zY wYij (y - cr)zi - cr + (y - cr) zilt 0 or cr gt 0

These observations may be summarized by substituting (11) into (17) bull

giving

(18)

i s

d -1 zz -

-

-

+ (y - cr) tz

d -1 0cr(I - l ) a a bull

cr 1 z - (y - cr) 0 a

o

If ai increases and the other a s are const t cr must be positive to havej

a positive effect on zi A positive cr also bull plies a negative ffect of aJ

f all a s in-on zi other a s (including a ) fixed j

eluding a1 change by the same percentage zi remains unchanged Finally k i

if cr bull 0 there is no brand-switching effect

For a to have no effect on p requires yij bull 0 From (10) thisj i

amounts to y bull cr that is the industry demand elasticity and the brandshyswitching elasticity are equal If y gt cr gt 0 the industry elasticity yij doninates If y lt cr y lt 0 the brand-switching elasticity dominates ij

making

Page 10

Substituting ( 1 1) now in (6) the Cournot case and in (9) the

Chamberlin ease gives

-(19) Cournot vO a + (y - a) z

Chamberli n vl - y lmiddot th

The 1- element is then

-(20) Cournot vO a+ (y - a) zi i

-Chamberlin vl yi

In (19) and (20) the superscript 0 is used to denote total

independence of decision and the superscript l is used to denote

total interdependence of decision making

The relation between v and vf depends solely on t relation between

y and a f y gt a so that the industry effect dominat 3 vf v with

equality in the trirlal case of z bull 1 Cooperative irms would have ai

higher advertising intensity than non-cooperative fi

If there is equality between the industry elasticity and the

y Whe therbrand-switching elasticity or y bull there is cooperation among the firms has no effect on advertising inten-sity And if brand-switching is more important with y lt a e get

vi lt v cooperative firms will have a lower advertising intensity than

non-cooperative firms The three situations are depicted in Figure L

Given the results for the firm level variables calculation of the

corresponding re sults for the industry is s-traightforward Let

B bull t zf bull z z be the Herfindahl index of concen tration and notethat

z - bull l z bull 1 and that V bull A S bull a i 5 bull (siIS) (asi)i

bull middot Then for the general case from (6) and (9)

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

Page 7

(15) may be written as

0 (AA)

lx 2x 1x

ith

1y

i

First assume no

that if there are

will be no changes in market shares

- 0a bull

Page 8

Equation (17) is a general statement of the relation betbulleen changes in

advertising levels and changes in market shares which would acompany them It

may be used to make some general observations about brand-switching effects

industry effect eg y bull r t bull 0 and assume further

equal percentage changes in all advertising le =ls then there

Under these further assumptions

0l and dz -1 bull (iA) ltr assumption the second term on the right hand side of this expression is

- By

zero

necessary for rt bull 0Consequently for market shares to be unaffected it is

when y bull r l bull 0 This requirement is satisfied by equation (11)

Secondly consider effects on market shares if one firm inc ases its abull ar-

tising and others do not As a general assumption we require smiddot ch a change o

lead to a decrease in the shares of all the other firms hat is let

0 0aiai gt 0 and a a bull 0 for j + i For any matrix X with N rows and its trans-j j

pose X let X

row of X

bull middotmiddotmiddot where is a column vector which contains the

elements of the Under the assumptions about the iis given just

d-1 0 0above it follows that r becomes (aiai) iimiddot ehFor jzj lt 0 under these conditions then it follows that the j- element

N of (I- l ) lt 0 so middotij - il lt 0 or yij - yik lt 0 If this

kbulll N condition holds for all Y ij where j + i then it follows that yii - z

k Y gta

k- 1 ik since the th firms share must increase to offset the decreases in all other

shares

ei ith

1v ( ) h i

7urning

where is the

leads to z

to the r matrix given in (11) we note that 1 = cr + (y - cr) i i zi elementary vector with 1 in the position and 0 elsewhere This

bull cr + (y - cr) zi Since bull required is thatcr at- zY wYij (y - cr)zi - cr + (y - cr) zilt 0 or cr gt 0

These observations may be summarized by substituting (11) into (17) bull

giving

(18)

i s

d -1 zz -

-

-

+ (y - cr) tz

d -1 0cr(I - l ) a a bull

cr 1 z - (y - cr) 0 a

o

If ai increases and the other a s are const t cr must be positive to havej

a positive effect on zi A positive cr also bull plies a negative ffect of aJ

f all a s in-on zi other a s (including a ) fixed j

eluding a1 change by the same percentage zi remains unchanged Finally k i

if cr bull 0 there is no brand-switching effect

For a to have no effect on p requires yij bull 0 From (10) thisj i

amounts to y bull cr that is the industry demand elasticity and the brandshyswitching elasticity are equal If y gt cr gt 0 the industry elasticity yij doninates If y lt cr y lt 0 the brand-switching elasticity dominates ij

making

Page 10

Substituting ( 1 1) now in (6) the Cournot case and in (9) the

Chamberlin ease gives

-(19) Cournot vO a + (y - a) z

Chamberli n vl - y lmiddot th

The 1- element is then

-(20) Cournot vO a+ (y - a) zi i

-Chamberlin vl yi

In (19) and (20) the superscript 0 is used to denote total

independence of decision and the superscript l is used to denote

total interdependence of decision making

The relation between v and vf depends solely on t relation between

y and a f y gt a so that the industry effect dominat 3 vf v with

equality in the trirlal case of z bull 1 Cooperative irms would have ai

higher advertising intensity than non-cooperative fi

If there is equality between the industry elasticity and the

y Whe therbrand-switching elasticity or y bull there is cooperation among the firms has no effect on advertising inten-sity And if brand-switching is more important with y lt a e get

vi lt v cooperative firms will have a lower advertising intensity than

non-cooperative firms The three situations are depicted in Figure L

Given the results for the firm level variables calculation of the

corresponding re sults for the industry is s-traightforward Let

B bull t zf bull z z be the Herfindahl index of concen tration and notethat

z - bull l z bull 1 and that V bull A S bull a i 5 bull (siIS) (asi)i

bull middot Then for the general case from (6) and (9)

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

0 (AA)

lx 2x 1x

ith

1y

i

First assume no

that if there are

will be no changes in market shares

- 0a bull

Page 8

Equation (17) is a general statement of the relation betbulleen changes in

advertising levels and changes in market shares which would acompany them It

may be used to make some general observations about brand-switching effects

industry effect eg y bull r t bull 0 and assume further

equal percentage changes in all advertising le =ls then there

Under these further assumptions

0l and dz -1 bull (iA) ltr assumption the second term on the right hand side of this expression is

- By

zero

necessary for rt bull 0Consequently for market shares to be unaffected it is

when y bull r l bull 0 This requirement is satisfied by equation (11)

Secondly consider effects on market shares if one firm inc ases its abull ar-

tising and others do not As a general assumption we require smiddot ch a change o

lead to a decrease in the shares of all the other firms hat is let

0 0aiai gt 0 and a a bull 0 for j + i For any matrix X with N rows and its trans-j j

pose X let X

row of X

bull middotmiddotmiddot where is a column vector which contains the

elements of the Under the assumptions about the iis given just

d-1 0 0above it follows that r becomes (aiai) iimiddot ehFor jzj lt 0 under these conditions then it follows that the j- element

N of (I- l ) lt 0 so middotij - il lt 0 or yij - yik lt 0 If this

kbulll N condition holds for all Y ij where j + i then it follows that yii - z

k Y gta

k- 1 ik since the th firms share must increase to offset the decreases in all other

shares

ei ith

1v ( ) h i

7urning

where is the

leads to z

to the r matrix given in (11) we note that 1 = cr + (y - cr) i i zi elementary vector with 1 in the position and 0 elsewhere This

bull cr + (y - cr) zi Since bull required is thatcr at- zY wYij (y - cr)zi - cr + (y - cr) zilt 0 or cr gt 0

These observations may be summarized by substituting (11) into (17) bull

giving

(18)

i s

d -1 zz -

-

-

+ (y - cr) tz

d -1 0cr(I - l ) a a bull

cr 1 z - (y - cr) 0 a

o

If ai increases and the other a s are const t cr must be positive to havej

a positive effect on zi A positive cr also bull plies a negative ffect of aJ

f all a s in-on zi other a s (including a ) fixed j

eluding a1 change by the same percentage zi remains unchanged Finally k i

if cr bull 0 there is no brand-switching effect

For a to have no effect on p requires yij bull 0 From (10) thisj i

amounts to y bull cr that is the industry demand elasticity and the brandshyswitching elasticity are equal If y gt cr gt 0 the industry elasticity yij doninates If y lt cr y lt 0 the brand-switching elasticity dominates ij

making

Page 10

Substituting ( 1 1) now in (6) the Cournot case and in (9) the

Chamberlin ease gives

-(19) Cournot vO a + (y - a) z

Chamberli n vl - y lmiddot th

The 1- element is then

-(20) Cournot vO a+ (y - a) zi i

-Chamberlin vl yi

In (19) and (20) the superscript 0 is used to denote total

independence of decision and the superscript l is used to denote

total interdependence of decision making

The relation between v and vf depends solely on t relation between

y and a f y gt a so that the industry effect dominat 3 vf v with

equality in the trirlal case of z bull 1 Cooperative irms would have ai

higher advertising intensity than non-cooperative fi

If there is equality between the industry elasticity and the

y Whe therbrand-switching elasticity or y bull there is cooperation among the firms has no effect on advertising inten-sity And if brand-switching is more important with y lt a e get

vi lt v cooperative firms will have a lower advertising intensity than

non-cooperative firms The three situations are depicted in Figure L

Given the results for the firm level variables calculation of the

corresponding re sults for the industry is s-traightforward Let

B bull t zf bull z z be the Herfindahl index of concen tration and notethat

z - bull l z bull 1 and that V bull A S bull a i 5 bull (siIS) (asi)i

bull middot Then for the general case from (6) and (9)

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

ei ith

1v ( ) h i

7urning

where is the

leads to z

to the r matrix given in (11) we note that 1 = cr + (y - cr) i i zi elementary vector with 1 in the position and 0 elsewhere This

bull cr + (y - cr) zi Since bull required is thatcr at- zY wYij (y - cr)zi - cr + (y - cr) zilt 0 or cr gt 0

These observations may be summarized by substituting (11) into (17) bull

giving

(18)

i s

d -1 zz -

-

-

+ (y - cr) tz

d -1 0cr(I - l ) a a bull

cr 1 z - (y - cr) 0 a

o

If ai increases and the other a s are const t cr must be positive to havej

a positive effect on zi A positive cr also bull plies a negative ffect of aJ

f all a s in-on zi other a s (including a ) fixed j

eluding a1 change by the same percentage zi remains unchanged Finally k i

if cr bull 0 there is no brand-switching effect

For a to have no effect on p requires yij bull 0 From (10) thisj i

amounts to y bull cr that is the industry demand elasticity and the brandshyswitching elasticity are equal If y gt cr gt 0 the industry elasticity yij doninates If y lt cr y lt 0 the brand-switching elasticity dominates ij

making

Page 10

Substituting ( 1 1) now in (6) the Cournot case and in (9) the

Chamberlin ease gives

-(19) Cournot vO a + (y - a) z

Chamberli n vl - y lmiddot th

The 1- element is then

-(20) Cournot vO a+ (y - a) zi i

-Chamberlin vl yi

In (19) and (20) the superscript 0 is used to denote total

independence of decision and the superscript l is used to denote

total interdependence of decision making

The relation between v and vf depends solely on t relation between

y and a f y gt a so that the industry effect dominat 3 vf v with

equality in the trirlal case of z bull 1 Cooperative irms would have ai

higher advertising intensity than non-cooperative fi

If there is equality between the industry elasticity and the

y Whe therbrand-switching elasticity or y bull there is cooperation among the firms has no effect on advertising inten-sity And if brand-switching is more important with y lt a e get

vi lt v cooperative firms will have a lower advertising intensity than

non-cooperative firms The three situations are depicted in Figure L

Given the results for the firm level variables calculation of the

corresponding re sults for the industry is s-traightforward Let

B bull t zf bull z z be the Herfindahl index of concen tration and notethat

z - bull l z bull 1 and that V bull A S bull a i 5 bull (siIS) (asi)i

bull middot Then for the general case from (6) and (9)

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

making

Page 10

Substituting ( 1 1) now in (6) the Cournot case and in (9) the

Chamberlin ease gives

-(19) Cournot vO a + (y - a) z

Chamberli n vl - y lmiddot th

The 1- element is then

-(20) Cournot vO a+ (y - a) zi i

-Chamberlin vl yi

In (19) and (20) the superscript 0 is used to denote total

independence of decision and the superscript l is used to denote

total interdependence of decision making

The relation between v and vf depends solely on t relation between

y and a f y gt a so that the industry effect dominat 3 vf v with

equality in the trirlal case of z bull 1 Cooperative irms would have ai

higher advertising intensity than non-cooperative fi

If there is equality between the industry elasticity and the

y Whe therbrand-switching elasticity or y bull there is cooperation among the firms has no effect on advertising inten-sity And if brand-switching is more important with y lt a e get

vi lt v cooperative firms will have a lower advertising intensity than

non-cooperative firms The three situations are depicted in Figure L

Given the results for the firm level variables calculation of the

corresponding re sults for the industry is s-traightforward Let

B bull t zf bull z z be the Herfindahl index of concen tration and notethat

z - bull l z bull 1 and that V bull A S bull a i 5 bull (siIS) (asi)i

bull middot Then for the general case from (6) and (9)

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

bull

Page lOa

y lt1 bull y y

10

f

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

V0 bull z [ a1 + (y - cr) J bull a + (y - a) H vl bull Y bull y

11Page

( 2 1) vo bull z d -1 r bull r z bull z- d d- i )11

l -1 N N v bull z d r z bull r z bull l y z - ij jibulll jbulll

and for the simplified case from (19)

(22

Since the forms of the equations in (22) are the same as in (20) all

of the analysis of (20) holdS for (22) except that His substituted for

middot z Advertising intensity will be higher for an industry with cooperativei

firms than for one with non-coope rative firms if the industry demand elas-

ticity dominates the brand-switchine lasticity If the ewo elasticities

are equal then so will be advertiSl intensity for the cooperative firm

and non-cooperative firm industries If brand-switching dominates the

cooperative firm industry will have lower advertising intensity

In the industry model context the possibility of a critical concen-

tration level may be easily introduced That is assume that at values

of R below R the firms are non-cooperative but that for alues equal to

or greater than H they are cooperative That is

(23) V bull a + (y - a) H if H lt H bull y if H gtmiddot H

This function is shown in Figure 2 for the three relamptions be eween y and a

IV THE D GRE OF COOEtRATION

The models depicted in Figure 2 are based on a very simple notion about

the relation between concentration and the cooperationnon-cooperation charac-

teristic They use what is essentilly a step function relating concentra-

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

Figure

I -

J H H

Page l la

2

v v v

a

I J I y a bull Y y ---i

I I I I I I II I

H 10 H H 10 H 1 0

bullbull

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

bull bull

Page 12

tion and the extent or degree of coo peration as shown in Figure 3 Using

o as a symbol for the degree of cooperation eq uation (23) can be rewritten

as

bull(24) v (1 - o) vo + ovl bull (1 o) [a+ - a) H ] + oy- (y

vhere

(25) o bull o(H) bull 0 if B lt B

Hbull 1 if B gt

The specific relation between concentration (H) and the deg ree of

cooperation ( o) shown in Figure 3 is more restrictive than necessary and

bas less appeal an one which shows a smooth increase of o from 0 to 1 as

B increases fro to 1 Such a smooth function is shown in Figure 4 he

degree of cooper ion is low until H gets close to H increases greatly as

B goes through R attaining a high level for an H larger than B but still

close to it and then goes to 1 as B goes to 1 More formally

(26) 0 bull o(H)

bull 0 if H bull 0

bull 1 if H bull 1

do gt (IdB

d2o- gt 0 if H B dBZ

0 if H H

lt 0 if R gt H-

If (26) is now substituted for (25) in (24) a corresponding smoothing

of the functions shown in Figure 2 is accomplished he smooth functions

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

Figure 3

I

10

H 10 H

Page 12a

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

Figure

Page 12b

4

10

H 10 H

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

l

(27)

Cl - o) o

[ (1 -

[ (1

t y ij z

j

are given in Figure 5

Page 13

The equation in (24) was constructed as a hybrid of two results derived

from first-order equations for the non-cooperative and cooperative models

It may also be constructed directly by using l bull (1 - o) + on as thei i

th 2objective function for the i-- firm Treating o as a constant the first

order equation is

0 an aa

i middot

n i

Using equations (3) and (7) and setting --- bull 0 givesaai

(28) - 0

After collecting terms and converting to matrix notation we get

(29) - Cl - o) + 0 z-1vi yii i

N

j bulll

+ 0

+ o v1

d-1 r z z

-(30) v Cl - o) rd

-

o) r +d

d r J _ -1- d z

and middot

d) r + 0 rjd

l r z

v - z --(31) zv

- (1 0- +d) t r z- d-

If we now impose the simplified demand structure by substituting (11)

we get

- (1 - o) a +( 32) + oy and

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

Figure

l

-y

v

Y

H

r

I I

v

a

y

H 10 H

v

a

bulla

HH 10

bullbull

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

(33)

i

Page 14

v - (1 - o) [ a l + (y - a) ] The corresponding equation for Vis given in (24)

If the relation between industry advertising intensity (V) and

concentration (H) is non - linear via the impact of concentration

on the degree of cooperation does the relation take the form of a

auadratic as some other investigators have proposed (Greer ( 1971 ) Martin (1979) Strickland amp Weiss (1976) ) That question can

be approached from two perspectives - conceptual and empirical In

the next section I will try to apply some statistical material to it

here I want to explore the question in the context of the models

developed above

Referring to equation (24) taking the deriviative with respect

to H and letting bull (H) gives

bull( 3 3a ) 3V (y - a) (1 - o) + (1 - H) 3H dH

Given that o and H each are bounded by 0 and 1 and that o is an in-

creasing function of H the term in the brackets in non-negative The

sign of the deriviative then is the same as the sign of (y - a) If the industry effect is dominant (y gt a) then advertising in-

tensity will increase with concentration If the two effects are equal

then advertising intensity will not vbullry with concentration and if the

brand-switching e ffect is larger advertising intensity will decrease

with concentration

For given advertising elasticity parameters then it is not pos-

sible to show an increase in A S up to some H and the n a decrease

he relation may be non - linear but it is monotonic over the permis-

sible range of H

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

Page 15

One possibility is to introduce a relation between (y - a) and H

If industries characterized as dominated by the brand-switching effect

also were more concentrated then a cross industry comparison would

show an inverted U shape relation between AS and H I know of no

support for such an association between ( y - a) and H

V ERROR SPECUCATION

So far I have implicitly assumed that there are no errors in the

model I now assume that the error

thvariable in the equation for the i- firm is additive that its mean is zero

that its variance is inversely proportionate to its sales and that all error

term covarlances are zero hat is

34) v bull (1 - o) [ a + (y - a) z ] + oy + u i i i

- - -

In vector notation

(35) bull (1 - o) [ at + lt - a) J +

E() bull 0 Cov (u) -

0

If we now ca lculate V bull bull we get

oy + U bull

(36) V bull (1 - o) la + (y - a)R J +

U bull E(U) bull 0 Var (U) bull

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

P age 16

The error term specifi c ation which follows Hall

wi th the ratio of profits

6 heir analysis seems

as wellbull particularly given

and Weiss was

applied by them to equa tions to equity or

asse ts as dependen t variables to carry the same

weight in the present context the substantial

evidence presented by marketing analysis on the tendency of company de-

cision makers t o use the advertising to sales ratio as the decision

7variable

The zero covariance assumption on the other hand1 is particularly

troublesome Within a probably not true since

many even ts outside the

single industry it is

industry would have

industries

similar effec ts on all the

8firms in the industry Between it is probably not true either

since many companies produce in more than one indus try and even ts in the

firm would tend to effect all of its activities The extension of the

model to allow for non-zero covariances is certainly called for

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

--- -

Page Ll

Athird characteristic of this specification also deserves some comment

only on equation is shown for the firm or industry Several haveinvestigators

included an advertising equation ina larger system of equations (Comanor and

Wilson (1974) (1979) and Weiss (1976) so in myMartin Strickland Idid

dissertation1 Ihave ewo defenses for presenting only single equation results

here One is the suggestion by Comanor Wilson that simultaneousand equation

verybias may not be important in this context he second is that Iam will-

ing to see the model extended to include a profitability equation and I intend

to move that direction in the near futurein

Onthe inclusion of aconcentration equation on the other hand I amskep-

tical he problem isthat in some fundamental sense equations in models of

industrial organization should be oriented to the decision-making contexts of firms

Ifeach firm in anindustry with Nfirms has only one decision variable then

there can be only Nindependent equations which are based on the first-order

optimization equations It not show large ofis difficult of course to a number

functional relations which follow from the first-order conditions point here he

isthat only Nof them can be independent

Consider for illustrative purposes only a situation in wich teh N

itsquantities say q are set exogeneously and each firm determines advertising1

of and level say ai where a is the true optimal value a a bulla

1 1 i i + i

Ifp a) then the Nq

s and the Na s will determine N p s say pii bullp

i(l i 1 i

Now given Eand 9 we can determine both the vector s andthe vector v since

- bull til

ands We can also determine S s z bull s-1 s-ii

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

v and we

industry concentration isHbull (alternatively

V and Hare functions of the same

pendent Furthermore if there are

VM) and (H1 H2 bull bull bull )contain

VI STATISTI CAL APPLICATIONS

Page 18

Given the observed values of might be tempted to conclude that we

have a two equation system in which v and z are jointly determined That would i i

be inappropriate however since the 2N random variables (v ) are determined by

onlt N basic random variables t The variance-covariance matrix for ( ) must

be singular bull

The extension of this observation to industry level variables is straightshy

forward Since observed industry advertising intensity is V bull l v and observed 4

C4 bull z ) it follows thati l i

set of random variables t and cannot be indeshy-

M industries then the variables (V1 v2 at most M independent random variables

Given the assumptions made above y a and o are constant within a

given industry That being the case (34) can be written as

(37)

s1 bull (1 - o) (y - a)

If and

So + +

(1 - o) a + oy

81 are esti mated for an industry using a suitable statisticalSo procedure giving and 81 an estimate of y is then available The sumSo

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

Intra-industry analysis

1974 of Business Re ort -

categories are identified

Page 19

of So and S1 is y so y bull So + S1 is the estimate of y

If o is assumed to be bounded by zero and one the sign of 61 is also

the sign of y - a The estimate of So is of cou se an estimate of

(1 - o ) a + oy Moreove if y gt a then a is less than 6o- (1 - B) a+ 0(

Cor esponding results would

hold if y bull a or y lt a

If 61 gt 0 then we would estimate that a lt 6o

bull

For purposes of estimating this model 32 manufacturing industry categories

were selected The data are fram the Line of Business forms filed with

the Federal Trade Commission they are discussed in detail in the Annual Line

which is available from the FTC The 32 industry

in Table 1

Simple regressions for equ ation (37) were run for each of the 32 industries

with data for each of the firms which filed in the industry constituting an ob-

servation The results are given in Table 2 lines lA 2A

1974

the intercept

For all the A

equations generalized least quares was used th both and market

share bein scaled bv the square root of sales

The 32 industries were taken from the larger set of all manufacturing industry

categories in the 1974 data files Two selection cr iteria were used thereLB

had to be at least ten reporting companies and the industry had to be a consumer

goods industry or a producer goods industry which is strongly associated with a

related consumer goods industry so that adve rtising by the firms in the producer

goods industry impacts on demand in the related industry (eg soft drink syrup

and soft drinks) There were 135 industries with at least ten companies - 103

producer goods and 32 consumer goods

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

PT386l

3949

273

274

TABLE 1 INDUSTRY CATEGORIES USED

FTC

COOE OESCRI P T I ON _

2001 MEAT PACKINGt SAUSAGE S ANO OTHER PREPARED

MEAT PROOUCTS

2004 DAIRY PRODUCTS EXC F LUID MILK

2005 CANNED SPECIALTIES

2001 FROZEN SPECIALTIES

OEHYORATFOt AND

I NC LU 0 ING PRE SERVE S

SOUP MIXESbull

SEASO lNGSt ANO

OTHER PET FOOJ

RAIN MILL PROOUCTSt

ANO PREPARED

RELATED PRODUCTS

PRODUCTS

Z008 CANNEOt ORIEOt PICKLED FRUITS

ANO VEGET ABLES JAMS JELLIES DEHYDRATED I G TA3t E

S40CES ANO SALAD ORESSINGS

2010 DOG CAT A O

2012 FlOUR t OTHER RICE

MILLING fiLENOE) FLOUR

2014 B EADt CAKE ANO

20113 CO FECTIONERY

2026 BOTTLED A O CANNED SOFT DRINKS 2021 FLAVORING EXTRACTS AND SYRUPS EC

2029 MISC FOOOS AND KINDRED PROJUCTS EXC

ROASTED COFFEE

2301 MENS AND BOYS SUITS AND COATS

2302 MENS ANO BOYS FURNISHINGS

230 3 kOMENS AND MISSES OUTER EAR

2551 HOUSEHOLD FURNITURE

2702 PERIODICALS

Pqe 19a 1

RELATED 1972

src cooe

2011 f 3

202tX2026

2032

203pound

2033t4t5

2047 2041t4t5

2051 2065 2086

2081

209XZ05

231

232

233

251 272

2703 BOOKS

2704 ISC PVeLISHING

2806 ORGANIC FlEERS

2807 DRUG$ ETHICAL

23234

PT 2 S 3

2808 ORUCSt PROPRIETARY

2809 PERFU ES t COSMETICS ANO OTHER TaiLET

PREPARATIONS

2810 SOAP AND OTHER CLEANING PREPARATIONS 2815

2901

PEST1CIDES AND AGR ICULTURAL

PE OLEUM REF I N ING CHEMICALS EC

3606 HOUSEHOLD COOKING EQUIPMENT

3612 HOUSEHOLD APPLIANC ES NEC INCLUJING ELECshy

rqlC HOUSE ARFS AND FANS ANO SE I G MACHINES

3617 RADIO AND T V RECE I VING SETS 3808 PHOTOG APHIC E UIP amp SUP LfESt EXC

3qo3

PHO TOCOPYING

SPOR TING A D E QU I P M ENT f SUP P L I E S ATHLETTC GOODS NEC

3904 DOLLS GAMESt TOYS AND CHLOqENtS VE ICLES

PT283

2844

234tX2844

287 9

291 3631

3634t6t9

36H

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3949

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T ABLE 2 REG ESSIOH RESULTS CCONTI

EO NR

IND CODE

iR bull

cos

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CEPT

t1ARKE T

SHA E

AOVER-

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SHARpound-cent

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C I T Y ELAST

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T ABLE 2 REG ESSIOH RESULTS CCONTI

EO NR

IND CODE

iR bull

cos

I TEq-

CEPT

t1ARKE T

SHA E

AOVER-

Tl SING

SHARpound-cent

AuVER

RSO ILAST1-

C I T Y ELAST

SH CPtf (lt Cl) bull 11 I 41 I 5I (61 171 I 8 I f9) c 10)

9A 2 0 1 8 19 002397181 -007640 367 -005 246 le46 6 000605 000550CAI 597

-000029 G14180 OOl654CAJ -024li01At

lOA 2026 12 0028901AI -OlZl90 -0114 0 1 1 1 5 759

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llA 2021

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12A lOZ9

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10

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19

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middot middot middotbullmiddot bull lraquo

TABLE 2 REGRE SION RESUlTS ICONTt

bull

EO I NO tHl I filER- f4A_K T AOVER- sbulluRE ttSQ flA Jl- iLAS T NR CODE cos CEPT SHARE JISING AOVfR bull (JTY SHR CiJCF

110Cl I f amp Itt 15J tbt bull 1c u caa

llA 2702 ll o079 6 81 Bt -019110 S6s -OlltO 111

a 004679 ooooo1 t69

( oOl26o -015160 001560 -022690 ltJr()I

ldA 270 3 19 0065lt -OIt2l60 220 -Ol57a2 11 8 e o 0 71t6IA t ol08 75tAt ( OOl983CiU -060llOC() OOl7191A t -O lltdOC A) middot 89

lqA 2704 10 005082 -Oil060 22b -l)i1977 lelO 6 -000080 oo2772C4 t 910 c 000907 -011 200 Oe04105CA t -046960 995

20A 2d06 1 II

O OlltStiAt -001120 837 00014 -))th O01380amp At -oooo 11 821 ( OOl526CAt -026700181 0002 5UAt 000530 969

2lA 2807 28 OOt9lt9CAt -00891 0 516 -0 03962 225I8 002095CCt OOOl lliAt 690 ( o02965CA t -056650((1 OOOt50CAJ -003l70ttl 911I

I 22A 2808 15 ot3l06 119730 655 1130) 090

0 - 007526CC t Oe003961At 835- middot-

c I oo7523 -067210 001l 2tA t -0091t80CCt 951

2lA 2809 21 Oe2067lCAt -1218101At 71 2 -10095((1 121 ttlIaOQ8 00797418) OOOI8lltt 686 Ill( 0092lU A t -Olltl70Ct t 000605CAt -OOit8701At 951 _

---- -

32 009506CAt

0 bull 06 981 I A J 006901 cA bull

00 24A 2810 -010960 5t 5 -OOltSO 7 56

8 -000011 s11 c -5811701At oooaoatAJ oot520IAI 888

-- 37 --- middot - -- -1 ) l lbull t5JJ r-l bullhmiddot1 --- - --

l5A

26A

27A

c

2RA

c

2 9A

31A

llA

24

13

597

Ci)55

14

l 6h

RSQ ELASTI- (lASTCOE f-

TABLE 2

EQ I NO NR CODE IU

REGRESSION RESULTS CCONTa

NR INTER- MARKET

(10S CEPT SHARE AOVER- SHARfcent

TIS lNG AOVER

) CITY StiR

c It) bull 5 co a I 1) bull 0 bull 9 c l 0 bull( 2 1

2815 16 003019 -009990 275 -o069bmiddotJ

6 001446 000224 282 c 002178 -054630 o02221CCI -0075 00 646

2901 29 00021t2 CAI 0)0520 592 0007 6 1 068

0 00105C8 t 000012141 60)g( OOOlJ51AJ -00126018) ooou271At -000u80CA) 974

36oa 1 3 003296(4) -oca29o -oo-q94

001755 000203 lt91t 002499((1 -04l820CCI OOl374CAI 0068)0 946

3612 0033281CI 011520 195 01684) oso

00 30 42C OI 00012 2 424 oo579ltAt -2 7l7801At 002 100IAI -003220 819

8 3617 btel 011789 081002259 009530

001448 oOOl OitCCI 732 OOl7 22CAI -0 46160CAI 0004961AI -OOll40181 989c

30A 3808 14 0021t 3 6fAI -000110 628 o023291C) -005 6 middot- _ middot- 0bull 02 04 1 IC I ooooo9 637 ( 001584((1 -0161)1)0 00021 91AI -0 00060

390) 14 002790CCt 006590 h8 t 0 0938 4 070

B OOl89bCCJ 000144 74

0021961(1 -OItlOlO OOl323CAI -004800 915

B

middot--- - middot 4 - middot- - dfll3904 12 004563181 0)8300 879 0428651(1 089 OQIll004 277CA I ooozstcea 919

c 0041)3181 -0-11250 0011881(1 -006270 972 0Ill

- J - bull bull bull bullbullbull middot - - middot - middot gt middotbull L)ofbullflbull middot middotfJltl -tn- middotmiddotmiddotmiddoto +f middot t middot bull

c

is

positive

2

Page 0 determineThe consumer goodproducer good split is sometimes difficult to

Sollle support for the split used in this paper is a comparison of goodness - of - fit

distributions of a

industries

set

advertising are

that industry

a sales increase of

the

highest aD10U3 those

measures for the two groups of industries Table 3 contains

measures for the 32- consumer goods industries and the 103 producer goods

2 Median R is 5 7 for the consumer goods set and 40 for the producer goods

Estimates - of y the elasticity of demand with respect to

given in column of Table 2 The hypothesis that y bull 0 with

alternative was applied for each ittdustry As shown in the

could not be rtjected for 24 of the 32 industries Of the

and 10 are positive For the remalnifg eight three are

and five are significantly positive

Of the threertegative elasetcities the largest (in absolute value)

cosmetics (code 2809) With all elasticity of -1 01 a one

industry advertising would gwerate a decrease in industry sales

more than one percetu

At the other extrema is toys and games (code 39 04) For

a one percent ittcrease in industry advertising would lead to

four-tenths of a pampreentmiddot Though not significantly different from zero

elasticity estimatbull for pt-bpuetary drugs (code 2808)

which are

Both drug industries have

to sales rafios (211 pe1 cent for 28 08 and 13 4 per cent

other hand flaIJo ing ext1ac s (mainly soft-drink SYUlS) also

is for

percent increase in

of slightly

a middottwo - tailed

table that hypothesis

24 14 are negative

significantly negative

9

the codetics and p-ropriacuy very high advertising

for 28 09) bull On the

has a high ind UY

advenisiltg t() sales ratio ( 8 0 per cent) bull but its estimated elasticity is very

small and not signifieantly different uom zero

middot It doe$ not seem unusual to find many elasticities near zero with a few

negative and a few positive If aggregate consumption is insensitive to aggregate

advertising as seems likely ld then what one industry gains must be lost by

others

Page 21

elasticity of demand does

(10) we can

if t 0 then

Finally a determination concerning the industry

not fix the individual firms elasticity Going back to equation

write y bull (1 - ) a + z y Since a gt 0 it follows thatii i i

Y gt 0 If Ylt 0 however y s sign is indeterminateij ij

Turning next to the coefficient of market share 20 of them are negative and

12 are positive with three of each sign being significantly different from zero

The largest positive value which is significant is for pet food (code 2010) and

a close second is mens amp boys suits and coats (code 23 01) The largest signifi

cant negative value is for cosmetics (code 28 09)

In the model some relations among y a 0 and 61 are implied If middota is

negative (1- y) is greater than one Since 61Y bull (1- a) (1 - ) 61Y is

pCsitive but it will be less than one if 0 is large enough Seventeen of the A

ys are negative in each of the seventeen industries 61 is also negative and les

1 (algebraicly) than y so 61Y is greater than one his is not evidence that the

degree of cooperation is low or zero in any industry of course A high o togethegt

with a negative y which is small (in absolute terms) relative to a can give a

value of 61Y greater than one On the other hand if 61Y were less than one

o would have to be greater than zero

For y gt 0 two conditions may hold If y lt a it follows that 61 lt 0 since

(y - a ) lt 0 It also follows that 61Y lt 0 regardless of the value of o bull

In addition the relation is an if-and-only-if one ie if 61Y is negative

then y lt a Three industries have negative values for 61y dairy products

except milk (code 20 04) synthetic fibers (code 2806) and photographic equipment

(code 3808) In all three cases y is quite small so a does not have to be very

large to give a negative value to al

If y gt a the model shows that 61-- gt 0 whatever the value of 0 bull There are

12 cases where both y and 61 are positive with 61 ranging from near zero

(grain milling code 20 12) to 1 20 ( proprietary drugs code 2808) Several

coeffiei-en_rs

--

15

o f to zero

Tab le 3 - Consumer Goods

Indus tr ies

2Distributions of R and Producer Goods

Page 20a

Consumer Producer

Goods Goods

0 - 9 9 0 3

10 - 19 9 0 1 1

20 - 29 9 3 20

30 - 39 9 3 17

40 - 49 9 5 16

50 - 59 9 8

69 9 6 Ii 1060

--f 670 79 9 2

80 - 89 9 4 4

90 - 100 1 1

Totals 32 10 3

Notes

2is used R i s cal-

culated as F F + ((N - K- 1 ) K ] 1 b_ F is the F

statistic Lor the hypothesis that all o f the non - intercept terms are simul taneously equal

1

2

--

-- Since generalized least squ-area regress ion

Page 12

o f these cases have values o f 6 1 Y rea ter than 0 8 (pet food (20 10) bread amp cakes

(20 14 ) miscellaneous processed foods (20 29 ) men s and boys suit s and coats

(23 01 ) p rop riet ary drugs (28 08 ) elect ric housewares (36 1 2) radio and

IV sets 17 and games and toys (39 For be than(36 ) 04)) 6 1 Y to greater 0 8

both o and cry mus t b e less than 0 2 That is in these industries the results

shown in Tab le 2 would hold only with very strong dominance of marke t demand

effects over brand swit ching e ffects and a very low degree o f cooperation

Using the concentration rat ios given in Table 4 the average concentration

ratio for the eight indust ries is 38 1 For the remaining 24 industries it is

43 2 This result would lend some support t o the proposition that concentrat ion

and cooperation are related if the group of eight industries are identi fied

as having low degrees of cooperation

One f inal note on model predict ions S ince both cr and o are assumed to

be non-negative 60 should also be non-negat ive In only one o f the 32 cas es

is 60 negative and it is not signif icant bull

cor pJ

7 1

7 0 4

1 4 7 5 1

)

7 3 z a o a t s 1 1 3 3 5 ( i V Z 8 tJ1 2 1 - 1 1 0 7 3 5 c middot v 2 8 1 0 3 2 -0 0 1 4 3 0 C 1 V 9 8 3 2 8 1 5 1 6 - 0 0 6 t1 6 9 C _ V 1 11 0 2 9 0 1 29 0 00 7 6 1 C l k V 7 3 1 3 6 08 1 3 - o n 4 9 9 4 3 3 3 6 1 2 2 4 0 1 6 4 3

3 1 7 1 3 0 1 1 7 d 7 8 3 3 8 0 8 0 0 2 3 i 2 3 0 6

P 4

3 9 0 3 1 4

1 2

0 09 3 8 4 39 1)1 0 4 l 8 6 5

T A LE 4 e I NCU S T R Y C A T E G O R Y

F TC NOM e tOOE ass

C 1 I c 2 )

2 0 0 1 1 6 2 0 0r 1 7 zo o l Z 2 0 0 7 1 8

z o o 2 6

z o t a 1 6

2 1) 1 2 1 5 2 0 1 4 1 1 2 0 1 a 1 9 2 0 26 1 2 2 0 2 7 1 0 2 0 29 - 3 5

2 3 0 1 10

2 3 02 z o

2 3 03 1 9

2 5 5 1 2 4 Z 1 0 Z 1 1 2 0 3 1 9 2 7 4 1 0 z a o 1 3

2 A 0 7 z s

E LA S T I -C I T Y

c 3 )

- 0 09 7 2 7

0 00 449

- 0 0 2 8 9 3

- 0 3 2 7 70 - 0 OZ il I q

o 4 u t s a 0 0 1 3 7 3

o 1 4 o o-0 0 5 2 4o -0 1 94 0 1

-C l 6 l l 4 0 1 JJ 3 7 0 3 t 0 4 2 0 0 4 0 9

- 0 4 1 8 44 - O l 7 t ) 4 -ll 7 1 4 0 b -0 3 5 7 8 Z

- 0 1 9 7 7 0 1)0 3 3 4

-o n 9 2

IJ A T A

CONV

ON-C ONV

( 4 )

t 1NV

C 1t-V C NV c ) v C - JNV C rlNV c n v c a v C ON V ( i) l V

C CtV

C t1tV C IJNV

C 1 V

c 1 v

Pa ge 2La

HEQ F t Noe x

c 5 )

6 2q

6 89 1 48

6 1 4 ) q 3

1 9 7 1 9

q z t s 5 a e z

l l 9 1

4 o 7 1 2 0

c oqt 1 Z

4 4 )-q 1 z

5 5 9 1 0 64 1 3 3

n 3

Inter industry analysi

Page 23

Equation ( 3 6 ) may be used to fo rmulate a rough test o f the cooperat ion

vs e f ficiency controversy I f we rest ricted ourselves to some subset o f

indus tries where the relat ion be tween y and a i s the same we would be lookingbull

at a sample o f indus tries for which the dependence o f V on H and o is a

quadratic wi th no squared terms

I f we now sub s titute (26) into ( 36 ) we get

(38) v bull a + (y - a) R + (y - a) o (H) - (y - a) H o (H) + u

If it is only d if ferences in marke t shares that affect advertising inten-

s i ty levels i f concentration does not af fect cooperation and i f o bull 0

( 38 ) reduces t o

( 39 ) V bull a + (y - a) H + U

Let this b e the null hyp o thes is and note that V is a linear func-

tion o f H If y gt a and the null hyp othesis holds the expected relat ion

between V and H is as shown by the pos itively sloped straight line in Figure

6 b etween points A and C

In this context the alterna ive hypothesis the degree o f

cooperation ( o) is a positive function o f concentrat ion

is that

(H) I f the func-

tion is as described in (26) and Figure 4 the relation between V and H

would be as shown by the curved line connec t ing po ints A and C in Figure 6 One way to test the null hypothe s is against this al ternative is to test fo r

the hypothesized curvature in the function relating V and H

Fi gure

R

6

v

ID c

H 1 0

I

i I I

sfigned

clasJ s

in def ini g

effec t is the

I

Page middot2lf

One charac teristic of produc ts which may be useful

classes wi th respec t to significanc e of the brand-switching

conveniencenon-convenienc e distinc tion developed by Porter ( 1 97 )

Using his identif ication of IRS indus tries as a s tar t ing point

each of the 32 industries used in this s tudy to one of the two

The ass ignments are not ed in Tab le 4

Using the conveniencenon-convenienc e dis t inc tion the

divided into two sub-samples

sample was

Four regressions were then run bull ene for e ch

sub-sample one for the to tal sample and one for the total sample with

a dummy variable for convenience goods Each regression was run wi th LB s

and wi th indus tries as ob servations The results are given in Tab le 5

For the LB level equations ( 1A - 1D) equation(37) was used ome

rearranging of terms gives v bull y - ( 1-o ) (y - a) ( 1-z ) + ui i i

bull y - 6 1 ( 1 - z ) + ui When observations are pooled across indus trif s yi

is an industry variable In these regressions the values o f y es t imated

in the first stage were used Since industries have been grouped so as

to reduce differences in (y - a) that term is t reated as a cons tant

within each group Finally H the Herfindahl index has been subst ituted

for o the degree of cooperation The resultant equation is linear

y ( 1 - z ) and H x ( l - z ) This is the equation for whi ch results arei i

reported in Table 5 In all regress ions all variables were weighted by the

square roo t of sales

in

raquo

- 34

3 1

i l T 4 8LE S R E G E S S I ON R E SUL T S i X T f N S I ON S T O T Y PE Of

AND L E V E L OF C ONC E kT R A T I O

E O O tt S

tP bull T Y P E NR C ONV O B S tO N-CONV

E L A S T I shy

T I C J T Y

O E - t-41( T SliA R E

H( fl F

1 1 - K O x middot K O X E R F

- H S a 1 1 - H S t 1 8 1 1 9 1

R S O

1 1 0 1

q z

t - bull 9 f 2 1

Z t P D l 6 fC ONV - 1 9 1 s s c 2 1

e - l O I e bull u q a

2 3 1 0 1 1 Nl N- t O V 5 7 1 ( 1 2 19 1 6 1 - J l S 2 5 4

l l l l t z q o a 1 - J o v z I

l ( I NO l l A l l ol u l t o o c bull J u l l

d S

c 3 4 t t r a l

bull Z D 1 0 l l 4 l l 2 3 -gt 2 l l 2 0 - 4 lS 5 4 l C 4 1 o e 6 t l b b 5 1 1 0 1 1 1 c - 1 9 5 1 t d S 2 1 tV

OQ10 T-R A T I O S A E G I VE N l P A RE N T H E S E S l E V E L S f S I G 1 F l C ANC E A - 99 5 B - q 9 t - s NS J UC E NO I Nl E R C ( P T I S U (j f middot) I N f Hf t OUA TIOI S 6 E f 3R E A O J U S T H E N T F OR 1-t E T E R O SIC E O A S T f C I T V pIraquo

1

middot

I

R SO I S C A L C UL A T E D A S f I f bull 1 1 bull 1lt 1 K t t- E E N I S THf U A1 B E R O f fJe S E fi V A T I O S F t S HtE F - S T A T I S

I N DE P E ND E N T y II

T I C F O T H E U Y P O HIE S I S f A l l C JE F F I C H N T A R E QU A L HI l f RO A f40 K I S T H f UUM 8 E R OF Q ( A fL f S

I l l

1 A

1 6

t C

f 1 r R I l l

1 2 1

L Jt

L B

l q

L 1

on s T Y P E bull 2 )

P OUC T

X

H S I l l

l O l A I bull l 0 7 1

O O b O J

1 2 00 1

1 b 2 1 C I l l Z U

l l S b 1 -1 1 0 1

rlt F X l l - fi C f l

bull 1 I

l l

- ()4 2 3 l f H

1 - 2 7 9 1

K O X

1 1 - ti E R F I

l d l

S4 l i A I 2 l b

1 3 00

K O X -t f R F t S J

I 1 - HER F t

)

60 9

z o bull

0

t l l

3 8 8

1 7 6

5 64

64

N f bull

tl S bull

I l l

I 4 1

t ONV

NON-t ONV

A l l

A ll

c o v NO- ( ONV

1 4 1

1 5 1

- l S b

c - 1 1 2 1

5 8 2 C A I 1 6 7 0 1

middot I l 9 H

l 1 il

1 4 1 6 1

E L A C) T J shy

l t C I T Y

I S I

l b l

- 0 2 0

1 - 1 4 9 1

O Z 3 2 1 A I C b 6 b l

0 0 9 2 -J

1 1 b 4 1

o z t t t l 1 2 2 1 1

oru - Ht tt F

1 gt X bull b I

Page 25 bull

Mean val -as ior relevan t variables for the two sub-samples are

Conv Non-Conv

Adv Sales 4 7 2 3

iit Share 2 7 3 2

Ela cicity - 05 3 02 2

Herf indahl 7 3 1 860

That the dist nct ion between coft9enienee goods and non - convenience

goods mat ters is supported not only by these means but also by the regression

results Equat ions lA and lB are different in almost every respec t Only the

concentrat ionmarket share int eract ion term seems to mat ter for convenience

good s Jus t he opposite holds for non - convenience goods both elasticity1

and market sl e are highly significant but the concentrat ionmarket share L

int erac t ion t=rm is not

Given that one minus market share is used these equ3 tions the coeffici t

of market share is the negative of what is sh in col (6) of Table 5 For the

regress ion for non - convenience LB s reported in equation lB then LB s with larger

market shares have lower advertising to sales ratios

On the question of the impact of the degree of cooperation the story is mixed

For convenienc good s the coefficient is pos itive as equation (31) predicts when

there is a po sitive degree of cooperat ion Fo r the non-convenience goods LB s middot

concentration has no effec t

Aggregat ion t o the indus try level and then rer unning the equations $ives the

results shown in (2a-2d) of Tab le 5 As expected R2 goes up and levels of significanc e

fmiddotJr individual coefficients gJ down In add ition the coeffic ient of H ( l -H) inmiddot

quat ion 2A is no t significant though it is po s i tive Since 2A is the indus try level

I

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

-- 37 --- middot - -- -1 ) l lbull t5JJ r-l bullhmiddot1 --- - --

l5A

26A

27A

c

2RA

c

2 9A

31A

llA

24

13

597

Ci)55

14

l 6h

RSQ ELASTI- (lASTCOE f-

TABLE 2

EQ I NO NR CODE IU

REGRESSION RESULTS CCONTa

NR INTER- MARKET

(10S CEPT SHARE AOVER- SHARfcent

TIS lNG AOVER

) CITY StiR

c It) bull 5 co a I 1) bull 0 bull 9 c l 0 bull( 2 1

2815 16 003019 -009990 275 -o069bmiddotJ

6 001446 000224 282 c 002178 -054630 o02221CCI -0075 00 646

2901 29 00021t2 CAI 0)0520 592 0007 6 1 068

0 00105C8 t 000012141 60)g( OOOlJ51AJ -00126018) ooou271At -000u80CA) 974

36oa 1 3 003296(4) -oca29o -oo-q94

001755 000203 lt91t 002499((1 -04l820CCI OOl374CAI 0068)0 946

3612 0033281CI 011520 195 01684) oso

00 30 42C OI 00012 2 424 oo579ltAt -2 7l7801At 002 100IAI -003220 819

8 3617 btel 011789 081002259 009530

001448 oOOl OitCCI 732 OOl7 22CAI -0 46160CAI 0004961AI -OOll40181 989c

30A 3808 14 0021t 3 6fAI -000110 628 o023291C) -005 6 middot- _ middot- 0bull 02 04 1 IC I ooooo9 637 ( 001584((1 -0161)1)0 00021 91AI -0 00060

390) 14 002790CCt 006590 h8 t 0 0938 4 070

B OOl89bCCJ 000144 74

0021961(1 -OItlOlO OOl323CAI -004800 915

B

middot--- - middot 4 - middot- - dfll3904 12 004563181 0)8300 879 0428651(1 089 OQIll004 277CA I ooozstcea 919

c 0041)3181 -0-11250 0011881(1 -006270 972 0Ill

- J - bull bull bull bullbullbull middot - - middot - middot gt middotbull L)ofbullflbull middot middotfJltl -tn- middotmiddotmiddotmiddoto +f middot t middot bull

c

is

positive

2

Page 0 determineThe consumer goodproducer good split is sometimes difficult to

Sollle support for the split used in this paper is a comparison of goodness - of - fit

distributions of a

industries

set

advertising are

that industry

a sales increase of

the

highest aD10U3 those

measures for the two groups of industries Table 3 contains

measures for the 32- consumer goods industries and the 103 producer goods

2 Median R is 5 7 for the consumer goods set and 40 for the producer goods

Estimates - of y the elasticity of demand with respect to

given in column of Table 2 The hypothesis that y bull 0 with

alternative was applied for each ittdustry As shown in the

could not be rtjected for 24 of the 32 industries Of the

and 10 are positive For the remalnifg eight three are

and five are significantly positive

Of the threertegative elasetcities the largest (in absolute value)

cosmetics (code 2809) With all elasticity of -1 01 a one

industry advertising would gwerate a decrease in industry sales

more than one percetu

At the other extrema is toys and games (code 39 04) For

a one percent ittcrease in industry advertising would lead to

four-tenths of a pampreentmiddot Though not significantly different from zero

elasticity estimatbull for pt-bpuetary drugs (code 2808)

which are

Both drug industries have

to sales rafios (211 pe1 cent for 28 08 and 13 4 per cent

other hand flaIJo ing ext1ac s (mainly soft-drink SYUlS) also

is for

percent increase in

of slightly

a middottwo - tailed

table that hypothesis

24 14 are negative

significantly negative

9

the codetics and p-ropriacuy very high advertising

for 28 09) bull On the

has a high ind UY

advenisiltg t() sales ratio ( 8 0 per cent) bull but its estimated elasticity is very

small and not signifieantly different uom zero

middot It doe$ not seem unusual to find many elasticities near zero with a few

negative and a few positive If aggregate consumption is insensitive to aggregate

advertising as seems likely ld then what one industry gains must be lost by

others

Page 21

elasticity of demand does

(10) we can

if t 0 then

Finally a determination concerning the industry

not fix the individual firms elasticity Going back to equation

write y bull (1 - ) a + z y Since a gt 0 it follows thatii i i

Y gt 0 If Ylt 0 however y s sign is indeterminateij ij

Turning next to the coefficient of market share 20 of them are negative and

12 are positive with three of each sign being significantly different from zero

The largest positive value which is significant is for pet food (code 2010) and

a close second is mens amp boys suits and coats (code 23 01) The largest signifi

cant negative value is for cosmetics (code 28 09)

In the model some relations among y a 0 and 61 are implied If middota is

negative (1- y) is greater than one Since 61Y bull (1- a) (1 - ) 61Y is

pCsitive but it will be less than one if 0 is large enough Seventeen of the A

ys are negative in each of the seventeen industries 61 is also negative and les

1 (algebraicly) than y so 61Y is greater than one his is not evidence that the

degree of cooperation is low or zero in any industry of course A high o togethegt

with a negative y which is small (in absolute terms) relative to a can give a

value of 61Y greater than one On the other hand if 61Y were less than one

o would have to be greater than zero

For y gt 0 two conditions may hold If y lt a it follows that 61 lt 0 since

(y - a ) lt 0 It also follows that 61Y lt 0 regardless of the value of o bull

In addition the relation is an if-and-only-if one ie if 61Y is negative

then y lt a Three industries have negative values for 61y dairy products

except milk (code 20 04) synthetic fibers (code 2806) and photographic equipment

(code 3808) In all three cases y is quite small so a does not have to be very

large to give a negative value to al

If y gt a the model shows that 61-- gt 0 whatever the value of 0 bull There are

12 cases where both y and 61 are positive with 61 ranging from near zero

(grain milling code 20 12) to 1 20 ( proprietary drugs code 2808) Several

coeffiei-en_rs

--

15

o f to zero

Tab le 3 - Consumer Goods

Indus tr ies

2Distributions of R and Producer Goods

Page 20a

Consumer Producer

Goods Goods

0 - 9 9 0 3

10 - 19 9 0 1 1

20 - 29 9 3 20

30 - 39 9 3 17

40 - 49 9 5 16

50 - 59 9 8

69 9 6 Ii 1060

--f 670 79 9 2

80 - 89 9 4 4

90 - 100 1 1

Totals 32 10 3

Notes

2is used R i s cal-

culated as F F + ((N - K- 1 ) K ] 1 b_ F is the F

statistic Lor the hypothesis that all o f the non - intercept terms are simul taneously equal

1

2

--

-- Since generalized least squ-area regress ion

Page 12

o f these cases have values o f 6 1 Y rea ter than 0 8 (pet food (20 10) bread amp cakes

(20 14 ) miscellaneous processed foods (20 29 ) men s and boys suit s and coats

(23 01 ) p rop riet ary drugs (28 08 ) elect ric housewares (36 1 2) radio and

IV sets 17 and games and toys (39 For be than(36 ) 04)) 6 1 Y to greater 0 8

both o and cry mus t b e less than 0 2 That is in these industries the results

shown in Tab le 2 would hold only with very strong dominance of marke t demand

effects over brand swit ching e ffects and a very low degree o f cooperation

Using the concentration rat ios given in Table 4 the average concentration

ratio for the eight indust ries is 38 1 For the remaining 24 industries it is

43 2 This result would lend some support t o the proposition that concentrat ion

and cooperation are related if the group of eight industries are identi fied

as having low degrees of cooperation

One f inal note on model predict ions S ince both cr and o are assumed to

be non-negative 60 should also be non-negat ive In only one o f the 32 cas es

is 60 negative and it is not signif icant bull

cor pJ

7 1

7 0 4

1 4 7 5 1

)

7 3 z a o a t s 1 1 3 3 5 ( i V Z 8 tJ1 2 1 - 1 1 0 7 3 5 c middot v 2 8 1 0 3 2 -0 0 1 4 3 0 C 1 V 9 8 3 2 8 1 5 1 6 - 0 0 6 t1 6 9 C _ V 1 11 0 2 9 0 1 29 0 00 7 6 1 C l k V 7 3 1 3 6 08 1 3 - o n 4 9 9 4 3 3 3 6 1 2 2 4 0 1 6 4 3

3 1 7 1 3 0 1 1 7 d 7 8 3 3 8 0 8 0 0 2 3 i 2 3 0 6

P 4

3 9 0 3 1 4

1 2

0 09 3 8 4 39 1)1 0 4 l 8 6 5

T A LE 4 e I NCU S T R Y C A T E G O R Y

F TC NOM e tOOE ass

C 1 I c 2 )

2 0 0 1 1 6 2 0 0r 1 7 zo o l Z 2 0 0 7 1 8

z o o 2 6

z o t a 1 6

2 1) 1 2 1 5 2 0 1 4 1 1 2 0 1 a 1 9 2 0 26 1 2 2 0 2 7 1 0 2 0 29 - 3 5

2 3 0 1 10

2 3 02 z o

2 3 03 1 9

2 5 5 1 2 4 Z 1 0 Z 1 1 2 0 3 1 9 2 7 4 1 0 z a o 1 3

2 A 0 7 z s

E LA S T I -C I T Y

c 3 )

- 0 09 7 2 7

0 00 449

- 0 0 2 8 9 3

- 0 3 2 7 70 - 0 OZ il I q

o 4 u t s a 0 0 1 3 7 3

o 1 4 o o-0 0 5 2 4o -0 1 94 0 1

-C l 6 l l 4 0 1 JJ 3 7 0 3 t 0 4 2 0 0 4 0 9

- 0 4 1 8 44 - O l 7 t ) 4 -ll 7 1 4 0 b -0 3 5 7 8 Z

- 0 1 9 7 7 0 1)0 3 3 4

-o n 9 2

IJ A T A

CONV

ON-C ONV

( 4 )

t 1NV

C 1t-V C NV c ) v C - JNV C rlNV c n v c a v C ON V ( i) l V

C CtV

C t1tV C IJNV

C 1 V

c 1 v

Pa ge 2La

HEQ F t Noe x

c 5 )

6 2q

6 89 1 48

6 1 4 ) q 3

1 9 7 1 9

q z t s 5 a e z

l l 9 1

4 o 7 1 2 0

c oqt 1 Z

4 4 )-q 1 z

5 5 9 1 0 64 1 3 3

n 3

Inter industry analysi

Page 23

Equation ( 3 6 ) may be used to fo rmulate a rough test o f the cooperat ion

vs e f ficiency controversy I f we rest ricted ourselves to some subset o f

indus tries where the relat ion be tween y and a i s the same we would be lookingbull

at a sample o f indus tries for which the dependence o f V on H and o is a

quadratic wi th no squared terms

I f we now sub s titute (26) into ( 36 ) we get

(38) v bull a + (y - a) R + (y - a) o (H) - (y - a) H o (H) + u

If it is only d if ferences in marke t shares that affect advertising inten-

s i ty levels i f concentration does not af fect cooperation and i f o bull 0

( 38 ) reduces t o

( 39 ) V bull a + (y - a) H + U

Let this b e the null hyp o thes is and note that V is a linear func-

tion o f H If y gt a and the null hyp othesis holds the expected relat ion

between V and H is as shown by the pos itively sloped straight line in Figure

6 b etween points A and C

In this context the alterna ive hypothesis the degree o f

cooperation ( o) is a positive function o f concentrat ion

is that

(H) I f the func-

tion is as described in (26) and Figure 4 the relation between V and H

would be as shown by the curved line connec t ing po ints A and C in Figure 6 One way to test the null hypothe s is against this al ternative is to test fo r

the hypothesized curvature in the function relating V and H

Fi gure

R

6

v

ID c

H 1 0

I

i I I

sfigned

clasJ s

in def ini g

effec t is the

I

Page middot2lf

One charac teristic of produc ts which may be useful

classes wi th respec t to significanc e of the brand-switching

conveniencenon-convenienc e distinc tion developed by Porter ( 1 97 )

Using his identif ication of IRS indus tries as a s tar t ing point

each of the 32 industries used in this s tudy to one of the two

The ass ignments are not ed in Tab le 4

Using the conveniencenon-convenienc e dis t inc tion the

divided into two sub-samples

sample was

Four regressions were then run bull ene for e ch

sub-sample one for the to tal sample and one for the total sample with

a dummy variable for convenience goods Each regression was run wi th LB s

and wi th indus tries as ob servations The results are given in Tab le 5

For the LB level equations ( 1A - 1D) equation(37) was used ome

rearranging of terms gives v bull y - ( 1-o ) (y - a) ( 1-z ) + ui i i

bull y - 6 1 ( 1 - z ) + ui When observations are pooled across indus trif s yi

is an industry variable In these regressions the values o f y es t imated

in the first stage were used Since industries have been grouped so as

to reduce differences in (y - a) that term is t reated as a cons tant

within each group Finally H the Herfindahl index has been subst ituted

for o the degree of cooperation The resultant equation is linear

y ( 1 - z ) and H x ( l - z ) This is the equation for whi ch results arei i

reported in Table 5 In all regress ions all variables were weighted by the

square roo t of sales

in

raquo

- 34

3 1

i l T 4 8LE S R E G E S S I ON R E SUL T S i X T f N S I ON S T O T Y PE Of

AND L E V E L OF C ONC E kT R A T I O

E O O tt S

tP bull T Y P E NR C ONV O B S tO N-CONV

E L A S T I shy

T I C J T Y

O E - t-41( T SliA R E

H( fl F

1 1 - K O x middot K O X E R F

- H S a 1 1 - H S t 1 8 1 1 9 1

R S O

1 1 0 1

q z

t - bull 9 f 2 1

Z t P D l 6 fC ONV - 1 9 1 s s c 2 1

e - l O I e bull u q a

2 3 1 0 1 1 Nl N- t O V 5 7 1 ( 1 2 19 1 6 1 - J l S 2 5 4

l l l l t z q o a 1 - J o v z I

l ( I NO l l A l l ol u l t o o c bull J u l l

d S

c 3 4 t t r a l

bull Z D 1 0 l l 4 l l 2 3 -gt 2 l l 2 0 - 4 lS 5 4 l C 4 1 o e 6 t l b b 5 1 1 0 1 1 1 c - 1 9 5 1 t d S 2 1 tV

OQ10 T-R A T I O S A E G I VE N l P A RE N T H E S E S l E V E L S f S I G 1 F l C ANC E A - 99 5 B - q 9 t - s NS J UC E NO I Nl E R C ( P T I S U (j f middot) I N f Hf t OUA TIOI S 6 E f 3R E A O J U S T H E N T F OR 1-t E T E R O SIC E O A S T f C I T V pIraquo

1

middot

I

R SO I S C A L C UL A T E D A S f I f bull 1 1 bull 1lt 1 K t t- E E N I S THf U A1 B E R O f fJe S E fi V A T I O S F t S HtE F - S T A T I S

I N DE P E ND E N T y II

T I C F O T H E U Y P O HIE S I S f A l l C JE F F I C H N T A R E QU A L HI l f RO A f40 K I S T H f UUM 8 E R OF Q ( A fL f S

I l l

1 A

1 6

t C

f 1 r R I l l

1 2 1

L Jt

L B

l q

L 1

on s T Y P E bull 2 )

P OUC T

X

H S I l l

l O l A I bull l 0 7 1

O O b O J

1 2 00 1

1 b 2 1 C I l l Z U

l l S b 1 -1 1 0 1

rlt F X l l - fi C f l

bull 1 I

l l

- ()4 2 3 l f H

1 - 2 7 9 1

K O X

1 1 - ti E R F I

l d l

S4 l i A I 2 l b

1 3 00

K O X -t f R F t S J

I 1 - HER F t

)

60 9

z o bull

0

t l l

3 8 8

1 7 6

5 64

64

N f bull

tl S bull

I l l

I 4 1

t ONV

NON-t ONV

A l l

A ll

c o v NO- ( ONV

1 4 1

1 5 1

- l S b

c - 1 1 2 1

5 8 2 C A I 1 6 7 0 1

middot I l 9 H

l 1 il

1 4 1 6 1

E L A C) T J shy

l t C I T Y

I S I

l b l

- 0 2 0

1 - 1 4 9 1

O Z 3 2 1 A I C b 6 b l

0 0 9 2 -J

1 1 b 4 1

o z t t t l 1 2 2 1 1

oru - Ht tt F

1 gt X bull b I

Page 25 bull

Mean val -as ior relevan t variables for the two sub-samples are

Conv Non-Conv

Adv Sales 4 7 2 3

iit Share 2 7 3 2

Ela cicity - 05 3 02 2

Herf indahl 7 3 1 860

That the dist nct ion between coft9enienee goods and non - convenience

goods mat ters is supported not only by these means but also by the regression

results Equat ions lA and lB are different in almost every respec t Only the

concentrat ionmarket share int eract ion term seems to mat ter for convenience

good s Jus t he opposite holds for non - convenience goods both elasticity1

and market sl e are highly significant but the concentrat ionmarket share L

int erac t ion t=rm is not

Given that one minus market share is used these equ3 tions the coeffici t

of market share is the negative of what is sh in col (6) of Table 5 For the

regress ion for non - convenience LB s reported in equation lB then LB s with larger

market shares have lower advertising to sales ratios

On the question of the impact of the degree of cooperation the story is mixed

For convenienc good s the coefficient is pos itive as equation (31) predicts when

there is a po sitive degree of cooperat ion Fo r the non-convenience goods LB s middot

concentration has no effec t

Aggregat ion t o the indus try level and then rer unning the equations $ives the

results shown in (2a-2d) of Tab le 5 As expected R2 goes up and levels of significanc e

fmiddotJr individual coefficients gJ down In add ition the coeffic ient of H ( l -H) inmiddot

quat ion 2A is no t significant though it is po s i tive Since 2A is the indus try level

I

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

is

positive

2

Page 0 determineThe consumer goodproducer good split is sometimes difficult to

Sollle support for the split used in this paper is a comparison of goodness - of - fit

distributions of a

industries

set

advertising are

that industry

a sales increase of

the

highest aD10U3 those

measures for the two groups of industries Table 3 contains

measures for the 32- consumer goods industries and the 103 producer goods

2 Median R is 5 7 for the consumer goods set and 40 for the producer goods

Estimates - of y the elasticity of demand with respect to

given in column of Table 2 The hypothesis that y bull 0 with

alternative was applied for each ittdustry As shown in the

could not be rtjected for 24 of the 32 industries Of the

and 10 are positive For the remalnifg eight three are

and five are significantly positive

Of the threertegative elasetcities the largest (in absolute value)

cosmetics (code 2809) With all elasticity of -1 01 a one

industry advertising would gwerate a decrease in industry sales

more than one percetu

At the other extrema is toys and games (code 39 04) For

a one percent ittcrease in industry advertising would lead to

four-tenths of a pampreentmiddot Though not significantly different from zero

elasticity estimatbull for pt-bpuetary drugs (code 2808)

which are

Both drug industries have

to sales rafios (211 pe1 cent for 28 08 and 13 4 per cent

other hand flaIJo ing ext1ac s (mainly soft-drink SYUlS) also

is for

percent increase in

of slightly

a middottwo - tailed

table that hypothesis

24 14 are negative

significantly negative

9

the codetics and p-ropriacuy very high advertising

for 28 09) bull On the

has a high ind UY

advenisiltg t() sales ratio ( 8 0 per cent) bull but its estimated elasticity is very

small and not signifieantly different uom zero

middot It doe$ not seem unusual to find many elasticities near zero with a few

negative and a few positive If aggregate consumption is insensitive to aggregate

advertising as seems likely ld then what one industry gains must be lost by

others

Page 21

elasticity of demand does

(10) we can

if t 0 then

Finally a determination concerning the industry

not fix the individual firms elasticity Going back to equation

write y bull (1 - ) a + z y Since a gt 0 it follows thatii i i

Y gt 0 If Ylt 0 however y s sign is indeterminateij ij

Turning next to the coefficient of market share 20 of them are negative and

12 are positive with three of each sign being significantly different from zero

The largest positive value which is significant is for pet food (code 2010) and

a close second is mens amp boys suits and coats (code 23 01) The largest signifi

cant negative value is for cosmetics (code 28 09)

In the model some relations among y a 0 and 61 are implied If middota is

negative (1- y) is greater than one Since 61Y bull (1- a) (1 - ) 61Y is

pCsitive but it will be less than one if 0 is large enough Seventeen of the A

ys are negative in each of the seventeen industries 61 is also negative and les

1 (algebraicly) than y so 61Y is greater than one his is not evidence that the

degree of cooperation is low or zero in any industry of course A high o togethegt

with a negative y which is small (in absolute terms) relative to a can give a

value of 61Y greater than one On the other hand if 61Y were less than one

o would have to be greater than zero

For y gt 0 two conditions may hold If y lt a it follows that 61 lt 0 since

(y - a ) lt 0 It also follows that 61Y lt 0 regardless of the value of o bull

In addition the relation is an if-and-only-if one ie if 61Y is negative

then y lt a Three industries have negative values for 61y dairy products

except milk (code 20 04) synthetic fibers (code 2806) and photographic equipment

(code 3808) In all three cases y is quite small so a does not have to be very

large to give a negative value to al

If y gt a the model shows that 61-- gt 0 whatever the value of 0 bull There are

12 cases where both y and 61 are positive with 61 ranging from near zero

(grain milling code 20 12) to 1 20 ( proprietary drugs code 2808) Several

coeffiei-en_rs

--

15

o f to zero

Tab le 3 - Consumer Goods

Indus tr ies

2Distributions of R and Producer Goods

Page 20a

Consumer Producer

Goods Goods

0 - 9 9 0 3

10 - 19 9 0 1 1

20 - 29 9 3 20

30 - 39 9 3 17

40 - 49 9 5 16

50 - 59 9 8

69 9 6 Ii 1060

--f 670 79 9 2

80 - 89 9 4 4

90 - 100 1 1

Totals 32 10 3

Notes

2is used R i s cal-

culated as F F + ((N - K- 1 ) K ] 1 b_ F is the F

statistic Lor the hypothesis that all o f the non - intercept terms are simul taneously equal

1

2

--

-- Since generalized least squ-area regress ion

Page 12

o f these cases have values o f 6 1 Y rea ter than 0 8 (pet food (20 10) bread amp cakes

(20 14 ) miscellaneous processed foods (20 29 ) men s and boys suit s and coats

(23 01 ) p rop riet ary drugs (28 08 ) elect ric housewares (36 1 2) radio and

IV sets 17 and games and toys (39 For be than(36 ) 04)) 6 1 Y to greater 0 8

both o and cry mus t b e less than 0 2 That is in these industries the results

shown in Tab le 2 would hold only with very strong dominance of marke t demand

effects over brand swit ching e ffects and a very low degree o f cooperation

Using the concentration rat ios given in Table 4 the average concentration

ratio for the eight indust ries is 38 1 For the remaining 24 industries it is

43 2 This result would lend some support t o the proposition that concentrat ion

and cooperation are related if the group of eight industries are identi fied

as having low degrees of cooperation

One f inal note on model predict ions S ince both cr and o are assumed to

be non-negative 60 should also be non-negat ive In only one o f the 32 cas es

is 60 negative and it is not signif icant bull

cor pJ

7 1

7 0 4

1 4 7 5 1

)

7 3 z a o a t s 1 1 3 3 5 ( i V Z 8 tJ1 2 1 - 1 1 0 7 3 5 c middot v 2 8 1 0 3 2 -0 0 1 4 3 0 C 1 V 9 8 3 2 8 1 5 1 6 - 0 0 6 t1 6 9 C _ V 1 11 0 2 9 0 1 29 0 00 7 6 1 C l k V 7 3 1 3 6 08 1 3 - o n 4 9 9 4 3 3 3 6 1 2 2 4 0 1 6 4 3

3 1 7 1 3 0 1 1 7 d 7 8 3 3 8 0 8 0 0 2 3 i 2 3 0 6

P 4

3 9 0 3 1 4

1 2

0 09 3 8 4 39 1)1 0 4 l 8 6 5

T A LE 4 e I NCU S T R Y C A T E G O R Y

F TC NOM e tOOE ass

C 1 I c 2 )

2 0 0 1 1 6 2 0 0r 1 7 zo o l Z 2 0 0 7 1 8

z o o 2 6

z o t a 1 6

2 1) 1 2 1 5 2 0 1 4 1 1 2 0 1 a 1 9 2 0 26 1 2 2 0 2 7 1 0 2 0 29 - 3 5

2 3 0 1 10

2 3 02 z o

2 3 03 1 9

2 5 5 1 2 4 Z 1 0 Z 1 1 2 0 3 1 9 2 7 4 1 0 z a o 1 3

2 A 0 7 z s

E LA S T I -C I T Y

c 3 )

- 0 09 7 2 7

0 00 449

- 0 0 2 8 9 3

- 0 3 2 7 70 - 0 OZ il I q

o 4 u t s a 0 0 1 3 7 3

o 1 4 o o-0 0 5 2 4o -0 1 94 0 1

-C l 6 l l 4 0 1 JJ 3 7 0 3 t 0 4 2 0 0 4 0 9

- 0 4 1 8 44 - O l 7 t ) 4 -ll 7 1 4 0 b -0 3 5 7 8 Z

- 0 1 9 7 7 0 1)0 3 3 4

-o n 9 2

IJ A T A

CONV

ON-C ONV

( 4 )

t 1NV

C 1t-V C NV c ) v C - JNV C rlNV c n v c a v C ON V ( i) l V

C CtV

C t1tV C IJNV

C 1 V

c 1 v

Pa ge 2La

HEQ F t Noe x

c 5 )

6 2q

6 89 1 48

6 1 4 ) q 3

1 9 7 1 9

q z t s 5 a e z

l l 9 1

4 o 7 1 2 0

c oqt 1 Z

4 4 )-q 1 z

5 5 9 1 0 64 1 3 3

n 3

Inter industry analysi

Page 23

Equation ( 3 6 ) may be used to fo rmulate a rough test o f the cooperat ion

vs e f ficiency controversy I f we rest ricted ourselves to some subset o f

indus tries where the relat ion be tween y and a i s the same we would be lookingbull

at a sample o f indus tries for which the dependence o f V on H and o is a

quadratic wi th no squared terms

I f we now sub s titute (26) into ( 36 ) we get

(38) v bull a + (y - a) R + (y - a) o (H) - (y - a) H o (H) + u

If it is only d if ferences in marke t shares that affect advertising inten-

s i ty levels i f concentration does not af fect cooperation and i f o bull 0

( 38 ) reduces t o

( 39 ) V bull a + (y - a) H + U

Let this b e the null hyp o thes is and note that V is a linear func-

tion o f H If y gt a and the null hyp othesis holds the expected relat ion

between V and H is as shown by the pos itively sloped straight line in Figure

6 b etween points A and C

In this context the alterna ive hypothesis the degree o f

cooperation ( o) is a positive function o f concentrat ion

is that

(H) I f the func-

tion is as described in (26) and Figure 4 the relation between V and H

would be as shown by the curved line connec t ing po ints A and C in Figure 6 One way to test the null hypothe s is against this al ternative is to test fo r

the hypothesized curvature in the function relating V and H

Fi gure

R

6

v

ID c

H 1 0

I

i I I

sfigned

clasJ s

in def ini g

effec t is the

I

Page middot2lf

One charac teristic of produc ts which may be useful

classes wi th respec t to significanc e of the brand-switching

conveniencenon-convenienc e distinc tion developed by Porter ( 1 97 )

Using his identif ication of IRS indus tries as a s tar t ing point

each of the 32 industries used in this s tudy to one of the two

The ass ignments are not ed in Tab le 4

Using the conveniencenon-convenienc e dis t inc tion the

divided into two sub-samples

sample was

Four regressions were then run bull ene for e ch

sub-sample one for the to tal sample and one for the total sample with

a dummy variable for convenience goods Each regression was run wi th LB s

and wi th indus tries as ob servations The results are given in Tab le 5

For the LB level equations ( 1A - 1D) equation(37) was used ome

rearranging of terms gives v bull y - ( 1-o ) (y - a) ( 1-z ) + ui i i

bull y - 6 1 ( 1 - z ) + ui When observations are pooled across indus trif s yi

is an industry variable In these regressions the values o f y es t imated

in the first stage were used Since industries have been grouped so as

to reduce differences in (y - a) that term is t reated as a cons tant

within each group Finally H the Herfindahl index has been subst ituted

for o the degree of cooperation The resultant equation is linear

y ( 1 - z ) and H x ( l - z ) This is the equation for whi ch results arei i

reported in Table 5 In all regress ions all variables were weighted by the

square roo t of sales

in

raquo

- 34

3 1

i l T 4 8LE S R E G E S S I ON R E SUL T S i X T f N S I ON S T O T Y PE Of

AND L E V E L OF C ONC E kT R A T I O

E O O tt S

tP bull T Y P E NR C ONV O B S tO N-CONV

E L A S T I shy

T I C J T Y

O E - t-41( T SliA R E

H( fl F

1 1 - K O x middot K O X E R F

- H S a 1 1 - H S t 1 8 1 1 9 1

R S O

1 1 0 1

q z

t - bull 9 f 2 1

Z t P D l 6 fC ONV - 1 9 1 s s c 2 1

e - l O I e bull u q a

2 3 1 0 1 1 Nl N- t O V 5 7 1 ( 1 2 19 1 6 1 - J l S 2 5 4

l l l l t z q o a 1 - J o v z I

l ( I NO l l A l l ol u l t o o c bull J u l l

d S

c 3 4 t t r a l

bull Z D 1 0 l l 4 l l 2 3 -gt 2 l l 2 0 - 4 lS 5 4 l C 4 1 o e 6 t l b b 5 1 1 0 1 1 1 c - 1 9 5 1 t d S 2 1 tV

OQ10 T-R A T I O S A E G I VE N l P A RE N T H E S E S l E V E L S f S I G 1 F l C ANC E A - 99 5 B - q 9 t - s NS J UC E NO I Nl E R C ( P T I S U (j f middot) I N f Hf t OUA TIOI S 6 E f 3R E A O J U S T H E N T F OR 1-t E T E R O SIC E O A S T f C I T V pIraquo

1

middot

I

R SO I S C A L C UL A T E D A S f I f bull 1 1 bull 1lt 1 K t t- E E N I S THf U A1 B E R O f fJe S E fi V A T I O S F t S HtE F - S T A T I S

I N DE P E ND E N T y II

T I C F O T H E U Y P O HIE S I S f A l l C JE F F I C H N T A R E QU A L HI l f RO A f40 K I S T H f UUM 8 E R OF Q ( A fL f S

I l l

1 A

1 6

t C

f 1 r R I l l

1 2 1

L Jt

L B

l q

L 1

on s T Y P E bull 2 )

P OUC T

X

H S I l l

l O l A I bull l 0 7 1

O O b O J

1 2 00 1

1 b 2 1 C I l l Z U

l l S b 1 -1 1 0 1

rlt F X l l - fi C f l

bull 1 I

l l

- ()4 2 3 l f H

1 - 2 7 9 1

K O X

1 1 - ti E R F I

l d l

S4 l i A I 2 l b

1 3 00

K O X -t f R F t S J

I 1 - HER F t

)

60 9

z o bull

0

t l l

3 8 8

1 7 6

5 64

64

N f bull

tl S bull

I l l

I 4 1

t ONV

NON-t ONV

A l l

A ll

c o v NO- ( ONV

1 4 1

1 5 1

- l S b

c - 1 1 2 1

5 8 2 C A I 1 6 7 0 1

middot I l 9 H

l 1 il

1 4 1 6 1

E L A C) T J shy

l t C I T Y

I S I

l b l

- 0 2 0

1 - 1 4 9 1

O Z 3 2 1 A I C b 6 b l

0 0 9 2 -J

1 1 b 4 1

o z t t t l 1 2 2 1 1

oru - Ht tt F

1 gt X bull b I

Page 25 bull

Mean val -as ior relevan t variables for the two sub-samples are

Conv Non-Conv

Adv Sales 4 7 2 3

iit Share 2 7 3 2

Ela cicity - 05 3 02 2

Herf indahl 7 3 1 860

That the dist nct ion between coft9enienee goods and non - convenience

goods mat ters is supported not only by these means but also by the regression

results Equat ions lA and lB are different in almost every respec t Only the

concentrat ionmarket share int eract ion term seems to mat ter for convenience

good s Jus t he opposite holds for non - convenience goods both elasticity1

and market sl e are highly significant but the concentrat ionmarket share L

int erac t ion t=rm is not

Given that one minus market share is used these equ3 tions the coeffici t

of market share is the negative of what is sh in col (6) of Table 5 For the

regress ion for non - convenience LB s reported in equation lB then LB s with larger

market shares have lower advertising to sales ratios

On the question of the impact of the degree of cooperation the story is mixed

For convenienc good s the coefficient is pos itive as equation (31) predicts when

there is a po sitive degree of cooperat ion Fo r the non-convenience goods LB s middot

concentration has no effec t

Aggregat ion t o the indus try level and then rer unning the equations $ives the

results shown in (2a-2d) of Tab le 5 As expected R2 goes up and levels of significanc e

fmiddotJr individual coefficients gJ down In add ition the coeffic ient of H ( l -H) inmiddot

quat ion 2A is no t significant though it is po s i tive Since 2A is the indus try level

I

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

Page 21

elasticity of demand does

(10) we can

if t 0 then

Finally a determination concerning the industry

not fix the individual firms elasticity Going back to equation

write y bull (1 - ) a + z y Since a gt 0 it follows thatii i i

Y gt 0 If Ylt 0 however y s sign is indeterminateij ij

Turning next to the coefficient of market share 20 of them are negative and

12 are positive with three of each sign being significantly different from zero

The largest positive value which is significant is for pet food (code 2010) and

a close second is mens amp boys suits and coats (code 23 01) The largest signifi

cant negative value is for cosmetics (code 28 09)

In the model some relations among y a 0 and 61 are implied If middota is

negative (1- y) is greater than one Since 61Y bull (1- a) (1 - ) 61Y is

pCsitive but it will be less than one if 0 is large enough Seventeen of the A

ys are negative in each of the seventeen industries 61 is also negative and les

1 (algebraicly) than y so 61Y is greater than one his is not evidence that the

degree of cooperation is low or zero in any industry of course A high o togethegt

with a negative y which is small (in absolute terms) relative to a can give a

value of 61Y greater than one On the other hand if 61Y were less than one

o would have to be greater than zero

For y gt 0 two conditions may hold If y lt a it follows that 61 lt 0 since

(y - a ) lt 0 It also follows that 61Y lt 0 regardless of the value of o bull

In addition the relation is an if-and-only-if one ie if 61Y is negative

then y lt a Three industries have negative values for 61y dairy products

except milk (code 20 04) synthetic fibers (code 2806) and photographic equipment

(code 3808) In all three cases y is quite small so a does not have to be very

large to give a negative value to al

If y gt a the model shows that 61-- gt 0 whatever the value of 0 bull There are

12 cases where both y and 61 are positive with 61 ranging from near zero

(grain milling code 20 12) to 1 20 ( proprietary drugs code 2808) Several

coeffiei-en_rs

--

15

o f to zero

Tab le 3 - Consumer Goods

Indus tr ies

2Distributions of R and Producer Goods

Page 20a

Consumer Producer

Goods Goods

0 - 9 9 0 3

10 - 19 9 0 1 1

20 - 29 9 3 20

30 - 39 9 3 17

40 - 49 9 5 16

50 - 59 9 8

69 9 6 Ii 1060

--f 670 79 9 2

80 - 89 9 4 4

90 - 100 1 1

Totals 32 10 3

Notes

2is used R i s cal-

culated as F F + ((N - K- 1 ) K ] 1 b_ F is the F

statistic Lor the hypothesis that all o f the non - intercept terms are simul taneously equal

1

2

--

-- Since generalized least squ-area regress ion

Page 12

o f these cases have values o f 6 1 Y rea ter than 0 8 (pet food (20 10) bread amp cakes

(20 14 ) miscellaneous processed foods (20 29 ) men s and boys suit s and coats

(23 01 ) p rop riet ary drugs (28 08 ) elect ric housewares (36 1 2) radio and

IV sets 17 and games and toys (39 For be than(36 ) 04)) 6 1 Y to greater 0 8

both o and cry mus t b e less than 0 2 That is in these industries the results

shown in Tab le 2 would hold only with very strong dominance of marke t demand

effects over brand swit ching e ffects and a very low degree o f cooperation

Using the concentration rat ios given in Table 4 the average concentration

ratio for the eight indust ries is 38 1 For the remaining 24 industries it is

43 2 This result would lend some support t o the proposition that concentrat ion

and cooperation are related if the group of eight industries are identi fied

as having low degrees of cooperation

One f inal note on model predict ions S ince both cr and o are assumed to

be non-negative 60 should also be non-negat ive In only one o f the 32 cas es

is 60 negative and it is not signif icant bull

cor pJ

7 1

7 0 4

1 4 7 5 1

)

7 3 z a o a t s 1 1 3 3 5 ( i V Z 8 tJ1 2 1 - 1 1 0 7 3 5 c middot v 2 8 1 0 3 2 -0 0 1 4 3 0 C 1 V 9 8 3 2 8 1 5 1 6 - 0 0 6 t1 6 9 C _ V 1 11 0 2 9 0 1 29 0 00 7 6 1 C l k V 7 3 1 3 6 08 1 3 - o n 4 9 9 4 3 3 3 6 1 2 2 4 0 1 6 4 3

3 1 7 1 3 0 1 1 7 d 7 8 3 3 8 0 8 0 0 2 3 i 2 3 0 6

P 4

3 9 0 3 1 4

1 2

0 09 3 8 4 39 1)1 0 4 l 8 6 5

T A LE 4 e I NCU S T R Y C A T E G O R Y

F TC NOM e tOOE ass

C 1 I c 2 )

2 0 0 1 1 6 2 0 0r 1 7 zo o l Z 2 0 0 7 1 8

z o o 2 6

z o t a 1 6

2 1) 1 2 1 5 2 0 1 4 1 1 2 0 1 a 1 9 2 0 26 1 2 2 0 2 7 1 0 2 0 29 - 3 5

2 3 0 1 10

2 3 02 z o

2 3 03 1 9

2 5 5 1 2 4 Z 1 0 Z 1 1 2 0 3 1 9 2 7 4 1 0 z a o 1 3

2 A 0 7 z s

E LA S T I -C I T Y

c 3 )

- 0 09 7 2 7

0 00 449

- 0 0 2 8 9 3

- 0 3 2 7 70 - 0 OZ il I q

o 4 u t s a 0 0 1 3 7 3

o 1 4 o o-0 0 5 2 4o -0 1 94 0 1

-C l 6 l l 4 0 1 JJ 3 7 0 3 t 0 4 2 0 0 4 0 9

- 0 4 1 8 44 - O l 7 t ) 4 -ll 7 1 4 0 b -0 3 5 7 8 Z

- 0 1 9 7 7 0 1)0 3 3 4

-o n 9 2

IJ A T A

CONV

ON-C ONV

( 4 )

t 1NV

C 1t-V C NV c ) v C - JNV C rlNV c n v c a v C ON V ( i) l V

C CtV

C t1tV C IJNV

C 1 V

c 1 v

Pa ge 2La

HEQ F t Noe x

c 5 )

6 2q

6 89 1 48

6 1 4 ) q 3

1 9 7 1 9

q z t s 5 a e z

l l 9 1

4 o 7 1 2 0

c oqt 1 Z

4 4 )-q 1 z

5 5 9 1 0 64 1 3 3

n 3

Inter industry analysi

Page 23

Equation ( 3 6 ) may be used to fo rmulate a rough test o f the cooperat ion

vs e f ficiency controversy I f we rest ricted ourselves to some subset o f

indus tries where the relat ion be tween y and a i s the same we would be lookingbull

at a sample o f indus tries for which the dependence o f V on H and o is a

quadratic wi th no squared terms

I f we now sub s titute (26) into ( 36 ) we get

(38) v bull a + (y - a) R + (y - a) o (H) - (y - a) H o (H) + u

If it is only d if ferences in marke t shares that affect advertising inten-

s i ty levels i f concentration does not af fect cooperation and i f o bull 0

( 38 ) reduces t o

( 39 ) V bull a + (y - a) H + U

Let this b e the null hyp o thes is and note that V is a linear func-

tion o f H If y gt a and the null hyp othesis holds the expected relat ion

between V and H is as shown by the pos itively sloped straight line in Figure

6 b etween points A and C

In this context the alterna ive hypothesis the degree o f

cooperation ( o) is a positive function o f concentrat ion

is that

(H) I f the func-

tion is as described in (26) and Figure 4 the relation between V and H

would be as shown by the curved line connec t ing po ints A and C in Figure 6 One way to test the null hypothe s is against this al ternative is to test fo r

the hypothesized curvature in the function relating V and H

Fi gure

R

6

v

ID c

H 1 0

I

i I I

sfigned

clasJ s

in def ini g

effec t is the

I

Page middot2lf

One charac teristic of produc ts which may be useful

classes wi th respec t to significanc e of the brand-switching

conveniencenon-convenienc e distinc tion developed by Porter ( 1 97 )

Using his identif ication of IRS indus tries as a s tar t ing point

each of the 32 industries used in this s tudy to one of the two

The ass ignments are not ed in Tab le 4

Using the conveniencenon-convenienc e dis t inc tion the

divided into two sub-samples

sample was

Four regressions were then run bull ene for e ch

sub-sample one for the to tal sample and one for the total sample with

a dummy variable for convenience goods Each regression was run wi th LB s

and wi th indus tries as ob servations The results are given in Tab le 5

For the LB level equations ( 1A - 1D) equation(37) was used ome

rearranging of terms gives v bull y - ( 1-o ) (y - a) ( 1-z ) + ui i i

bull y - 6 1 ( 1 - z ) + ui When observations are pooled across indus trif s yi

is an industry variable In these regressions the values o f y es t imated

in the first stage were used Since industries have been grouped so as

to reduce differences in (y - a) that term is t reated as a cons tant

within each group Finally H the Herfindahl index has been subst ituted

for o the degree of cooperation The resultant equation is linear

y ( 1 - z ) and H x ( l - z ) This is the equation for whi ch results arei i

reported in Table 5 In all regress ions all variables were weighted by the

square roo t of sales

in

raquo

- 34

3 1

i l T 4 8LE S R E G E S S I ON R E SUL T S i X T f N S I ON S T O T Y PE Of

AND L E V E L OF C ONC E kT R A T I O

E O O tt S

tP bull T Y P E NR C ONV O B S tO N-CONV

E L A S T I shy

T I C J T Y

O E - t-41( T SliA R E

H( fl F

1 1 - K O x middot K O X E R F

- H S a 1 1 - H S t 1 8 1 1 9 1

R S O

1 1 0 1

q z

t - bull 9 f 2 1

Z t P D l 6 fC ONV - 1 9 1 s s c 2 1

e - l O I e bull u q a

2 3 1 0 1 1 Nl N- t O V 5 7 1 ( 1 2 19 1 6 1 - J l S 2 5 4

l l l l t z q o a 1 - J o v z I

l ( I NO l l A l l ol u l t o o c bull J u l l

d S

c 3 4 t t r a l

bull Z D 1 0 l l 4 l l 2 3 -gt 2 l l 2 0 - 4 lS 5 4 l C 4 1 o e 6 t l b b 5 1 1 0 1 1 1 c - 1 9 5 1 t d S 2 1 tV

OQ10 T-R A T I O S A E G I VE N l P A RE N T H E S E S l E V E L S f S I G 1 F l C ANC E A - 99 5 B - q 9 t - s NS J UC E NO I Nl E R C ( P T I S U (j f middot) I N f Hf t OUA TIOI S 6 E f 3R E A O J U S T H E N T F OR 1-t E T E R O SIC E O A S T f C I T V pIraquo

1

middot

I

R SO I S C A L C UL A T E D A S f I f bull 1 1 bull 1lt 1 K t t- E E N I S THf U A1 B E R O f fJe S E fi V A T I O S F t S HtE F - S T A T I S

I N DE P E ND E N T y II

T I C F O T H E U Y P O HIE S I S f A l l C JE F F I C H N T A R E QU A L HI l f RO A f40 K I S T H f UUM 8 E R OF Q ( A fL f S

I l l

1 A

1 6

t C

f 1 r R I l l

1 2 1

L Jt

L B

l q

L 1

on s T Y P E bull 2 )

P OUC T

X

H S I l l

l O l A I bull l 0 7 1

O O b O J

1 2 00 1

1 b 2 1 C I l l Z U

l l S b 1 -1 1 0 1

rlt F X l l - fi C f l

bull 1 I

l l

- ()4 2 3 l f H

1 - 2 7 9 1

K O X

1 1 - ti E R F I

l d l

S4 l i A I 2 l b

1 3 00

K O X -t f R F t S J

I 1 - HER F t

)

60 9

z o bull

0

t l l

3 8 8

1 7 6

5 64

64

N f bull

tl S bull

I l l

I 4 1

t ONV

NON-t ONV

A l l

A ll

c o v NO- ( ONV

1 4 1

1 5 1

- l S b

c - 1 1 2 1

5 8 2 C A I 1 6 7 0 1

middot I l 9 H

l 1 il

1 4 1 6 1

E L A C) T J shy

l t C I T Y

I S I

l b l

- 0 2 0

1 - 1 4 9 1

O Z 3 2 1 A I C b 6 b l

0 0 9 2 -J

1 1 b 4 1

o z t t t l 1 2 2 1 1

oru - Ht tt F

1 gt X bull b I

Page 25 bull

Mean val -as ior relevan t variables for the two sub-samples are

Conv Non-Conv

Adv Sales 4 7 2 3

iit Share 2 7 3 2

Ela cicity - 05 3 02 2

Herf indahl 7 3 1 860

That the dist nct ion between coft9enienee goods and non - convenience

goods mat ters is supported not only by these means but also by the regression

results Equat ions lA and lB are different in almost every respec t Only the

concentrat ionmarket share int eract ion term seems to mat ter for convenience

good s Jus t he opposite holds for non - convenience goods both elasticity1

and market sl e are highly significant but the concentrat ionmarket share L

int erac t ion t=rm is not

Given that one minus market share is used these equ3 tions the coeffici t

of market share is the negative of what is sh in col (6) of Table 5 For the

regress ion for non - convenience LB s reported in equation lB then LB s with larger

market shares have lower advertising to sales ratios

On the question of the impact of the degree of cooperation the story is mixed

For convenienc good s the coefficient is pos itive as equation (31) predicts when

there is a po sitive degree of cooperat ion Fo r the non-convenience goods LB s middot

concentration has no effec t

Aggregat ion t o the indus try level and then rer unning the equations $ives the

results shown in (2a-2d) of Tab le 5 As expected R2 goes up and levels of significanc e

fmiddotJr individual coefficients gJ down In add ition the coeffic ient of H ( l -H) inmiddot

quat ion 2A is no t significant though it is po s i tive Since 2A is the indus try level

I

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

coeffiei-en_rs

--

15

o f to zero

Tab le 3 - Consumer Goods

Indus tr ies

2Distributions of R and Producer Goods

Page 20a

Consumer Producer

Goods Goods

0 - 9 9 0 3

10 - 19 9 0 1 1

20 - 29 9 3 20

30 - 39 9 3 17

40 - 49 9 5 16

50 - 59 9 8

69 9 6 Ii 1060

--f 670 79 9 2

80 - 89 9 4 4

90 - 100 1 1

Totals 32 10 3

Notes

2is used R i s cal-

culated as F F + ((N - K- 1 ) K ] 1 b_ F is the F

statistic Lor the hypothesis that all o f the non - intercept terms are simul taneously equal

1

2

--

-- Since generalized least squ-area regress ion

Page 12

o f these cases have values o f 6 1 Y rea ter than 0 8 (pet food (20 10) bread amp cakes

(20 14 ) miscellaneous processed foods (20 29 ) men s and boys suit s and coats

(23 01 ) p rop riet ary drugs (28 08 ) elect ric housewares (36 1 2) radio and

IV sets 17 and games and toys (39 For be than(36 ) 04)) 6 1 Y to greater 0 8

both o and cry mus t b e less than 0 2 That is in these industries the results

shown in Tab le 2 would hold only with very strong dominance of marke t demand

effects over brand swit ching e ffects and a very low degree o f cooperation

Using the concentration rat ios given in Table 4 the average concentration

ratio for the eight indust ries is 38 1 For the remaining 24 industries it is

43 2 This result would lend some support t o the proposition that concentrat ion

and cooperation are related if the group of eight industries are identi fied

as having low degrees of cooperation

One f inal note on model predict ions S ince both cr and o are assumed to

be non-negative 60 should also be non-negat ive In only one o f the 32 cas es

is 60 negative and it is not signif icant bull

cor pJ

7 1

7 0 4

1 4 7 5 1

)

7 3 z a o a t s 1 1 3 3 5 ( i V Z 8 tJ1 2 1 - 1 1 0 7 3 5 c middot v 2 8 1 0 3 2 -0 0 1 4 3 0 C 1 V 9 8 3 2 8 1 5 1 6 - 0 0 6 t1 6 9 C _ V 1 11 0 2 9 0 1 29 0 00 7 6 1 C l k V 7 3 1 3 6 08 1 3 - o n 4 9 9 4 3 3 3 6 1 2 2 4 0 1 6 4 3

3 1 7 1 3 0 1 1 7 d 7 8 3 3 8 0 8 0 0 2 3 i 2 3 0 6

P 4

3 9 0 3 1 4

1 2

0 09 3 8 4 39 1)1 0 4 l 8 6 5

T A LE 4 e I NCU S T R Y C A T E G O R Y

F TC NOM e tOOE ass

C 1 I c 2 )

2 0 0 1 1 6 2 0 0r 1 7 zo o l Z 2 0 0 7 1 8

z o o 2 6

z o t a 1 6

2 1) 1 2 1 5 2 0 1 4 1 1 2 0 1 a 1 9 2 0 26 1 2 2 0 2 7 1 0 2 0 29 - 3 5

2 3 0 1 10

2 3 02 z o

2 3 03 1 9

2 5 5 1 2 4 Z 1 0 Z 1 1 2 0 3 1 9 2 7 4 1 0 z a o 1 3

2 A 0 7 z s

E LA S T I -C I T Y

c 3 )

- 0 09 7 2 7

0 00 449

- 0 0 2 8 9 3

- 0 3 2 7 70 - 0 OZ il I q

o 4 u t s a 0 0 1 3 7 3

o 1 4 o o-0 0 5 2 4o -0 1 94 0 1

-C l 6 l l 4 0 1 JJ 3 7 0 3 t 0 4 2 0 0 4 0 9

- 0 4 1 8 44 - O l 7 t ) 4 -ll 7 1 4 0 b -0 3 5 7 8 Z

- 0 1 9 7 7 0 1)0 3 3 4

-o n 9 2

IJ A T A

CONV

ON-C ONV

( 4 )

t 1NV

C 1t-V C NV c ) v C - JNV C rlNV c n v c a v C ON V ( i) l V

C CtV

C t1tV C IJNV

C 1 V

c 1 v

Pa ge 2La

HEQ F t Noe x

c 5 )

6 2q

6 89 1 48

6 1 4 ) q 3

1 9 7 1 9

q z t s 5 a e z

l l 9 1

4 o 7 1 2 0

c oqt 1 Z

4 4 )-q 1 z

5 5 9 1 0 64 1 3 3

n 3

Inter industry analysi

Page 23

Equation ( 3 6 ) may be used to fo rmulate a rough test o f the cooperat ion

vs e f ficiency controversy I f we rest ricted ourselves to some subset o f

indus tries where the relat ion be tween y and a i s the same we would be lookingbull

at a sample o f indus tries for which the dependence o f V on H and o is a

quadratic wi th no squared terms

I f we now sub s titute (26) into ( 36 ) we get

(38) v bull a + (y - a) R + (y - a) o (H) - (y - a) H o (H) + u

If it is only d if ferences in marke t shares that affect advertising inten-

s i ty levels i f concentration does not af fect cooperation and i f o bull 0

( 38 ) reduces t o

( 39 ) V bull a + (y - a) H + U

Let this b e the null hyp o thes is and note that V is a linear func-

tion o f H If y gt a and the null hyp othesis holds the expected relat ion

between V and H is as shown by the pos itively sloped straight line in Figure

6 b etween points A and C

In this context the alterna ive hypothesis the degree o f

cooperation ( o) is a positive function o f concentrat ion

is that

(H) I f the func-

tion is as described in (26) and Figure 4 the relation between V and H

would be as shown by the curved line connec t ing po ints A and C in Figure 6 One way to test the null hypothe s is against this al ternative is to test fo r

the hypothesized curvature in the function relating V and H

Fi gure

R

6

v

ID c

H 1 0

I

i I I

sfigned

clasJ s

in def ini g

effec t is the

I

Page middot2lf

One charac teristic of produc ts which may be useful

classes wi th respec t to significanc e of the brand-switching

conveniencenon-convenienc e distinc tion developed by Porter ( 1 97 )

Using his identif ication of IRS indus tries as a s tar t ing point

each of the 32 industries used in this s tudy to one of the two

The ass ignments are not ed in Tab le 4

Using the conveniencenon-convenienc e dis t inc tion the

divided into two sub-samples

sample was

Four regressions were then run bull ene for e ch

sub-sample one for the to tal sample and one for the total sample with

a dummy variable for convenience goods Each regression was run wi th LB s

and wi th indus tries as ob servations The results are given in Tab le 5

For the LB level equations ( 1A - 1D) equation(37) was used ome

rearranging of terms gives v bull y - ( 1-o ) (y - a) ( 1-z ) + ui i i

bull y - 6 1 ( 1 - z ) + ui When observations are pooled across indus trif s yi

is an industry variable In these regressions the values o f y es t imated

in the first stage were used Since industries have been grouped so as

to reduce differences in (y - a) that term is t reated as a cons tant

within each group Finally H the Herfindahl index has been subst ituted

for o the degree of cooperation The resultant equation is linear

y ( 1 - z ) and H x ( l - z ) This is the equation for whi ch results arei i

reported in Table 5 In all regress ions all variables were weighted by the

square roo t of sales

in

raquo

- 34

3 1

i l T 4 8LE S R E G E S S I ON R E SUL T S i X T f N S I ON S T O T Y PE Of

AND L E V E L OF C ONC E kT R A T I O

E O O tt S

tP bull T Y P E NR C ONV O B S tO N-CONV

E L A S T I shy

T I C J T Y

O E - t-41( T SliA R E

H( fl F

1 1 - K O x middot K O X E R F

- H S a 1 1 - H S t 1 8 1 1 9 1

R S O

1 1 0 1

q z

t - bull 9 f 2 1

Z t P D l 6 fC ONV - 1 9 1 s s c 2 1

e - l O I e bull u q a

2 3 1 0 1 1 Nl N- t O V 5 7 1 ( 1 2 19 1 6 1 - J l S 2 5 4

l l l l t z q o a 1 - J o v z I

l ( I NO l l A l l ol u l t o o c bull J u l l

d S

c 3 4 t t r a l

bull Z D 1 0 l l 4 l l 2 3 -gt 2 l l 2 0 - 4 lS 5 4 l C 4 1 o e 6 t l b b 5 1 1 0 1 1 1 c - 1 9 5 1 t d S 2 1 tV

OQ10 T-R A T I O S A E G I VE N l P A RE N T H E S E S l E V E L S f S I G 1 F l C ANC E A - 99 5 B - q 9 t - s NS J UC E NO I Nl E R C ( P T I S U (j f middot) I N f Hf t OUA TIOI S 6 E f 3R E A O J U S T H E N T F OR 1-t E T E R O SIC E O A S T f C I T V pIraquo

1

middot

I

R SO I S C A L C UL A T E D A S f I f bull 1 1 bull 1lt 1 K t t- E E N I S THf U A1 B E R O f fJe S E fi V A T I O S F t S HtE F - S T A T I S

I N DE P E ND E N T y II

T I C F O T H E U Y P O HIE S I S f A l l C JE F F I C H N T A R E QU A L HI l f RO A f40 K I S T H f UUM 8 E R OF Q ( A fL f S

I l l

1 A

1 6

t C

f 1 r R I l l

1 2 1

L Jt

L B

l q

L 1

on s T Y P E bull 2 )

P OUC T

X

H S I l l

l O l A I bull l 0 7 1

O O b O J

1 2 00 1

1 b 2 1 C I l l Z U

l l S b 1 -1 1 0 1

rlt F X l l - fi C f l

bull 1 I

l l

- ()4 2 3 l f H

1 - 2 7 9 1

K O X

1 1 - ti E R F I

l d l

S4 l i A I 2 l b

1 3 00

K O X -t f R F t S J

I 1 - HER F t

)

60 9

z o bull

0

t l l

3 8 8

1 7 6

5 64

64

N f bull

tl S bull

I l l

I 4 1

t ONV

NON-t ONV

A l l

A ll

c o v NO- ( ONV

1 4 1

1 5 1

- l S b

c - 1 1 2 1

5 8 2 C A I 1 6 7 0 1

middot I l 9 H

l 1 il

1 4 1 6 1

E L A C) T J shy

l t C I T Y

I S I

l b l

- 0 2 0

1 - 1 4 9 1

O Z 3 2 1 A I C b 6 b l

0 0 9 2 -J

1 1 b 4 1

o z t t t l 1 2 2 1 1

oru - Ht tt F

1 gt X bull b I

Page 25 bull

Mean val -as ior relevan t variables for the two sub-samples are

Conv Non-Conv

Adv Sales 4 7 2 3

iit Share 2 7 3 2

Ela cicity - 05 3 02 2

Herf indahl 7 3 1 860

That the dist nct ion between coft9enienee goods and non - convenience

goods mat ters is supported not only by these means but also by the regression

results Equat ions lA and lB are different in almost every respec t Only the

concentrat ionmarket share int eract ion term seems to mat ter for convenience

good s Jus t he opposite holds for non - convenience goods both elasticity1

and market sl e are highly significant but the concentrat ionmarket share L

int erac t ion t=rm is not

Given that one minus market share is used these equ3 tions the coeffici t

of market share is the negative of what is sh in col (6) of Table 5 For the

regress ion for non - convenience LB s reported in equation lB then LB s with larger

market shares have lower advertising to sales ratios

On the question of the impact of the degree of cooperation the story is mixed

For convenienc good s the coefficient is pos itive as equation (31) predicts when

there is a po sitive degree of cooperat ion Fo r the non-convenience goods LB s middot

concentration has no effec t

Aggregat ion t o the indus try level and then rer unning the equations $ives the

results shown in (2a-2d) of Tab le 5 As expected R2 goes up and levels of significanc e

fmiddotJr individual coefficients gJ down In add ition the coeffic ient of H ( l -H) inmiddot

quat ion 2A is no t significant though it is po s i tive Since 2A is the indus try level

I

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

Page 12

o f these cases have values o f 6 1 Y rea ter than 0 8 (pet food (20 10) bread amp cakes

(20 14 ) miscellaneous processed foods (20 29 ) men s and boys suit s and coats

(23 01 ) p rop riet ary drugs (28 08 ) elect ric housewares (36 1 2) radio and

IV sets 17 and games and toys (39 For be than(36 ) 04)) 6 1 Y to greater 0 8

both o and cry mus t b e less than 0 2 That is in these industries the results

shown in Tab le 2 would hold only with very strong dominance of marke t demand

effects over brand swit ching e ffects and a very low degree o f cooperation

Using the concentration rat ios given in Table 4 the average concentration

ratio for the eight indust ries is 38 1 For the remaining 24 industries it is

43 2 This result would lend some support t o the proposition that concentrat ion

and cooperation are related if the group of eight industries are identi fied

as having low degrees of cooperation

One f inal note on model predict ions S ince both cr and o are assumed to

be non-negative 60 should also be non-negat ive In only one o f the 32 cas es

is 60 negative and it is not signif icant bull

cor pJ

7 1

7 0 4

1 4 7 5 1

)

7 3 z a o a t s 1 1 3 3 5 ( i V Z 8 tJ1 2 1 - 1 1 0 7 3 5 c middot v 2 8 1 0 3 2 -0 0 1 4 3 0 C 1 V 9 8 3 2 8 1 5 1 6 - 0 0 6 t1 6 9 C _ V 1 11 0 2 9 0 1 29 0 00 7 6 1 C l k V 7 3 1 3 6 08 1 3 - o n 4 9 9 4 3 3 3 6 1 2 2 4 0 1 6 4 3

3 1 7 1 3 0 1 1 7 d 7 8 3 3 8 0 8 0 0 2 3 i 2 3 0 6

P 4

3 9 0 3 1 4

1 2

0 09 3 8 4 39 1)1 0 4 l 8 6 5

T A LE 4 e I NCU S T R Y C A T E G O R Y

F TC NOM e tOOE ass

C 1 I c 2 )

2 0 0 1 1 6 2 0 0r 1 7 zo o l Z 2 0 0 7 1 8

z o o 2 6

z o t a 1 6

2 1) 1 2 1 5 2 0 1 4 1 1 2 0 1 a 1 9 2 0 26 1 2 2 0 2 7 1 0 2 0 29 - 3 5

2 3 0 1 10

2 3 02 z o

2 3 03 1 9

2 5 5 1 2 4 Z 1 0 Z 1 1 2 0 3 1 9 2 7 4 1 0 z a o 1 3

2 A 0 7 z s

E LA S T I -C I T Y

c 3 )

- 0 09 7 2 7

0 00 449

- 0 0 2 8 9 3

- 0 3 2 7 70 - 0 OZ il I q

o 4 u t s a 0 0 1 3 7 3

o 1 4 o o-0 0 5 2 4o -0 1 94 0 1

-C l 6 l l 4 0 1 JJ 3 7 0 3 t 0 4 2 0 0 4 0 9

- 0 4 1 8 44 - O l 7 t ) 4 -ll 7 1 4 0 b -0 3 5 7 8 Z

- 0 1 9 7 7 0 1)0 3 3 4

-o n 9 2

IJ A T A

CONV

ON-C ONV

( 4 )

t 1NV

C 1t-V C NV c ) v C - JNV C rlNV c n v c a v C ON V ( i) l V

C CtV

C t1tV C IJNV

C 1 V

c 1 v

Pa ge 2La

HEQ F t Noe x

c 5 )

6 2q

6 89 1 48

6 1 4 ) q 3

1 9 7 1 9

q z t s 5 a e z

l l 9 1

4 o 7 1 2 0

c oqt 1 Z

4 4 )-q 1 z

5 5 9 1 0 64 1 3 3

n 3

Inter industry analysi

Page 23

Equation ( 3 6 ) may be used to fo rmulate a rough test o f the cooperat ion

vs e f ficiency controversy I f we rest ricted ourselves to some subset o f

indus tries where the relat ion be tween y and a i s the same we would be lookingbull

at a sample o f indus tries for which the dependence o f V on H and o is a

quadratic wi th no squared terms

I f we now sub s titute (26) into ( 36 ) we get

(38) v bull a + (y - a) R + (y - a) o (H) - (y - a) H o (H) + u

If it is only d if ferences in marke t shares that affect advertising inten-

s i ty levels i f concentration does not af fect cooperation and i f o bull 0

( 38 ) reduces t o

( 39 ) V bull a + (y - a) H + U

Let this b e the null hyp o thes is and note that V is a linear func-

tion o f H If y gt a and the null hyp othesis holds the expected relat ion

between V and H is as shown by the pos itively sloped straight line in Figure

6 b etween points A and C

In this context the alterna ive hypothesis the degree o f

cooperation ( o) is a positive function o f concentrat ion

is that

(H) I f the func-

tion is as described in (26) and Figure 4 the relation between V and H

would be as shown by the curved line connec t ing po ints A and C in Figure 6 One way to test the null hypothe s is against this al ternative is to test fo r

the hypothesized curvature in the function relating V and H

Fi gure

R

6

v

ID c

H 1 0

I

i I I

sfigned

clasJ s

in def ini g

effec t is the

I

Page middot2lf

One charac teristic of produc ts which may be useful

classes wi th respec t to significanc e of the brand-switching

conveniencenon-convenienc e distinc tion developed by Porter ( 1 97 )

Using his identif ication of IRS indus tries as a s tar t ing point

each of the 32 industries used in this s tudy to one of the two

The ass ignments are not ed in Tab le 4

Using the conveniencenon-convenienc e dis t inc tion the

divided into two sub-samples

sample was

Four regressions were then run bull ene for e ch

sub-sample one for the to tal sample and one for the total sample with

a dummy variable for convenience goods Each regression was run wi th LB s

and wi th indus tries as ob servations The results are given in Tab le 5

For the LB level equations ( 1A - 1D) equation(37) was used ome

rearranging of terms gives v bull y - ( 1-o ) (y - a) ( 1-z ) + ui i i

bull y - 6 1 ( 1 - z ) + ui When observations are pooled across indus trif s yi

is an industry variable In these regressions the values o f y es t imated

in the first stage were used Since industries have been grouped so as

to reduce differences in (y - a) that term is t reated as a cons tant

within each group Finally H the Herfindahl index has been subst ituted

for o the degree of cooperation The resultant equation is linear

y ( 1 - z ) and H x ( l - z ) This is the equation for whi ch results arei i

reported in Table 5 In all regress ions all variables were weighted by the

square roo t of sales

in

raquo

- 34

3 1

i l T 4 8LE S R E G E S S I ON R E SUL T S i X T f N S I ON S T O T Y PE Of

AND L E V E L OF C ONC E kT R A T I O

E O O tt S

tP bull T Y P E NR C ONV O B S tO N-CONV

E L A S T I shy

T I C J T Y

O E - t-41( T SliA R E

H( fl F

1 1 - K O x middot K O X E R F

- H S a 1 1 - H S t 1 8 1 1 9 1

R S O

1 1 0 1

q z

t - bull 9 f 2 1

Z t P D l 6 fC ONV - 1 9 1 s s c 2 1

e - l O I e bull u q a

2 3 1 0 1 1 Nl N- t O V 5 7 1 ( 1 2 19 1 6 1 - J l S 2 5 4

l l l l t z q o a 1 - J o v z I

l ( I NO l l A l l ol u l t o o c bull J u l l

d S

c 3 4 t t r a l

bull Z D 1 0 l l 4 l l 2 3 -gt 2 l l 2 0 - 4 lS 5 4 l C 4 1 o e 6 t l b b 5 1 1 0 1 1 1 c - 1 9 5 1 t d S 2 1 tV

OQ10 T-R A T I O S A E G I VE N l P A RE N T H E S E S l E V E L S f S I G 1 F l C ANC E A - 99 5 B - q 9 t - s NS J UC E NO I Nl E R C ( P T I S U (j f middot) I N f Hf t OUA TIOI S 6 E f 3R E A O J U S T H E N T F OR 1-t E T E R O SIC E O A S T f C I T V pIraquo

1

middot

I

R SO I S C A L C UL A T E D A S f I f bull 1 1 bull 1lt 1 K t t- E E N I S THf U A1 B E R O f fJe S E fi V A T I O S F t S HtE F - S T A T I S

I N DE P E ND E N T y II

T I C F O T H E U Y P O HIE S I S f A l l C JE F F I C H N T A R E QU A L HI l f RO A f40 K I S T H f UUM 8 E R OF Q ( A fL f S

I l l

1 A

1 6

t C

f 1 r R I l l

1 2 1

L Jt

L B

l q

L 1

on s T Y P E bull 2 )

P OUC T

X

H S I l l

l O l A I bull l 0 7 1

O O b O J

1 2 00 1

1 b 2 1 C I l l Z U

l l S b 1 -1 1 0 1

rlt F X l l - fi C f l

bull 1 I

l l

- ()4 2 3 l f H

1 - 2 7 9 1

K O X

1 1 - ti E R F I

l d l

S4 l i A I 2 l b

1 3 00

K O X -t f R F t S J

I 1 - HER F t

)

60 9

z o bull

0

t l l

3 8 8

1 7 6

5 64

64

N f bull

tl S bull

I l l

I 4 1

t ONV

NON-t ONV

A l l

A ll

c o v NO- ( ONV

1 4 1

1 5 1

- l S b

c - 1 1 2 1

5 8 2 C A I 1 6 7 0 1

middot I l 9 H

l 1 il

1 4 1 6 1

E L A C) T J shy

l t C I T Y

I S I

l b l

- 0 2 0

1 - 1 4 9 1

O Z 3 2 1 A I C b 6 b l

0 0 9 2 -J

1 1 b 4 1

o z t t t l 1 2 2 1 1

oru - Ht tt F

1 gt X bull b I

Page 25 bull

Mean val -as ior relevan t variables for the two sub-samples are

Conv Non-Conv

Adv Sales 4 7 2 3

iit Share 2 7 3 2

Ela cicity - 05 3 02 2

Herf indahl 7 3 1 860

That the dist nct ion between coft9enienee goods and non - convenience

goods mat ters is supported not only by these means but also by the regression

results Equat ions lA and lB are different in almost every respec t Only the

concentrat ionmarket share int eract ion term seems to mat ter for convenience

good s Jus t he opposite holds for non - convenience goods both elasticity1

and market sl e are highly significant but the concentrat ionmarket share L

int erac t ion t=rm is not

Given that one minus market share is used these equ3 tions the coeffici t

of market share is the negative of what is sh in col (6) of Table 5 For the

regress ion for non - convenience LB s reported in equation lB then LB s with larger

market shares have lower advertising to sales ratios

On the question of the impact of the degree of cooperation the story is mixed

For convenienc good s the coefficient is pos itive as equation (31) predicts when

there is a po sitive degree of cooperat ion Fo r the non-convenience goods LB s middot

concentration has no effec t

Aggregat ion t o the indus try level and then rer unning the equations $ives the

results shown in (2a-2d) of Tab le 5 As expected R2 goes up and levels of significanc e

fmiddotJr individual coefficients gJ down In add ition the coeffic ient of H ( l -H) inmiddot

quat ion 2A is no t significant though it is po s i tive Since 2A is the indus try level

I

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

cor pJ

7 1

7 0 4

1 4 7 5 1

)

7 3 z a o a t s 1 1 3 3 5 ( i V Z 8 tJ1 2 1 - 1 1 0 7 3 5 c middot v 2 8 1 0 3 2 -0 0 1 4 3 0 C 1 V 9 8 3 2 8 1 5 1 6 - 0 0 6 t1 6 9 C _ V 1 11 0 2 9 0 1 29 0 00 7 6 1 C l k V 7 3 1 3 6 08 1 3 - o n 4 9 9 4 3 3 3 6 1 2 2 4 0 1 6 4 3

3 1 7 1 3 0 1 1 7 d 7 8 3 3 8 0 8 0 0 2 3 i 2 3 0 6

P 4

3 9 0 3 1 4

1 2

0 09 3 8 4 39 1)1 0 4 l 8 6 5

T A LE 4 e I NCU S T R Y C A T E G O R Y

F TC NOM e tOOE ass

C 1 I c 2 )

2 0 0 1 1 6 2 0 0r 1 7 zo o l Z 2 0 0 7 1 8

z o o 2 6

z o t a 1 6

2 1) 1 2 1 5 2 0 1 4 1 1 2 0 1 a 1 9 2 0 26 1 2 2 0 2 7 1 0 2 0 29 - 3 5

2 3 0 1 10

2 3 02 z o

2 3 03 1 9

2 5 5 1 2 4 Z 1 0 Z 1 1 2 0 3 1 9 2 7 4 1 0 z a o 1 3

2 A 0 7 z s

E LA S T I -C I T Y

c 3 )

- 0 09 7 2 7

0 00 449

- 0 0 2 8 9 3

- 0 3 2 7 70 - 0 OZ il I q

o 4 u t s a 0 0 1 3 7 3

o 1 4 o o-0 0 5 2 4o -0 1 94 0 1

-C l 6 l l 4 0 1 JJ 3 7 0 3 t 0 4 2 0 0 4 0 9

- 0 4 1 8 44 - O l 7 t ) 4 -ll 7 1 4 0 b -0 3 5 7 8 Z

- 0 1 9 7 7 0 1)0 3 3 4

-o n 9 2

IJ A T A

CONV

ON-C ONV

( 4 )

t 1NV

C 1t-V C NV c ) v C - JNV C rlNV c n v c a v C ON V ( i) l V

C CtV

C t1tV C IJNV

C 1 V

c 1 v

Pa ge 2La

HEQ F t Noe x

c 5 )

6 2q

6 89 1 48

6 1 4 ) q 3

1 9 7 1 9

q z t s 5 a e z

l l 9 1

4 o 7 1 2 0

c oqt 1 Z

4 4 )-q 1 z

5 5 9 1 0 64 1 3 3

n 3

Inter industry analysi

Page 23

Equation ( 3 6 ) may be used to fo rmulate a rough test o f the cooperat ion

vs e f ficiency controversy I f we rest ricted ourselves to some subset o f

indus tries where the relat ion be tween y and a i s the same we would be lookingbull

at a sample o f indus tries for which the dependence o f V on H and o is a

quadratic wi th no squared terms

I f we now sub s titute (26) into ( 36 ) we get

(38) v bull a + (y - a) R + (y - a) o (H) - (y - a) H o (H) + u

If it is only d if ferences in marke t shares that affect advertising inten-

s i ty levels i f concentration does not af fect cooperation and i f o bull 0

( 38 ) reduces t o

( 39 ) V bull a + (y - a) H + U

Let this b e the null hyp o thes is and note that V is a linear func-

tion o f H If y gt a and the null hyp othesis holds the expected relat ion

between V and H is as shown by the pos itively sloped straight line in Figure

6 b etween points A and C

In this context the alterna ive hypothesis the degree o f

cooperation ( o) is a positive function o f concentrat ion

is that

(H) I f the func-

tion is as described in (26) and Figure 4 the relation between V and H

would be as shown by the curved line connec t ing po ints A and C in Figure 6 One way to test the null hypothe s is against this al ternative is to test fo r

the hypothesized curvature in the function relating V and H

Fi gure

R

6

v

ID c

H 1 0

I

i I I

sfigned

clasJ s

in def ini g

effec t is the

I

Page middot2lf

One charac teristic of produc ts which may be useful

classes wi th respec t to significanc e of the brand-switching

conveniencenon-convenienc e distinc tion developed by Porter ( 1 97 )

Using his identif ication of IRS indus tries as a s tar t ing point

each of the 32 industries used in this s tudy to one of the two

The ass ignments are not ed in Tab le 4

Using the conveniencenon-convenienc e dis t inc tion the

divided into two sub-samples

sample was

Four regressions were then run bull ene for e ch

sub-sample one for the to tal sample and one for the total sample with

a dummy variable for convenience goods Each regression was run wi th LB s

and wi th indus tries as ob servations The results are given in Tab le 5

For the LB level equations ( 1A - 1D) equation(37) was used ome

rearranging of terms gives v bull y - ( 1-o ) (y - a) ( 1-z ) + ui i i

bull y - 6 1 ( 1 - z ) + ui When observations are pooled across indus trif s yi

is an industry variable In these regressions the values o f y es t imated

in the first stage were used Since industries have been grouped so as

to reduce differences in (y - a) that term is t reated as a cons tant

within each group Finally H the Herfindahl index has been subst ituted

for o the degree of cooperation The resultant equation is linear

y ( 1 - z ) and H x ( l - z ) This is the equation for whi ch results arei i

reported in Table 5 In all regress ions all variables were weighted by the

square roo t of sales

in

raquo

- 34

3 1

i l T 4 8LE S R E G E S S I ON R E SUL T S i X T f N S I ON S T O T Y PE Of

AND L E V E L OF C ONC E kT R A T I O

E O O tt S

tP bull T Y P E NR C ONV O B S tO N-CONV

E L A S T I shy

T I C J T Y

O E - t-41( T SliA R E

H( fl F

1 1 - K O x middot K O X E R F

- H S a 1 1 - H S t 1 8 1 1 9 1

R S O

1 1 0 1

q z

t - bull 9 f 2 1

Z t P D l 6 fC ONV - 1 9 1 s s c 2 1

e - l O I e bull u q a

2 3 1 0 1 1 Nl N- t O V 5 7 1 ( 1 2 19 1 6 1 - J l S 2 5 4

l l l l t z q o a 1 - J o v z I

l ( I NO l l A l l ol u l t o o c bull J u l l

d S

c 3 4 t t r a l

bull Z D 1 0 l l 4 l l 2 3 -gt 2 l l 2 0 - 4 lS 5 4 l C 4 1 o e 6 t l b b 5 1 1 0 1 1 1 c - 1 9 5 1 t d S 2 1 tV

OQ10 T-R A T I O S A E G I VE N l P A RE N T H E S E S l E V E L S f S I G 1 F l C ANC E A - 99 5 B - q 9 t - s NS J UC E NO I Nl E R C ( P T I S U (j f middot) I N f Hf t OUA TIOI S 6 E f 3R E A O J U S T H E N T F OR 1-t E T E R O SIC E O A S T f C I T V pIraquo

1

middot

I

R SO I S C A L C UL A T E D A S f I f bull 1 1 bull 1lt 1 K t t- E E N I S THf U A1 B E R O f fJe S E fi V A T I O S F t S HtE F - S T A T I S

I N DE P E ND E N T y II

T I C F O T H E U Y P O HIE S I S f A l l C JE F F I C H N T A R E QU A L HI l f RO A f40 K I S T H f UUM 8 E R OF Q ( A fL f S

I l l

1 A

1 6

t C

f 1 r R I l l

1 2 1

L Jt

L B

l q

L 1

on s T Y P E bull 2 )

P OUC T

X

H S I l l

l O l A I bull l 0 7 1

O O b O J

1 2 00 1

1 b 2 1 C I l l Z U

l l S b 1 -1 1 0 1

rlt F X l l - fi C f l

bull 1 I

l l

- ()4 2 3 l f H

1 - 2 7 9 1

K O X

1 1 - ti E R F I

l d l

S4 l i A I 2 l b

1 3 00

K O X -t f R F t S J

I 1 - HER F t

)

60 9

z o bull

0

t l l

3 8 8

1 7 6

5 64

64

N f bull

tl S bull

I l l

I 4 1

t ONV

NON-t ONV

A l l

A ll

c o v NO- ( ONV

1 4 1

1 5 1

- l S b

c - 1 1 2 1

5 8 2 C A I 1 6 7 0 1

middot I l 9 H

l 1 il

1 4 1 6 1

E L A C) T J shy

l t C I T Y

I S I

l b l

- 0 2 0

1 - 1 4 9 1

O Z 3 2 1 A I C b 6 b l

0 0 9 2 -J

1 1 b 4 1

o z t t t l 1 2 2 1 1

oru - Ht tt F

1 gt X bull b I

Page 25 bull

Mean val -as ior relevan t variables for the two sub-samples are

Conv Non-Conv

Adv Sales 4 7 2 3

iit Share 2 7 3 2

Ela cicity - 05 3 02 2

Herf indahl 7 3 1 860

That the dist nct ion between coft9enienee goods and non - convenience

goods mat ters is supported not only by these means but also by the regression

results Equat ions lA and lB are different in almost every respec t Only the

concentrat ionmarket share int eract ion term seems to mat ter for convenience

good s Jus t he opposite holds for non - convenience goods both elasticity1

and market sl e are highly significant but the concentrat ionmarket share L

int erac t ion t=rm is not

Given that one minus market share is used these equ3 tions the coeffici t

of market share is the negative of what is sh in col (6) of Table 5 For the

regress ion for non - convenience LB s reported in equation lB then LB s with larger

market shares have lower advertising to sales ratios

On the question of the impact of the degree of cooperation the story is mixed

For convenienc good s the coefficient is pos itive as equation (31) predicts when

there is a po sitive degree of cooperat ion Fo r the non-convenience goods LB s middot

concentration has no effec t

Aggregat ion t o the indus try level and then rer unning the equations $ives the

results shown in (2a-2d) of Tab le 5 As expected R2 goes up and levels of significanc e

fmiddotJr individual coefficients gJ down In add ition the coeffic ient of H ( l -H) inmiddot

quat ion 2A is no t significant though it is po s i tive Since 2A is the indus try level

I

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

Inter industry analysi

Page 23

Equation ( 3 6 ) may be used to fo rmulate a rough test o f the cooperat ion

vs e f ficiency controversy I f we rest ricted ourselves to some subset o f

indus tries where the relat ion be tween y and a i s the same we would be lookingbull

at a sample o f indus tries for which the dependence o f V on H and o is a

quadratic wi th no squared terms

I f we now sub s titute (26) into ( 36 ) we get

(38) v bull a + (y - a) R + (y - a) o (H) - (y - a) H o (H) + u

If it is only d if ferences in marke t shares that affect advertising inten-

s i ty levels i f concentration does not af fect cooperation and i f o bull 0

( 38 ) reduces t o

( 39 ) V bull a + (y - a) H + U

Let this b e the null hyp o thes is and note that V is a linear func-

tion o f H If y gt a and the null hyp othesis holds the expected relat ion

between V and H is as shown by the pos itively sloped straight line in Figure

6 b etween points A and C

In this context the alterna ive hypothesis the degree o f

cooperation ( o) is a positive function o f concentrat ion

is that

(H) I f the func-

tion is as described in (26) and Figure 4 the relation between V and H

would be as shown by the curved line connec t ing po ints A and C in Figure 6 One way to test the null hypothe s is against this al ternative is to test fo r

the hypothesized curvature in the function relating V and H

Fi gure

R

6

v

ID c

H 1 0

I

i I I

sfigned

clasJ s

in def ini g

effec t is the

I

Page middot2lf

One charac teristic of produc ts which may be useful

classes wi th respec t to significanc e of the brand-switching

conveniencenon-convenienc e distinc tion developed by Porter ( 1 97 )

Using his identif ication of IRS indus tries as a s tar t ing point

each of the 32 industries used in this s tudy to one of the two

The ass ignments are not ed in Tab le 4

Using the conveniencenon-convenienc e dis t inc tion the

divided into two sub-samples

sample was

Four regressions were then run bull ene for e ch

sub-sample one for the to tal sample and one for the total sample with

a dummy variable for convenience goods Each regression was run wi th LB s

and wi th indus tries as ob servations The results are given in Tab le 5

For the LB level equations ( 1A - 1D) equation(37) was used ome

rearranging of terms gives v bull y - ( 1-o ) (y - a) ( 1-z ) + ui i i

bull y - 6 1 ( 1 - z ) + ui When observations are pooled across indus trif s yi

is an industry variable In these regressions the values o f y es t imated

in the first stage were used Since industries have been grouped so as

to reduce differences in (y - a) that term is t reated as a cons tant

within each group Finally H the Herfindahl index has been subst ituted

for o the degree of cooperation The resultant equation is linear

y ( 1 - z ) and H x ( l - z ) This is the equation for whi ch results arei i

reported in Table 5 In all regress ions all variables were weighted by the

square roo t of sales

in

raquo

- 34

3 1

i l T 4 8LE S R E G E S S I ON R E SUL T S i X T f N S I ON S T O T Y PE Of

AND L E V E L OF C ONC E kT R A T I O

E O O tt S

tP bull T Y P E NR C ONV O B S tO N-CONV

E L A S T I shy

T I C J T Y

O E - t-41( T SliA R E

H( fl F

1 1 - K O x middot K O X E R F

- H S a 1 1 - H S t 1 8 1 1 9 1

R S O

1 1 0 1

q z

t - bull 9 f 2 1

Z t P D l 6 fC ONV - 1 9 1 s s c 2 1

e - l O I e bull u q a

2 3 1 0 1 1 Nl N- t O V 5 7 1 ( 1 2 19 1 6 1 - J l S 2 5 4

l l l l t z q o a 1 - J o v z I

l ( I NO l l A l l ol u l t o o c bull J u l l

d S

c 3 4 t t r a l

bull Z D 1 0 l l 4 l l 2 3 -gt 2 l l 2 0 - 4 lS 5 4 l C 4 1 o e 6 t l b b 5 1 1 0 1 1 1 c - 1 9 5 1 t d S 2 1 tV

OQ10 T-R A T I O S A E G I VE N l P A RE N T H E S E S l E V E L S f S I G 1 F l C ANC E A - 99 5 B - q 9 t - s NS J UC E NO I Nl E R C ( P T I S U (j f middot) I N f Hf t OUA TIOI S 6 E f 3R E A O J U S T H E N T F OR 1-t E T E R O SIC E O A S T f C I T V pIraquo

1

middot

I

R SO I S C A L C UL A T E D A S f I f bull 1 1 bull 1lt 1 K t t- E E N I S THf U A1 B E R O f fJe S E fi V A T I O S F t S HtE F - S T A T I S

I N DE P E ND E N T y II

T I C F O T H E U Y P O HIE S I S f A l l C JE F F I C H N T A R E QU A L HI l f RO A f40 K I S T H f UUM 8 E R OF Q ( A fL f S

I l l

1 A

1 6

t C

f 1 r R I l l

1 2 1

L Jt

L B

l q

L 1

on s T Y P E bull 2 )

P OUC T

X

H S I l l

l O l A I bull l 0 7 1

O O b O J

1 2 00 1

1 b 2 1 C I l l Z U

l l S b 1 -1 1 0 1

rlt F X l l - fi C f l

bull 1 I

l l

- ()4 2 3 l f H

1 - 2 7 9 1

K O X

1 1 - ti E R F I

l d l

S4 l i A I 2 l b

1 3 00

K O X -t f R F t S J

I 1 - HER F t

)

60 9

z o bull

0

t l l

3 8 8

1 7 6

5 64

64

N f bull

tl S bull

I l l

I 4 1

t ONV

NON-t ONV

A l l

A ll

c o v NO- ( ONV

1 4 1

1 5 1

- l S b

c - 1 1 2 1

5 8 2 C A I 1 6 7 0 1

middot I l 9 H

l 1 il

1 4 1 6 1

E L A C) T J shy

l t C I T Y

I S I

l b l

- 0 2 0

1 - 1 4 9 1

O Z 3 2 1 A I C b 6 b l

0 0 9 2 -J

1 1 b 4 1

o z t t t l 1 2 2 1 1

oru - Ht tt F

1 gt X bull b I

Page 25 bull

Mean val -as ior relevan t variables for the two sub-samples are

Conv Non-Conv

Adv Sales 4 7 2 3

iit Share 2 7 3 2

Ela cicity - 05 3 02 2

Herf indahl 7 3 1 860

That the dist nct ion between coft9enienee goods and non - convenience

goods mat ters is supported not only by these means but also by the regression

results Equat ions lA and lB are different in almost every respec t Only the

concentrat ionmarket share int eract ion term seems to mat ter for convenience

good s Jus t he opposite holds for non - convenience goods both elasticity1

and market sl e are highly significant but the concentrat ionmarket share L

int erac t ion t=rm is not

Given that one minus market share is used these equ3 tions the coeffici t

of market share is the negative of what is sh in col (6) of Table 5 For the

regress ion for non - convenience LB s reported in equation lB then LB s with larger

market shares have lower advertising to sales ratios

On the question of the impact of the degree of cooperation the story is mixed

For convenienc good s the coefficient is pos itive as equation (31) predicts when

there is a po sitive degree of cooperat ion Fo r the non-convenience goods LB s middot

concentration has no effec t

Aggregat ion t o the indus try level and then rer unning the equations $ives the

results shown in (2a-2d) of Tab le 5 As expected R2 goes up and levels of significanc e

fmiddotJr individual coefficients gJ down In add ition the coeffic ient of H ( l -H) inmiddot

quat ion 2A is no t significant though it is po s i tive Since 2A is the indus try level

I

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

Fi gure

R

6

v

ID c

H 1 0

I

i I I

sfigned

clasJ s

in def ini g

effec t is the

I

Page middot2lf

One charac teristic of produc ts which may be useful

classes wi th respec t to significanc e of the brand-switching

conveniencenon-convenienc e distinc tion developed by Porter ( 1 97 )

Using his identif ication of IRS indus tries as a s tar t ing point

each of the 32 industries used in this s tudy to one of the two

The ass ignments are not ed in Tab le 4

Using the conveniencenon-convenienc e dis t inc tion the

divided into two sub-samples

sample was

Four regressions were then run bull ene for e ch

sub-sample one for the to tal sample and one for the total sample with

a dummy variable for convenience goods Each regression was run wi th LB s

and wi th indus tries as ob servations The results are given in Tab le 5

For the LB level equations ( 1A - 1D) equation(37) was used ome

rearranging of terms gives v bull y - ( 1-o ) (y - a) ( 1-z ) + ui i i

bull y - 6 1 ( 1 - z ) + ui When observations are pooled across indus trif s yi

is an industry variable In these regressions the values o f y es t imated

in the first stage were used Since industries have been grouped so as

to reduce differences in (y - a) that term is t reated as a cons tant

within each group Finally H the Herfindahl index has been subst ituted

for o the degree of cooperation The resultant equation is linear

y ( 1 - z ) and H x ( l - z ) This is the equation for whi ch results arei i

reported in Table 5 In all regress ions all variables were weighted by the

square roo t of sales

in

raquo

- 34

3 1

i l T 4 8LE S R E G E S S I ON R E SUL T S i X T f N S I ON S T O T Y PE Of

AND L E V E L OF C ONC E kT R A T I O

E O O tt S

tP bull T Y P E NR C ONV O B S tO N-CONV

E L A S T I shy

T I C J T Y

O E - t-41( T SliA R E

H( fl F

1 1 - K O x middot K O X E R F

- H S a 1 1 - H S t 1 8 1 1 9 1

R S O

1 1 0 1

q z

t - bull 9 f 2 1

Z t P D l 6 fC ONV - 1 9 1 s s c 2 1

e - l O I e bull u q a

2 3 1 0 1 1 Nl N- t O V 5 7 1 ( 1 2 19 1 6 1 - J l S 2 5 4

l l l l t z q o a 1 - J o v z I

l ( I NO l l A l l ol u l t o o c bull J u l l

d S

c 3 4 t t r a l

bull Z D 1 0 l l 4 l l 2 3 -gt 2 l l 2 0 - 4 lS 5 4 l C 4 1 o e 6 t l b b 5 1 1 0 1 1 1 c - 1 9 5 1 t d S 2 1 tV

OQ10 T-R A T I O S A E G I VE N l P A RE N T H E S E S l E V E L S f S I G 1 F l C ANC E A - 99 5 B - q 9 t - s NS J UC E NO I Nl E R C ( P T I S U (j f middot) I N f Hf t OUA TIOI S 6 E f 3R E A O J U S T H E N T F OR 1-t E T E R O SIC E O A S T f C I T V pIraquo

1

middot

I

R SO I S C A L C UL A T E D A S f I f bull 1 1 bull 1lt 1 K t t- E E N I S THf U A1 B E R O f fJe S E fi V A T I O S F t S HtE F - S T A T I S

I N DE P E ND E N T y II

T I C F O T H E U Y P O HIE S I S f A l l C JE F F I C H N T A R E QU A L HI l f RO A f40 K I S T H f UUM 8 E R OF Q ( A fL f S

I l l

1 A

1 6

t C

f 1 r R I l l

1 2 1

L Jt

L B

l q

L 1

on s T Y P E bull 2 )

P OUC T

X

H S I l l

l O l A I bull l 0 7 1

O O b O J

1 2 00 1

1 b 2 1 C I l l Z U

l l S b 1 -1 1 0 1

rlt F X l l - fi C f l

bull 1 I

l l

- ()4 2 3 l f H

1 - 2 7 9 1

K O X

1 1 - ti E R F I

l d l

S4 l i A I 2 l b

1 3 00

K O X -t f R F t S J

I 1 - HER F t

)

60 9

z o bull

0

t l l

3 8 8

1 7 6

5 64

64

N f bull

tl S bull

I l l

I 4 1

t ONV

NON-t ONV

A l l

A ll

c o v NO- ( ONV

1 4 1

1 5 1

- l S b

c - 1 1 2 1

5 8 2 C A I 1 6 7 0 1

middot I l 9 H

l 1 il

1 4 1 6 1

E L A C) T J shy

l t C I T Y

I S I

l b l

- 0 2 0

1 - 1 4 9 1

O Z 3 2 1 A I C b 6 b l

0 0 9 2 -J

1 1 b 4 1

o z t t t l 1 2 2 1 1

oru - Ht tt F

1 gt X bull b I

Page 25 bull

Mean val -as ior relevan t variables for the two sub-samples are

Conv Non-Conv

Adv Sales 4 7 2 3

iit Share 2 7 3 2

Ela cicity - 05 3 02 2

Herf indahl 7 3 1 860

That the dist nct ion between coft9enienee goods and non - convenience

goods mat ters is supported not only by these means but also by the regression

results Equat ions lA and lB are different in almost every respec t Only the

concentrat ionmarket share int eract ion term seems to mat ter for convenience

good s Jus t he opposite holds for non - convenience goods both elasticity1

and market sl e are highly significant but the concentrat ionmarket share L

int erac t ion t=rm is not

Given that one minus market share is used these equ3 tions the coeffici t

of market share is the negative of what is sh in col (6) of Table 5 For the

regress ion for non - convenience LB s reported in equation lB then LB s with larger

market shares have lower advertising to sales ratios

On the question of the impact of the degree of cooperation the story is mixed

For convenienc good s the coefficient is pos itive as equation (31) predicts when

there is a po sitive degree of cooperat ion Fo r the non-convenience goods LB s middot

concentration has no effec t

Aggregat ion t o the indus try level and then rer unning the equations $ives the

results shown in (2a-2d) of Tab le 5 As expected R2 goes up and levels of significanc e

fmiddotJr individual coefficients gJ down In add ition the coeffic ient of H ( l -H) inmiddot

quat ion 2A is no t significant though it is po s i tive Since 2A is the indus try level

I

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

i I I

sfigned

clasJ s

in def ini g

effec t is the

I

Page middot2lf

One charac teristic of produc ts which may be useful

classes wi th respec t to significanc e of the brand-switching

conveniencenon-convenienc e distinc tion developed by Porter ( 1 97 )

Using his identif ication of IRS indus tries as a s tar t ing point

each of the 32 industries used in this s tudy to one of the two

The ass ignments are not ed in Tab le 4

Using the conveniencenon-convenienc e dis t inc tion the

divided into two sub-samples

sample was

Four regressions were then run bull ene for e ch

sub-sample one for the to tal sample and one for the total sample with

a dummy variable for convenience goods Each regression was run wi th LB s

and wi th indus tries as ob servations The results are given in Tab le 5

For the LB level equations ( 1A - 1D) equation(37) was used ome

rearranging of terms gives v bull y - ( 1-o ) (y - a) ( 1-z ) + ui i i

bull y - 6 1 ( 1 - z ) + ui When observations are pooled across indus trif s yi

is an industry variable In these regressions the values o f y es t imated

in the first stage were used Since industries have been grouped so as

to reduce differences in (y - a) that term is t reated as a cons tant

within each group Finally H the Herfindahl index has been subst ituted

for o the degree of cooperation The resultant equation is linear

y ( 1 - z ) and H x ( l - z ) This is the equation for whi ch results arei i

reported in Table 5 In all regress ions all variables were weighted by the

square roo t of sales

in

raquo

- 34

3 1

i l T 4 8LE S R E G E S S I ON R E SUL T S i X T f N S I ON S T O T Y PE Of

AND L E V E L OF C ONC E kT R A T I O

E O O tt S

tP bull T Y P E NR C ONV O B S tO N-CONV

E L A S T I shy

T I C J T Y

O E - t-41( T SliA R E

H( fl F

1 1 - K O x middot K O X E R F

- H S a 1 1 - H S t 1 8 1 1 9 1

R S O

1 1 0 1

q z

t - bull 9 f 2 1

Z t P D l 6 fC ONV - 1 9 1 s s c 2 1

e - l O I e bull u q a

2 3 1 0 1 1 Nl N- t O V 5 7 1 ( 1 2 19 1 6 1 - J l S 2 5 4

l l l l t z q o a 1 - J o v z I

l ( I NO l l A l l ol u l t o o c bull J u l l

d S

c 3 4 t t r a l

bull Z D 1 0 l l 4 l l 2 3 -gt 2 l l 2 0 - 4 lS 5 4 l C 4 1 o e 6 t l b b 5 1 1 0 1 1 1 c - 1 9 5 1 t d S 2 1 tV

OQ10 T-R A T I O S A E G I VE N l P A RE N T H E S E S l E V E L S f S I G 1 F l C ANC E A - 99 5 B - q 9 t - s NS J UC E NO I Nl E R C ( P T I S U (j f middot) I N f Hf t OUA TIOI S 6 E f 3R E A O J U S T H E N T F OR 1-t E T E R O SIC E O A S T f C I T V pIraquo

1

middot

I

R SO I S C A L C UL A T E D A S f I f bull 1 1 bull 1lt 1 K t t- E E N I S THf U A1 B E R O f fJe S E fi V A T I O S F t S HtE F - S T A T I S

I N DE P E ND E N T y II

T I C F O T H E U Y P O HIE S I S f A l l C JE F F I C H N T A R E QU A L HI l f RO A f40 K I S T H f UUM 8 E R OF Q ( A fL f S

I l l

1 A

1 6

t C

f 1 r R I l l

1 2 1

L Jt

L B

l q

L 1

on s T Y P E bull 2 )

P OUC T

X

H S I l l

l O l A I bull l 0 7 1

O O b O J

1 2 00 1

1 b 2 1 C I l l Z U

l l S b 1 -1 1 0 1

rlt F X l l - fi C f l

bull 1 I

l l

- ()4 2 3 l f H

1 - 2 7 9 1

K O X

1 1 - ti E R F I

l d l

S4 l i A I 2 l b

1 3 00

K O X -t f R F t S J

I 1 - HER F t

)

60 9

z o bull

0

t l l

3 8 8

1 7 6

5 64

64

N f bull

tl S bull

I l l

I 4 1

t ONV

NON-t ONV

A l l

A ll

c o v NO- ( ONV

1 4 1

1 5 1

- l S b

c - 1 1 2 1

5 8 2 C A I 1 6 7 0 1

middot I l 9 H

l 1 il

1 4 1 6 1

E L A C) T J shy

l t C I T Y

I S I

l b l

- 0 2 0

1 - 1 4 9 1

O Z 3 2 1 A I C b 6 b l

0 0 9 2 -J

1 1 b 4 1

o z t t t l 1 2 2 1 1

oru - Ht tt F

1 gt X bull b I

Page 25 bull

Mean val -as ior relevan t variables for the two sub-samples are

Conv Non-Conv

Adv Sales 4 7 2 3

iit Share 2 7 3 2

Ela cicity - 05 3 02 2

Herf indahl 7 3 1 860

That the dist nct ion between coft9enienee goods and non - convenience

goods mat ters is supported not only by these means but also by the regression

results Equat ions lA and lB are different in almost every respec t Only the

concentrat ionmarket share int eract ion term seems to mat ter for convenience

good s Jus t he opposite holds for non - convenience goods both elasticity1

and market sl e are highly significant but the concentrat ionmarket share L

int erac t ion t=rm is not

Given that one minus market share is used these equ3 tions the coeffici t

of market share is the negative of what is sh in col (6) of Table 5 For the

regress ion for non - convenience LB s reported in equation lB then LB s with larger

market shares have lower advertising to sales ratios

On the question of the impact of the degree of cooperation the story is mixed

For convenienc good s the coefficient is pos itive as equation (31) predicts when

there is a po sitive degree of cooperat ion Fo r the non-convenience goods LB s middot

concentration has no effec t

Aggregat ion t o the indus try level and then rer unning the equations $ives the

results shown in (2a-2d) of Tab le 5 As expected R2 goes up and levels of significanc e

fmiddotJr individual coefficients gJ down In add ition the coeffic ient of H ( l -H) inmiddot

quat ion 2A is no t significant though it is po s i tive Since 2A is the indus try level

I

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

raquo

- 34

3 1

i l T 4 8LE S R E G E S S I ON R E SUL T S i X T f N S I ON S T O T Y PE Of

AND L E V E L OF C ONC E kT R A T I O

E O O tt S

tP bull T Y P E NR C ONV O B S tO N-CONV

E L A S T I shy

T I C J T Y

O E - t-41( T SliA R E

H( fl F

1 1 - K O x middot K O X E R F

- H S a 1 1 - H S t 1 8 1 1 9 1

R S O

1 1 0 1

q z

t - bull 9 f 2 1

Z t P D l 6 fC ONV - 1 9 1 s s c 2 1

e - l O I e bull u q a

2 3 1 0 1 1 Nl N- t O V 5 7 1 ( 1 2 19 1 6 1 - J l S 2 5 4

l l l l t z q o a 1 - J o v z I

l ( I NO l l A l l ol u l t o o c bull J u l l

d S

c 3 4 t t r a l

bull Z D 1 0 l l 4 l l 2 3 -gt 2 l l 2 0 - 4 lS 5 4 l C 4 1 o e 6 t l b b 5 1 1 0 1 1 1 c - 1 9 5 1 t d S 2 1 tV

OQ10 T-R A T I O S A E G I VE N l P A RE N T H E S E S l E V E L S f S I G 1 F l C ANC E A - 99 5 B - q 9 t - s NS J UC E NO I Nl E R C ( P T I S U (j f middot) I N f Hf t OUA TIOI S 6 E f 3R E A O J U S T H E N T F OR 1-t E T E R O SIC E O A S T f C I T V pIraquo

1

middot

I

R SO I S C A L C UL A T E D A S f I f bull 1 1 bull 1lt 1 K t t- E E N I S THf U A1 B E R O f fJe S E fi V A T I O S F t S HtE F - S T A T I S

I N DE P E ND E N T y II

T I C F O T H E U Y P O HIE S I S f A l l C JE F F I C H N T A R E QU A L HI l f RO A f40 K I S T H f UUM 8 E R OF Q ( A fL f S

I l l

1 A

1 6

t C

f 1 r R I l l

1 2 1

L Jt

L B

l q

L 1

on s T Y P E bull 2 )

P OUC T

X

H S I l l

l O l A I bull l 0 7 1

O O b O J

1 2 00 1

1 b 2 1 C I l l Z U

l l S b 1 -1 1 0 1

rlt F X l l - fi C f l

bull 1 I

l l

- ()4 2 3 l f H

1 - 2 7 9 1

K O X

1 1 - ti E R F I

l d l

S4 l i A I 2 l b

1 3 00

K O X -t f R F t S J

I 1 - HER F t

)

60 9

z o bull

0

t l l

3 8 8

1 7 6

5 64

64

N f bull

tl S bull

I l l

I 4 1

t ONV

NON-t ONV

A l l

A ll

c o v NO- ( ONV

1 4 1

1 5 1

- l S b

c - 1 1 2 1

5 8 2 C A I 1 6 7 0 1

middot I l 9 H

l 1 il

1 4 1 6 1

E L A C) T J shy

l t C I T Y

I S I

l b l

- 0 2 0

1 - 1 4 9 1

O Z 3 2 1 A I C b 6 b l

0 0 9 2 -J

1 1 b 4 1

o z t t t l 1 2 2 1 1

oru - Ht tt F

1 gt X bull b I

Page 25 bull

Mean val -as ior relevan t variables for the two sub-samples are

Conv Non-Conv

Adv Sales 4 7 2 3

iit Share 2 7 3 2

Ela cicity - 05 3 02 2

Herf indahl 7 3 1 860

That the dist nct ion between coft9enienee goods and non - convenience

goods mat ters is supported not only by these means but also by the regression

results Equat ions lA and lB are different in almost every respec t Only the

concentrat ionmarket share int eract ion term seems to mat ter for convenience

good s Jus t he opposite holds for non - convenience goods both elasticity1

and market sl e are highly significant but the concentrat ionmarket share L

int erac t ion t=rm is not

Given that one minus market share is used these equ3 tions the coeffici t

of market share is the negative of what is sh in col (6) of Table 5 For the

regress ion for non - convenience LB s reported in equation lB then LB s with larger

market shares have lower advertising to sales ratios

On the question of the impact of the degree of cooperation the story is mixed

For convenienc good s the coefficient is pos itive as equation (31) predicts when

there is a po sitive degree of cooperat ion Fo r the non-convenience goods LB s middot

concentration has no effec t

Aggregat ion t o the indus try level and then rer unning the equations $ives the

results shown in (2a-2d) of Tab le 5 As expected R2 goes up and levels of significanc e

fmiddotJr individual coefficients gJ down In add ition the coeffic ient of H ( l -H) inmiddot

quat ion 2A is no t significant though it is po s i tive Since 2A is the indus try level

I

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

Page 25 bull

Mean val -as ior relevan t variables for the two sub-samples are

Conv Non-Conv

Adv Sales 4 7 2 3

iit Share 2 7 3 2

Ela cicity - 05 3 02 2

Herf indahl 7 3 1 860

That the dist nct ion between coft9enienee goods and non - convenience

goods mat ters is supported not only by these means but also by the regression

results Equat ions lA and lB are different in almost every respec t Only the

concentrat ionmarket share int eract ion term seems to mat ter for convenience

good s Jus t he opposite holds for non - convenience goods both elasticity1

and market sl e are highly significant but the concentrat ionmarket share L

int erac t ion t=rm is not

Given that one minus market share is used these equ3 tions the coeffici t

of market share is the negative of what is sh in col (6) of Table 5 For the

regress ion for non - convenience LB s reported in equation lB then LB s with larger

market shares have lower advertising to sales ratios

On the question of the impact of the degree of cooperation the story is mixed

For convenienc good s the coefficient is pos itive as equation (31) predicts when

there is a po sitive degree of cooperat ion Fo r the non-convenience goods LB s middot

concentration has no effec t

Aggregat ion t o the indus try level and then rer unning the equations $ives the

results shown in (2a-2d) of Tab le 5 As expected R2 goes up and levels of significanc e

fmiddotJr individual coefficients gJ down In add ition the coeffic ient of H ( l -H) inmiddot

quat ion 2A is no t significant though it is po s i tive Since 2A is the indus try level

I

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

--

all but one of them and that one is not significant For 18 of the 31

wo uld have on its adve rtising to sal es ratio

cognate of LA the variable H ( l-H) pl ays the same role in 2A as H ( l -z 1) p lays

in LA

Vconomies of scale in advert ising

The literature on advert ing contains a number of definitionbull o f economies

of scale and of findings eone rning its presence and magnitude Before I loo k

a t the data with the hope o f mmenting about scale effect s then I wan t to

define the term as I use it

By economies of scale I mean a decrease in the number o f units of adver-

tising which are needed to generate a unit of sales as advert ising is increased

Given the definition of the firm s own elast icity of demand with respect to

advertising (see the text foll wing equation (1) ) the technical definition

is that rii gt 1 Diseconomies of scale are def ined symmetrically i e

Yu lt 1

ith a cro s s - section oi observations on advertising intensity

(v bull a s1) and onmiddot advertising (a ) we may regress the former on the latter 1 i i

The results of such regress ions for the 32 industries are given in Table 2

lines lB ZB bull bull bull 32B For the 32 eases the regression coefficient is positive it

positive coefficients the coefficient i s signif icant

The que tion now is whether these results ar e evidence of pervasive dis-

economies of scale in advertislng I think no t Given my as sumption that the

data I observe are equilibrium results I may ri ghtly conclud e that almost every-

where high levels of advert ising are as sociated in equilibrium with high ratios

of advertising to sales I may no t conclud e anything however about the

impact that a move by some firm away from its equilibrium level o f advertising

middot- Page 27

Given the assumed relation in equation ( 37 ) there is a corre spondshy

ing equilibrium equation relating v and ai The equation is non - linear i

and I have not found a simp le way to characterize it It is po ssib le to

det ermi ne its deriviative with respect to a b y takin$ tne de riviative of ( 3 7 ) i

When that is done the result is

v - 1(40) i bull sl a a z ( 1-z )i i ira-l

Sinc e all the other terms in (40) are non-negative the sign dep ends only

on the sign of 6 1 which is in turn de pend ent only on the sign of (y - a)

That the signs of the coefficients of a in equations lB 2B bull bull bull 32B arei

not always equal to the signs of the coefficients of z in LA 2A bull bull bull 32A i

is still a mystery to me and something to be explored

bull

Summary

My purpose in writing this pa per wa s t o attempt to integrate explicit micro-

economic mode lling reasoned econome tric specification of error terms and high

quality data to exp lore some questions about adver tising by large firms

al quite important improvements could be made in the first two of those areas

and much data ma ssag ing is yet to be done in the third

Concerning the subst an ce of what I have done I think six things are im-

Page 2 8

Severshy

V and Conclusions

portant

1 Explicit modeling is worth the ef for t if for no other reas on than

that it provides a basis for choosing fr om a varie ty of funct ional

forms

2 The same is true for error specif ica t ion I did in fact look at scatshy

ter diagrams for all 32 industry categor ies and they vir tually all show

the het eroscedast icity which I as sumed and for which I correc ted

3 The predicted relation be tween advertis ing in tensity and market share

shows up clearly in on ly 25 of the case s examined I have ye t to

explore why that may b e the cas e

4 Some evidence concerning the presence and impact of coopera tion was

produced but it is not clear ly pervasive

5 The dis tinction between convenience goods and non-c onvenie nce goods is

unambiguously a good one

6 Virtually no evidence concerning econ omies of scale in adver tis ing can

be gleaned fr om this study given its assumpt ions

More work is called for on many of these issues my study seems to have

raised more questions than it has answer ed This is pr obab lly due to the richshy

ne ss of the data source since I had the oppor tunity to address several issue s

at once

- -- - Q --

Foo tnotes

Manager Line o f Business Program Federal Trade Commission The author depended heavily on several staf f members of the LB Pro gram for statistical and clerical support in particular Joe Cholka George Pascoe and Haro lene Jenkins Helpful comments were given b y Richard Caves Dennis Mueller Michael Porter and F M Scherer When the paper was in its early stages o f development both S teve Garber and Jon Rasmussen former economists in the LB Program provided eery useful cri tiques The views expressed here are my own o f course

1 The basic exp licit model of the role of advertising is Dorfman and S teiner ( 1954 ) and the models in this paper may be seen as ano ther extens ion of their work

2 For a review o f models of oligopoly which treat prices and quantities as relevant variables see Shubik ( 1 959) Extens ions to take advertis ing int o account are fairly s traightforward

3 Dorfman and S teiner dealt with a price-setting firm For a monopolis t inverting the demand relation to show Pbull P (Q A) _instead o f Q- (P A) has no effect on the results o f the analysis For oligopolists who face a sys tem of demand relations inversion does have some impac t on the results The dif ferences are not trivial nonetheless they will no t be explored in this study

4 Shubik ( 1 959) p

5 From a formal mathematical point o f view the function is similar to a1 i Legrangian funct ion of the form - r rr

L bull 11 + A ( j - (i i i+j

where the indicates some fixed level of the profits industry Following the same logic which resul ts in and income constraint as the marginal utility of the of the indus tr in the obj ective of firm i

6 Hall amp Weiss ( 1 967) p 323

7 See Schmallensee ( 1 97 2 ) Ch 2 pp 1 6-47

8 On this poin t see Imel amp Helmberger ( 1 9 7 1 )

9 Long ( 1 970) p 130 - 1 39

1 0 See Schmallensee ( 1 972) Ch 3 pp 48-8 7

rrj i+j ) of the rest of the

the identification profits of the rest

Advertising

- -- -middot

J Econ Lit

Rev

Rev

Study Manufacturing Industry

Henning Econ

Journal

Advertising

Strategy

Econ

Report

BIBLIOGRAPHY

Brow Randall S Estimating Advantages to Large-Scale Advertising Rev Econ Stat ist August 1978 60 pp 428-3 7

Comancr William S and WUson Thomas A and Market P ower Cambridge Harvard University Press 1 974

The Effect of Advertising on Competition A Survey June 1979 17 pp 453-476

Dorfman Robert and Steiner Peter 0 Optimal Advertis ing and Optimal Quality Amer Econ Dec 1954 44 pp 826-36

Hall Marshall amp Weiss Leonard W Firm Size and Profitab ility Rev Econ Statist August 1967 4 9 pp 3 1 9-33 1

mel Blake and Helmberger Peter Estimation of Structure-Profit Relationship s with Application to the Food Proc es sion Sector Amer Econ Sep t 1971 6 1 (4) pp 6 14-27

Long William F An Econometric of Performance in American 1955-1958 Unpublished Ph D Dissertation

Berkeley University of California 1 970

Mann H Michael J A and Meehan J W Jr Advertising and Concentration An Empirical Investigation J Ind Nov 1967 1 6 pp 34-45

Martin Stephen Advertising Concentration and Prof itability the Simultaniety Problem Bell Autumn 1979 10middot pp 639-647

Schmalensee Richard The Economics o f Amsterdam North-Holland 1972

Shubik Martin and Market Structure New York Wil y 1959

Strickland Allyn D and Weiss Leonard W Advertising Concentration Price-ltost Margins Polit Oct 197 6 84 (5) pp 1 109-2 1

U S Federal Trade Commis sion Annual Line of Bus ine ss 1 97 4 -

Washington 1980

Summary

My purpose in writing this pa per wa s t o attempt to integrate explicit micro-

economic mode lling reasoned econome tric specification of error terms and high

quality data to exp lore some questions about adver tising by large firms

al quite important improvements could be made in the first two of those areas

and much data ma ssag ing is yet to be done in the third

Concerning the subst an ce of what I have done I think six things are im-

Page 2 8

Severshy

V and Conclusions

portant

1 Explicit modeling is worth the ef for t if for no other reas on than

that it provides a basis for choosing fr om a varie ty of funct ional

forms

2 The same is true for error specif ica t ion I did in fact look at scatshy

ter diagrams for all 32 industry categor ies and they vir tually all show

the het eroscedast icity which I as sumed and for which I correc ted

3 The predicted relation be tween advertis ing in tensity and market share

shows up clearly in on ly 25 of the case s examined I have ye t to

explore why that may b e the cas e

4 Some evidence concerning the presence and impact of coopera tion was

produced but it is not clear ly pervasive

5 The dis tinction between convenience goods and non-c onvenie nce goods is

unambiguously a good one

6 Virtually no evidence concerning econ omies of scale in adver tis ing can

be gleaned fr om this study given its assumpt ions

More work is called for on many of these issues my study seems to have

raised more questions than it has answer ed This is pr obab lly due to the richshy

ne ss of the data source since I had the oppor tunity to address several issue s

at once

- -- - Q --

Foo tnotes

Manager Line o f Business Program Federal Trade Commission The author depended heavily on several staf f members of the LB Pro gram for statistical and clerical support in particular Joe Cholka George Pascoe and Haro lene Jenkins Helpful comments were given b y Richard Caves Dennis Mueller Michael Porter and F M Scherer When the paper was in its early stages o f development both S teve Garber and Jon Rasmussen former economists in the LB Program provided eery useful cri tiques The views expressed here are my own o f course

1 The basic exp licit model of the role of advertising is Dorfman and S teiner ( 1954 ) and the models in this paper may be seen as ano ther extens ion of their work

2 For a review o f models of oligopoly which treat prices and quantities as relevant variables see Shubik ( 1 959) Extens ions to take advertis ing int o account are fairly s traightforward

3 Dorfman and S teiner dealt with a price-setting firm For a monopolis t inverting the demand relation to show Pbull P (Q A) _instead o f Q- (P A) has no effect on the results o f the analysis For oligopolists who face a sys tem of demand relations inversion does have some impac t on the results The dif ferences are not trivial nonetheless they will no t be explored in this study

4 Shubik ( 1 959) p

5 From a formal mathematical point o f view the function is similar to a1 i Legrangian funct ion of the form - r rr

L bull 11 + A ( j - (i i i+j

where the indicates some fixed level of the profits industry Following the same logic which resul ts in and income constraint as the marginal utility of the of the indus tr in the obj ective of firm i

6 Hall amp Weiss ( 1 967) p 323

7 See Schmallensee ( 1 97 2 ) Ch 2 pp 1 6-47

8 On this poin t see Imel amp Helmberger ( 1 9 7 1 )

9 Long ( 1 970) p 130 - 1 39

1 0 See Schmallensee ( 1 972) Ch 3 pp 48-8 7

rrj i+j ) of the rest of the

the identification profits of the rest

Advertising

- -- -middot

J Econ Lit

Rev

Rev

Study Manufacturing Industry

Henning Econ

Journal

Advertising

Strategy

Econ

Report

BIBLIOGRAPHY

Brow Randall S Estimating Advantages to Large-Scale Advertising Rev Econ Stat ist August 1978 60 pp 428-3 7

Comancr William S and WUson Thomas A and Market P ower Cambridge Harvard University Press 1 974

The Effect of Advertising on Competition A Survey June 1979 17 pp 453-476

Dorfman Robert and Steiner Peter 0 Optimal Advertis ing and Optimal Quality Amer Econ Dec 1954 44 pp 826-36

Hall Marshall amp Weiss Leonard W Firm Size and Profitab ility Rev Econ Statist August 1967 4 9 pp 3 1 9-33 1

mel Blake and Helmberger Peter Estimation of Structure-Profit Relationship s with Application to the Food Proc es sion Sector Amer Econ Sep t 1971 6 1 (4) pp 6 14-27

Long William F An Econometric of Performance in American 1955-1958 Unpublished Ph D Dissertation

Berkeley University of California 1 970

Mann H Michael J A and Meehan J W Jr Advertising and Concentration An Empirical Investigation J Ind Nov 1967 1 6 pp 34-45

Martin Stephen Advertising Concentration and Prof itability the Simultaniety Problem Bell Autumn 1979 10middot pp 639-647

Schmalensee Richard The Economics o f Amsterdam North-Holland 1972

Shubik Martin and Market Structure New York Wil y 1959

Strickland Allyn D and Weiss Leonard W Advertising Concentration Price-ltost Margins Polit Oct 197 6 84 (5) pp 1 109-2 1

U S Federal Trade Commis sion Annual Line of Bus ine ss 1 97 4 -

Washington 1980

- -- - Q --

Foo tnotes

Manager Line o f Business Program Federal Trade Commission The author depended heavily on several staf f members of the LB Pro gram for statistical and clerical support in particular Joe Cholka George Pascoe and Haro lene Jenkins Helpful comments were given b y Richard Caves Dennis Mueller Michael Porter and F M Scherer When the paper was in its early stages o f development both S teve Garber and Jon Rasmussen former economists in the LB Program provided eery useful cri tiques The views expressed here are my own o f course

1 The basic exp licit model of the role of advertising is Dorfman and S teiner ( 1954 ) and the models in this paper may be seen as ano ther extens ion of their work

2 For a review o f models of oligopoly which treat prices and quantities as relevant variables see Shubik ( 1 959) Extens ions to take advertis ing int o account are fairly s traightforward

3 Dorfman and S teiner dealt with a price-setting firm For a monopolis t inverting the demand relation to show Pbull P (Q A) _instead o f Q- (P A) has no effect on the results o f the analysis For oligopolists who face a sys tem of demand relations inversion does have some impac t on the results The dif ferences are not trivial nonetheless they will no t be explored in this study

4 Shubik ( 1 959) p

5 From a formal mathematical point o f view the function is similar to a1 i Legrangian funct ion of the form - r rr

L bull 11 + A ( j - (i i i+j

where the indicates some fixed level of the profits industry Following the same logic which resul ts in and income constraint as the marginal utility of the of the indus tr in the obj ective of firm i

6 Hall amp Weiss ( 1 967) p 323

7 See Schmallensee ( 1 97 2 ) Ch 2 pp 1 6-47

8 On this poin t see Imel amp Helmberger ( 1 9 7 1 )

9 Long ( 1 970) p 130 - 1 39

1 0 See Schmallensee ( 1 972) Ch 3 pp 48-8 7

rrj i+j ) of the rest of the

the identification profits of the rest

Advertising

- -- -middot

J Econ Lit

Rev

Rev

Study Manufacturing Industry

Henning Econ

Journal

Advertising

Strategy

Econ

Report

BIBLIOGRAPHY

Brow Randall S Estimating Advantages to Large-Scale Advertising Rev Econ Stat ist August 1978 60 pp 428-3 7

Comancr William S and WUson Thomas A and Market P ower Cambridge Harvard University Press 1 974

The Effect of Advertising on Competition A Survey June 1979 17 pp 453-476

Dorfman Robert and Steiner Peter 0 Optimal Advertis ing and Optimal Quality Amer Econ Dec 1954 44 pp 826-36

Hall Marshall amp Weiss Leonard W Firm Size and Profitab ility Rev Econ Statist August 1967 4 9 pp 3 1 9-33 1

mel Blake and Helmberger Peter Estimation of Structure-Profit Relationship s with Application to the Food Proc es sion Sector Amer Econ Sep t 1971 6 1 (4) pp 6 14-27

Long William F An Econometric of Performance in American 1955-1958 Unpublished Ph D Dissertation

Berkeley University of California 1 970

Mann H Michael J A and Meehan J W Jr Advertising and Concentration An Empirical Investigation J Ind Nov 1967 1 6 pp 34-45

Martin Stephen Advertising Concentration and Prof itability the Simultaniety Problem Bell Autumn 1979 10middot pp 639-647

Schmalensee Richard The Economics o f Amsterdam North-Holland 1972

Shubik Martin and Market Structure New York Wil y 1959

Strickland Allyn D and Weiss Leonard W Advertising Concentration Price-ltost Margins Polit Oct 197 6 84 (5) pp 1 109-2 1

U S Federal Trade Commis sion Annual Line of Bus ine ss 1 97 4 -

Washington 1980

Advertising

- -- -middot

J Econ Lit

Rev

Rev

Study Manufacturing Industry

Henning Econ

Journal

Advertising

Strategy

Econ

Report

BIBLIOGRAPHY

Brow Randall S Estimating Advantages to Large-Scale Advertising Rev Econ Stat ist August 1978 60 pp 428-3 7

Comancr William S and WUson Thomas A and Market P ower Cambridge Harvard University Press 1 974

The Effect of Advertising on Competition A Survey June 1979 17 pp 453-476

Dorfman Robert and Steiner Peter 0 Optimal Advertis ing and Optimal Quality Amer Econ Dec 1954 44 pp 826-36

Hall Marshall amp Weiss Leonard W Firm Size and Profitab ility Rev Econ Statist August 1967 4 9 pp 3 1 9-33 1

mel Blake and Helmberger Peter Estimation of Structure-Profit Relationship s with Application to the Food Proc es sion Sector Amer Econ Sep t 1971 6 1 (4) pp 6 14-27

Long William F An Econometric of Performance in American 1955-1958 Unpublished Ph D Dissertation

Berkeley University of California 1 970

Mann H Michael J A and Meehan J W Jr Advertising and Concentration An Empirical Investigation J Ind Nov 1967 1 6 pp 34-45

Martin Stephen Advertising Concentration and Prof itability the Simultaniety Problem Bell Autumn 1979 10middot pp 639-647

Schmalensee Richard The Economics o f Amsterdam North-Holland 1972

Shubik Martin and Market Structure New York Wil y 1959

Strickland Allyn D and Weiss Leonard W Advertising Concentration Price-ltost Margins Polit Oct 197 6 84 (5) pp 1 109-2 1

U S Federal Trade Commis sion Annual Line of Bus ine ss 1 97 4 -

Washington 1980