Analysis of consumer demand for selected species of fresh

University of Massachusetts Amherst University of Massachusetts Amherst

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Masters Theses 1911 - February 2014

1969

Analysis of consumer demand for selected species of fresh fish Analysis of consumer demand for selected species of fresh fish

based on data from five retail stores. based on data from five retail stores.

Robert Edward Lee University of Massachusetts Amherst

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ANALYSIS OF CONSUMER DEMAND FOR SELECTED SPECIESOF FRESH FISH BASED ON DATA

FROM FIVE RETAIL STORES

A Thesis Presented

by

Robert I. Lee

Submitted to the Graduate Seho^ 1 of the

University of Massachusetts inpartial fulfillment of the requirements for the degree o:

MASTER OF SCIENCE

June 1969

ii

ANALYSIS OF CONSUMER DEMAND FOR SELECTED SPECIESOF FRESH FISfe BASED ON DATA FROM FIVE RETAIL STORES

A Thesis Presented

Robert E. Lee

Approved as to style and content by:

(montfT) (year)

iii

ACKNOWLEDGMENTS

A sincere note of appreciation is extended to those many individuals

of the case study chain, which we have agreed not to identify, who cooper-

ated completely to provide data for this study. Especial thanks are also

due to Dr. David A. Storey and Dr. James K. Kindahl for their patience and

direction. Thanks are also extended to my typist, Miss Kathy Godek, who

displayed unusual diligence in preparing the final manuscript.

iv

TABLE OF CONTENTS

PageNo.

ACKNOWLEDGEMENTS iii

TABLE OF CONTENTS iv

LIST OF TABLES vi

LIST OF FIGURES vii

CHAPTER

I INTRODUCTION 1

II REVIEW OF LITERATURE 3

III RESEARCH PROCEDURE 9

Coverage of the Study ' 9

Data Collection . 11

Analysis of the Data 12

IV DESCRIPTION OF THE CASE STUDY CHAIN AND ITS FISHMERCHANDISING PRACTICES 13

The Chain and Its Place in the Industry 13

Comparison of the Five Stores 13

Description of Fish Merchandising Practices 14

V PRELIMINARY ANALYSIS OF FRESH FISH SALES FOR FIVE

LEADING SPECIES 20

Sales in Pounds 20

Retail Prices .24

Special Promotions 27

Summary 34

VI REGRESSION ANALYSIS OF FRESH FISH SALES FOR FIVE

LEADING SPECIES 3j

Theoretical Consd derations 35

The Model 39

Results 48

Summary of Results of Regression Analysis 71

V

TABLE OF CONTENTS (continued)PageNo.

VII SUMMARY AND CONCLUSIONS 74

APPENDICIES

A MANAGER QUESTIONNAIRE 79

B FORM FOR COLLECTION OF DATA FROM INDIVIDUAL STORES 84

C SIMPLE CORRELATION TABLES 86

BIBLIOGRAPHY 97

LIST OF TABLES

Title

Carry-over of fresh fish and seafood

Location of fish display relative to normal direc-tion of traffic flow

Aggregate weekly mean pounds ordered and total reve-nue by species

Coincidence of individual species' peak quantitieswith aggregate peak quantities

Proportion of sales accounted for by the singlefeatured species

Relative importance of special and nonspecial pricesby species

Effect of specials of other species on pounds or-

dered of haddock-

Haddock adjustments for five stores

Coefficient and statistical test values for six

regressions

Model No. 1 - All variables free to enter

equation

Coefficients and statistical test values for six

regressions

J-lodel No. 2 - Significant variables free to

enter equation


regressions

Model. No- 3 - Haddock slope dummy variable

omitted

Coefficients, elasticities, and statistical test

values for six regressions

Model No. 4 - Haddock dummy variables omitted


regressions

Model No. 5 - Nonspecial data only

I

LIST OF TABLES (continued)

TableNo. Title

6-7 Number of weeks particular species were not sold

LIST OF FIGURES

FigureNo. Title

4- 1 Store manager's estimate of weekly sales distribu-

tion

5- 1 Quantity of each species and total aggregate plottedover time

5-2 Price trends of five species

5-3 Percent of five species aggregate made up of single

featured species

5- 4 Individual price-quantity ordered relationships

6- 1 Theoretical representation of the supply-demand sit-

uation

CHAPTER I

INTRODUCTION

In the early 1950 Ts Donald White in his book The New England Fish-

ing Industry [35] forecast a rather dim future for the Nevz England fish-

ing industry. At that time it faced a declining resource base, labor

problems, and growing competition from foreign countries. Through the

early 1960's White's pessimism was borne out as foreigners, with their

superior technology and cheaper labor, made large inroads into the U.S.

market. Recently, however, the introduction of stern trawling to the

Atlantic fleet and the passage of the 1964 Fishing Fleet Improvement Act

have given new promise to the industry. This act compensates fishermen

for up to 50 percent of the cost of new fishing vessels, making the adop-

tion of new technology more feasible.

Marketing problems have plagued the industry also. Historically

there has been a preference for meat in the United States which has

severely curtailed the market for fish and fish products. The pattern

of consumption of fish has been linked closely to religious factors and

custom, with tne heaviest consumption occurring on Fridays and during

the Lenten season. In 1966, the Pope removed the restrictions of the

Catholic Church on the consumption of meat, so religion may no longer

be a major factor influencing fish consumption. Whether or not the de-

mand for fish has changed because of this new ruling could be an inter-

esting topic for economic research itself, and certainly suggests the

comparison of research conducted since the ruling with that conducted

before it.

2

The possible impact of new technology which is now likely to be

adopted by the industry is also a subject for research. A question

which might L>e asked is whether or not the demand for fish justifies

new expenditures on equipment. Possibly it would be preferable to

allow the New England industry to continue declining and meet domestic

demand with the cheaper, imported product.

These are questions which are difficu.lt to answer because very lit-

tle, of a specific nature is known about the demand for fish in the United

States. Relatively little research has been conducted in this area at

any level of the marketing system, and particularly at the retail level.

Past studies have tended to use annual data with several species lumped

together..Those studies which have disaggregated by species normally

lumped fresh and frozen forms of the species together or else used only

data on the frozen form. While this certainly is of interest, the New

England fishermen cater primarily to the fresh market, since they have

a locational advantage over foreign suppliers, and the price for fresh

fish can be twice that for frozen fish. Thus, the market of most im-

mediate interest is the fresh market.

This study was intended to partially fill this informational gap.

Stated most, generally, its purpose was to improve the state of knowledge

about consumer demand for selected- species of fresh, salt-water fish.

Weekly data collected from individual supermarkets of a case study food

chain was used to construct, demand equations for the fresh form of in-

dividual species. By using weekly data, short-run relationships could

be studied instead of lon<? term trends. Factors which were of primary

interest in this study were the prices of competing species and the e

feet of promoting a species at a reduced price. From the functions

utilizing these data it was possible to calculate price and cross ela

ticies of demand. Other factors which could have been included, such

as the effects of ethnic origin, religion, and consumer income, were

beyond the scope of this study.

CHAPTER II

REVIEW OF LITERATURE

It was stated previously that relatively few studies have been con-

ducted on the consumer demand for fish. In this chapter those few which

have been conducted will be discussed along with other useful demand

studies .

-

Joseph Farrell and Harlan Lampe [11] conducted a study in 1965 to

determine the price elasticity of demand for fish. The. authors built a

model to study five market levels for haddock. Supply and demand func-

tions were estimated at the landings, wholesale, imports, cold storage,

and retail jLeve Is . Monthly data from 1954 through 1962 were analyzed by

the limited-information maximum- likelihood technique. Since monthly data

were used, the authors had no opportunity to examine weekly price move-

ments, but were able to analyze seasonal changes in demand.

At the retail level the authors found a substantial increase in de-

mand during the Lenten season, but because of high multicollinearity among

some of the independent variables, much of the statistical results was in-

conclusive „ From the retail demand equation for frozen fillets of haddock

a price elasticity was estimated. The data were separated into three cate-

gories,allowing the calculation of three distinct elasticity estimates.

From the equation describing the retail market from January through June

the price elasticity of demand was +4.93 For the period from July throuw

December the estimate was -A. 409. An equation for the whole year was es-

timated also, but the haddock quantity variable was insignificant. Of the

two elasticity estimates that were obtained, it is interesting to note

that both were highly elastic. However, for some reason, left unexplained

by the authors, the sign for the spring of the year estimate was positive.

A more recent study on consumer demand for fish has been reported by

Darrel Nash [24] of the Bureau of Commercial Fisheries. At the time of

the preliminary report on the study, time series data had been analyzed

by the single-equation least-squares regression technique. Additional

analysis was planned utilizing cross-section data from a Michigan State

University consumer panel in an attempt to obtain information about one

period in time.

From the aggregated time series data the Bureau was able to derive

demand functions for fresh and frozen flounder individually, but lumped

fresh and frozen together for haddock. For the years 1950 to- 1963, fresh

flounder had a price elasticity ranging from -4.0 to -6.0 at the mean price

and quantity. The estimate of price elasticity for frozen flounder fillets

was based on the years of 1954 to 1963. At the mean price and quantity it

was approximately -3.5. Unexpectedly, the elasticity for both forms of

flounder was higher at lower prices than at higher prices. Since Nash

was talking of 'linear functions this statement at first seemed implausible,

but apparently he was thinking of shifts in the short-run demand curves,

rather than elasticities calculated along the long-run functions. Over

the period covered by the data, price trended upward and apparently the

short-run demand curves became more inelastic.

In the haddock equation, the fresh and frozen forms of the species

were combined and treated as a single commodity. Data were available

for the years 1954 to 1964. At the mean price- and quantity for this

period the price elasticity estimate was -1.4. It will be noted that all

these estimates were negative, as normally expected for demand equations,

and greater than one. The latter factor shows demand for these individual

species to be elastic, which means that at the retail level, as the price

of the species is lowered, the quantity consumed will increase by a pro-

portionately greater amount, thus increasing total revenue.

One article particularly useful in developing the methodology for

this study was that published by Fred Nordhauser and Paul Farris [26] in

the November, 1959 issue of the Journal of Farm Economics . In their study,

weekly price and quantity data from six supermarkets in four mid-western

cities were used to estimate the short-run price elasticity for fryers.

Stores were selected from the same chain so as to have consistent pricing

and merchandising policies. When selecting stores, consideration was also

given to representing a variety of clientele - Whites, Negroes, and vari-

ous income levels.

The problem of handling advertised price specials was encountered in

their study. So as not to bias their estimates of price elasticity in

non-special weeks, the authors omitted from their analysis the weeks in

which specials 'occurred. They did notice, however, that when fryers were

offered on special one week, there xâs no noticeable effect on sales the

following week. Therefore, the increase in sales in special weeks seemed

to be a net gain in sales.

A study conducted by the National Association of Food Chains reached

similar conclusions about the effects of price specials for meat [25]= It

stated, "Changes in proportion of the total [meat, poultry and fish ton-

nage] caused by a price special do not see- to affect tonnage of the feature

item adversely in the following week. The price special can greatly in-

crease volume in the short-run, but the amount sold in the following weeks

remains near the long-run normal [25, p. 6].'" In addition, the researchers

found that f, ...a price special raises the tonnage of the featured item, but

does not depress volume of the non-featured items by an equivalent amount.

It appears from this that the added tonnage sold during a sale is largely

'plus tonnage' [25, p. 6]." Another finding of this study was that the

tonnage of a particular item may rise by as much as five or ten times the

normal volume when offered on special.

A studywhich handled the analysis of price specials differently from

Nordhauser and Farris is that conducted by Leo R. Gray [16]. He collected

weekly sales volume and poultry price data from a representative sample of

firms in the Washington, D. C. , metropolitan area. In an attempt to meas-

ure the effects of price specials, Gray employed dummy variables. One was

a normal zero-one variable to detect any shift in the level of the demand

curve as a result of price specials. The other was a uniquely constructed

variable to measure structural changes in demand. He constructed this

"slope dummy' 1 by multiplying the week's poultry price by -1 on nonsale

weeks, and +1 on sale xêeks . He then expressed his function as:

Vt

= a0+b 1p tH-b

2vt-1+b 3

Dt;

+b4SD

t-f-u

t

where:

Vt= Weekly volume of estimated sales by all retailers in the

market area.

Pt

= Deviation from the average weekly prices for corresponding

weeks of each year,

v t„l= Deviation from the average of lagged weekly volumes for cor-

responding weeks of each year.

8

Dfc

= A dummy shift variable used to differentiate between a saleweek and a nonsale week. The sale week was given a value of1, the nonsale week 0.

SDt = The dummy slope variable. It is the product of the modified

dummy shift variable (Dlt ) and p tfor that week.

Djt

= -1-1 in a sale weekD]_

t- -1 in a nonsale week

If the coefficient of Dfc

is significant it is known that there is a

significant difference in the level of the demand curve between sale and

nonsale weeks. To be able to determine if there is a difference in slope

of the two curves, the coefficient of SD t must be tested. Should it be

significant, then it is known that the structure of demand is different

for the item when it is on sale as compared to when it is not,

er method of cons t ruct ing a s lope dummy to perform the same

task as the one just discussed, is explained by Arthur Goldberger [15].

The concept of multiplying a price by one value for a special week and by

another value for a nonspecial week is the same as that employed by Gray.

The difference is in the coefficients used. Goldberger uses 0 and 1 as

his multipliers instead of -1 and +1. If a 0 is used in a nonspecial week

and a 1 is used in a special week, then the slope dummy takes on the value

of zero on weeks where there is no price special, and a value of that week

price when there is a price special. The general result is the same as by

Gray's method, but the technique propounded by Goldberger is in more com-

mon usage

.

A recent publication worthy of mention in any study of fisheries eco-

nomics,although not used extensively in this study, is Recent Development

and Research in Fisheries Economics , edited by Frederick W. Bell and .Tared

Hazieton [3]. It contains reports of several recent studies conducted on

the economics of our fisheries

.

9

CHAPTER III

RESEARCH PROCEDURE

The procedure followed in this study could not be completely pre-

dicted, because the merchandising practices of the case study firm had

to be determined first. Once this was accomplished, full development of

the procedure followed. A summary of this procedure is given below.

Coverage of the Study

This report is a case study of a chain operating supermarkets in the

Springfield-Holyoke area of western Massachusetts. By designing the ex-

periment as a case study, rather than a sampling survey, several problems

were eliminated. One was the comparability of data collected fron differ-

ent sources. Most firms have a unique way of keeping records. Ey select-

ing stores from just one chain, the records from each store were assured

to be the same.

Another advantage of the case study was the similarity of pricing and

merchandising policies in each of the stores. These policies, while ex-

pected to be similar in different chains, would not be identical, Since

these policies would affect the demand for fish, they would have to be ac-

counted for if comparing data from different chains.

If the findings of this report are to be generalized to other chains,

it must be assumed that other chains are similar to the case study chain.

This assumption seems plausible for chains in the same geographical re-

gion, though it is not the purpose of this study to generalize in this

fashion. The express purpose here is to isolate some of the factors of

demand for fresh fish.

10

onThe particular firm selected for this study was chosen primarily

the basis of convenience. No advantages of one firm over another, rela-

tive to fish sales, were apparent. The chain which was selected operated

typical supermarkets throughout the local region, and its management dis-

played a gratifying spirit of cooperation.

It was not desired to survey all the stores of the chain, so a few

were selected on the basis of the following criteria. By surveying the

stores of the chain, it was found that there existed very few differences

among them relative to sales of fresh fish, A few sold fish through the

delicatessen counter, but most sold it through the meat case. It was felt

that stores selected for the study should represent both sales methods.

Additional criteria used in selecting the stores were their proximity to

each other, and their age. Since there were no major differences among

the stores it was decided to select stores which were close enough to each

other for all to be visited in one or two days. The age of the stores was

considered originally so that several years' data could be observed. Only

stores which had been operated for at least seven years were selected.

From the experience of another similar type study [26] it was decided that

five, stores from the chain could provide the data necessary for the study.

On the basis of all the above information, five stores were selected in

the western Massachusetts region, two of which sold fish through the deli-

catessen couiiter, and three of which sola it through the meat case.

The time period covered by the study was forty-two weeks, from July,

1967 through April, 1968. The historical records kept by the firm did not

provide ail the information necessary for the study, and July was the earl-

iest it was possible to start weekly record keeping procedures. Data

II

collection was continued until the week after Easter so as to include the

Lenten season

Five of a possible forty fish items were chosen for the study on the

bases, first of compatibility with the goals of the study, and second of

importance in sales. Since this study was concerned with fresh, salt-water

finfish, the fresh-water species and shellfish were immediately removed from

primary consideration. Of the species remaining after this division, five

were sold throughout the year and in noticeably larger volume. These, five,

haddock, swordfish, flounder, halibut, and codfish, were chosen for major

consideration.

Data Collection

Descriptive information about the operations of the stores was col-

lected by personal visits to the head office, to individual stores, and

by a manager questionnaire. The head office was visited at the beginning

of the study, and whenever problems relevant to the duties performed there

arose. Individual stores were visited at the beginning of the study, and

at approximately five week intervals thereafter. The original visit was

used to familiarize the researcher with each of the stores in the study,

and to explain to each meat manager the nature of the information he was

being asked to record. Later visits to the stores were utilized to dis-

cuss with the meat managers problems relating to their record keeping, and

to answer further questions in the resea oner's mind about store practice.;.

After several of these visits, it was deemed worthwhile to organize the

various questions which had arisen into a specific questionnaire, the pur-

pose of which was to systematically provide information about the handling

and merchandising of fish in each of the five stores [See Appendix A].

12

Numerical data were collected both from the head office and from the

individual stores. Basic information about quantities of fish purchased

by each store, broken down by species, was kept in the records of the main

office. Weekly wholesale and retail prices were also available from the

main office.

To supplement this, the meat manager in each store agreed to fill

out a weekly form recording the quantity, in pounds, of each species left

over at the end of the week. He also recorded the day and time that he

ran out of any species. This information was used to adjust the quantity

purchased figure, obtained from the head office, into the desired quantity

sold figures.

Analysis of the Data

In the early stages of analysis, the data were graphed and tabled for

simple, visual analysis. While this type of analysis will reveal some of

the more obvious relationships, it does not provide estimates of statis-

tical .significance, nor does it adequately identify multivariate relation-

ships .

A second and major stage of analysis involved the use of least-squares

multip.l e regression . This technique analyzes the effects of several inde-

pendent variables at. the same time. It also provides measurements of sta-

tistical significance.

The preliminary analysis handled aggregate data from the five stores

for each of the five individual species of fresh fish. In the regression

analysis, on the other hand, study was concentrated on fresh haddock fil-

lets. Here, the planned procedure was to first analyze each store and

then to compare the different stores by means of the Chow test.

13

CHAPTER IV

DESCRIPTION OF THE CASE STUDY CHAIN AND ITSFISH MERCHANDISING PRACTICES

The Chain and Its Place in the Industry

The chain selected for this study operated several supermarkets in

the greater Springfield area of Massachusetts. Within this region it ac-

counted for about 6.5 percent of all retail food business [17, p. 27], or

16.5 percent of total chain store business. Its stores were of average

supermarket size, each handling about $40,000 of total sales weekly, which

was also the per store mean for all the other major chains in the region

taken together [17, p. 27]

.

Fish and seafood sold by the meat department in the case study chain

accounted for about two percent of the department's sales. No comparable

figure was available for the region, but on a national basis, fresh fish

and seafood items accounted for almost three percent of meat department

sales [8, p. 32]. Relative to total store food sales, fresh fish and sea-

food accounted for approximately ,6 percent of sales in the chain and ap-

proximately .7 percent nationally.

Comparison of the Five Stores

The stores selected for this study averaged about $55,000 gross weekly

sales, slightly higher than the average for the entire chain. Most catered

to a mixed religious and ethnic clientele, but one store served a large

Jewish population. In this particular store about forty percent of the

customers were Jewish, but they accounted for an estimated fifty percent,

of the fish sales. This store and one other displayed their fish on ice

14

in the delicatessen counter. The other three stores displayed prepackaged

fish in the meat case in the same fashion as other meat items.

The peak sales periods for fish varied from store to store. Peak

sales occurred on Thursday evenings and Friday for two stores, on Thurs-

day morning and Friday for a third, and of the remaining two, one peaked

on Tuesdays and Fridays, while the other peaked on Wednesdays and Fridays

(see Figure 4-1)

.

The slack sales periods had more similarities than the peak periods,

but varied somewhat from store to store, also. On Mondays virtually no

sales were made at any of the stores, the reason being that fish was not

normally displayed in the case. Saturday sales were also quite low, ex-

cept at one store which made fifteen percent of its weekly sales on that

day (Figure 4-1). In addition to these slack periods, Tuesdays were light

for fish sales at three stores, and Wednesdays were light at two, one of

these and another. Most of the stores made some sales almost every day

except Monday, but store D T

s sales were limited strictly to Thursdays and

Fridays. A major factor in this unique pattern of sales may have been the

very difficult competitive position that this store faced. In the imme-

diate area there were three or four other large supermarkets , the closest

of which featured a large, fresh fish delicatessen display.

Description of Fish Merchandising Practices

Placement of weekly order . All fish to be sold through the meat de-

partment was delivered to the stores on Tuesday and Thursday mornings.

The meat managers placed their orders on Saturday for the following Tues-

day's delivery, and on Wednesday for Thursday's delivery. At the time the

15

Figure 4-1. store manager's estimate ofweekly sales distribution

% of weeklysales

STORE A

% of weeklysales

60

50

40

30

20

10

STORE C

E3*

1

1

13 EES

—

M W T

Day

% of weeklysales

80

70

60

50

40

30

20

10

L L

M T

% of weeklysales

60 STORE B

50

40

30

20

il10

m mM T W T F

% of weeklysales

60

50

40

30

20

10

Day

STORE E

M T W T

Day

E3

JUE3LF S

STORE D

w T

Day

16

original order was placed, neither the wholesale nor the retail prices

were normally known to the managers. They were usually informed, how-

ever, if a drab tic change was expected in the wholesale price. This in-

variably coincided with the offering of a species on a special promotion,

which fact was also made known to the managers a week in advance. In

neither case were they informed of the actual prices

-

When ordering, managers normally purchased only that amount of each

species which they estimated would be sold. To do this they worked from

the "normal 11 level of sales, purchasing a standard amount of each species,

particularly on Saturday orders. This order was then adjusted with the

second order of the week if sales of a particular species seemed to be

unusually high or low. The primary adjustments that occurred to the Sat-

urday orders resulted from the offering of a species on special. Then

the manager increased his Saturday order considerably, to the size nor-

mally used whenever that species was offered on special. Adjustments

were occasionally made for specific religious days, also. For instance,

the order would be increased for the first week of Lent, and decreased

for Roman Catholic fast days.

Carry-over from one week to th e next. Fish was carried from one week

to the next, and it was necessary to investigate the nature and extent of

this practice. It appears that fresh fist? was never carried to the follow-

ing week and sold as fresh (see Table 4-1). However, sometimes part of

Thursday's delivery was placed in the freezer immediately upon delivery.

Then, if it was not removed from the freezer for display in the meat case,

it was carried over for sale the following week as frozen fish. When this

17

was done, it was displayed separately from the fresh form of that species

and was normally priced ten cents per pound lower* Of the five stores,

only one frequently froze fresh fish and carried it over to the next week

Table 4-1. Carry-over of fresh fish and seafood.

Stores

Fresh fi

andsh carried oversold as

Frozen fish carried overand sold as

Fresh Frozen Frozen

A No Seldom Yes

B No Seldom Yes

C No Frequently Yes

D No Seldom No

E No Seldom Yes

Source: Manager questionnaire, see Appendix A..

The length of time that carried-over fish was held varied, but nor-

mally it was not kept more than one or two weeks. Two managers claimed

that they never held fish more than one week, and seldom held it at all.

The other three said that they might hold it as long as four weeks. Shrimp

was the one species that all managers agreed was more apt to be held over

for the longer periods of time.

In general, fish was ordered for a one week time period and carry-

over was the result of an overes timation of sales. However, on occasion

excessively large orders were intentionally placed. This occurred most

frequently when a manager knew that the wholesale price was going to be

unusually low, such as when a species was going to be offered on special.

As stated previously, the manager would not know the exact wholesale price

18

of an item to be featured, but he did know it would be considerably lower

than normal. One manager claimed that the meat buyer for the firm would

occasionally suggest that he purchase an extra supply of some commodity

when it was going to be cheaper.

On those occasions when the meat managers did deliberately over-order

they would order from half again as much as normal, to twice as much. The

species most frequently included in this practice were haddock fillets,

swordfish steaks, and certain shellfish items. One manager claimed that

he never deliberately ordered an amount greater than he expected to sell

that week.

" Packaging. Some packaging was done at the store and some was done

before the fish was delivered to retail stores. With the exception of

mackerel, salt-water fish were filleted, steaked, or dressed before reach-

ing the retail store. With mackerel, the heads were removed after they

were delivered. Haddock fillets, halibut fillets and ocean perch fillets

were normally wrapped before delivery, but smelts, flounder, swordfish,

codfish, clams, and halibut steaks had to be wrapped at the stores. Ex-

ceptions to this were the two stores which sold fish through the delica-

tessen counter. There, fish was displayed unwrapped on ice. At one of

the delicatessens, a large amount of fresh-water fish was sold; these

species were cleaned, and dressed or filleted in the store.

Fish display. The linear feet of the meat case allocated to fish

ranged from three to twelve feet, depending on the store (see Table 4-2).

At both stores where fish was sold through the delicatessen counter, a

full twelve foot case was used. At two of the other stores, six feet of

the meat case was allocated to fish, and at the fifth store, three feet.

19

Table 4-2. Location of fish display relative toNormal direction of traffic flow.

Linear feetStore Location in fish i

A Before major meat items 6

B Delicatessen case , before major meat items 12

C Before major meat items 6

D After major meat items 3

E Delicatessen case, before major meat i terns 12

Source: Manager Questionnaires, see Appendix A.

With one exception, fish was displayed at the beginning of the meat

case, so customers would see it before the major meat items (see Table 4-2)

Since the delicatessen case was located before the main meat case, this

meant that fish was either sold from the delicatessen case, or was dis-

played immediately after it. At the fifth store, fish was displayed after

the main meat case, but before the one with frozen sausage, turkey, and

beef patties. This also was the store that allocated only three feet of

the meat case to fish.

The location of the fish display area in the meat department did not

change on any short term basis. It may change every few years as the pat-

tern of sales changes or when a new man comes to the head office. Within

the allocated area, little changing was done either. The one major excep-

tion occur- -.a -when a species was offered on special, and then it was al-

lowed twice the amount of space it normally had.

20

CHAPTER V

PRELIMINARY ANALYSIS OF FRESH FISH SALESFOR FIVE LEADING SPECIES

This chapter is designed to acquaint the reader with the data and

present some of the more obvious relationships among the variables. It

is divided into the following major categories: sales in pounds, retail

prices, special promotions, and conclusions.

Sales in Pounds

Pounds orde red. Of the five major species considered in this study,

haddock appeared to be the most important (Table 5-1). At least this was

true when comparing the nonspecial data and the combined, special and non-

special, data. The aggregate, mean quantity ordered in normal weeks of

250 pounds was almost 100 pounds greater than for swordfish, the second

largest seller. The same situation existed when looking at the combined

data. Haddock also had the advantage in mean, weekly, total revenue, but

by a less noticeable amount. Following in importance were halibut and

flounder, and least important by far, in terms of both quantity and reve-

rtue, was codfish.

When observing just the price special data, swordfish was the most

important species. On the average, it sold greater than 100 pounds a

week more than haddock, its closest competitor, and brought an average

weekly total revenue of approximately 250 dollars more than haddock. It

showed an almost fivefold increase in sales, and a somewhat smaller in-

crease in revenue over the nonspecial weeks. The importance of price

21

specials was quite noticeable for all the species, although not all in-

creased by as great an amount as swordfish. All, with the exception of

haddock, however, did increase by at least fourfold on a quantity basis,

and at least threefold on a total revenue basis when they were offered

on special.

_

Table 5-1. Aggregate weekly mean pounds orderedand total revenue by species.

Pounds Orderedlbs.

Total Revenue

$

a

Species-

Specialweeks

1

Non-specialweeks

2

All weekscombined

3

Specialweeks

4

Non-specialweeks

5

All weekscombined

6

Haddock 619 250 322 347 198 229

Swordfish 737 163 231 590 163. 215

Halibut 466 92 163 317 62 117

Flounder 404 90 140 263 75 103

Codfish 570 39 52 336 27 35

^Total Revenue = Aggregate Mean Pounds Ordered x Mean Retail . Price.

Almost every" week, one of the above five species was featured as a

price special. It might be expected, therefore, that were all five species

aggregated, the aggregate would not fluctuate much from one week to another

However, this was not the case, as can be seen from the aggregate curve in

Figure 5-1. Tt shows considerable fluctuation, the peaks of which always

coincide with a peak of some individual species' curve. Of a total of

eleven aggregate peaks, six of these coincide with peaks of the swordfish

curve, two with the haddock curve, and one each with the flounder, codfish,

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

s

ed Figure 5-1. Aggregate Quantity of Each Species and Total Aggregate Plotted Over Time

22

WeeksJuly, '67 I Aug, *67 I Sept, '67 I Oct, '67 / Nov, '67 I Dec, '67 "1 Jan, '68 I Feb, '68 I

Mar, '68JApr, '68

23

and halibut curves (Table 5-2). It might be noted that these frequencies

follow the same general order of importance as the pounds ordered figures

of Table 5-1, column 1.

Table 5-2. Coincidence of individual species' peak quantitieswith aggregate peak quantities.

Simultaneous aggregateSpecies Number of peaks pe aks

Haddock 8 2

Swordfish 8 6

Halibut 9 1

Flounder 7 1

Codfish 1 1

The importance of price specials was further supported by the obser-

vation that the deepest troughs of the aggregate curve occur when none of

the five species were offered on special. On those occasions when there

is a trough in the aggregate curve, and also a special on some species,

the trough is not as deep as in many other instances. An example of this

is the trough on week number sixteen, as compared to weeks eleven and

twenty-one. The former trough occurs when flounder was on special, wherea

the two latter ones occur when there were no specials.

Actual pounds sold . The analysis in this chapter was based upon

"pounds ordered" data whenever quantity data was used, rather than the

actual "pounds sold" data. The reason for this stems from the fact that

in this chapter the data were aggregated by species over the five stores.

Each store had data missing, which meant that a five-store aggregate on

24

those weeks could not be calculated. Since, those occasions for each store

did not always overlap with other stores, only fifteen weeks of useful

data were available. It had been determined that the meat manager's es-

timates of how much should be sold was close enough to what was actually

sold to make the pounds ordered figures a useful approximation of pounds

sold. In Chapter 6, where the analysis was broken down by individual

stores, this problem was less acute and pounds sold figures were used.

Retail Prices

Fish prices, like other retail food prices, were administered by the

head office of the chain. The effects of this fact were immediately ap-

parent by the lack of week to week fluctuation in the prices for fresh

fish (Figure 5-2) . These retail prices were established by applying a

fairly constant markup to a mildly fluctuating wholesale price. Normally,

the retail price from the previous week was not changed unless the whole-

sale price had changed by at least three cents. The one or two cents

fluctuations which occurred frequently in the wholesale price did not

usually result in a changed retail price.

When information from both Figure 5-1 and Figure 5-2 was combined,

some evidence developed for suspecting a slightly higher level of demand

for fish in the late winter and early spring than at other periods of

time covered by this study. Obviously, the existence of seasonal shifts

in demand cannot be established with less than one year's data. However,

it is interesting to notice that the aggregate curve of Figure 5-1 is

somewhat higher after mid-January (week number 29) than before, and with

26

exception of halibut, prices tended to be somewhat higher also (Figure 5 2),

indicating that demand may have shifted upwards.

For instance, the price of haddock increased about ten cents, from

a normal range of $.69 and $.75 for the last half of 1967, to a normal

range of $.79 to $.89 and even $.99, briefly, in the first few months of

1968. Flounder prices made a similar increase from a general level of

about $.79 in the last half of 1967 to $.89 and $.99 in the early months

of 1968. Swordfish also increased, but fresh swordfish was not always

available, and it is difficult to say exactly how the fresh price would

have acted had any been available.

Fresh swordfish was available only until about the middle of Novem-

ber, after which the frozen form of the species was sold. For the dura-

tion of the study the weekly frozen price was adjusted to estimate the

fresh price. Implicit in the decision to make this adjustment was the

assumption that the demand for frozen swordfish was very similar to the

demand for fresh swordfish.

Hie increase from the actual fresh swordfish price in the last half

of 1967 to the adjusted price in early 1968 was from $.95 to $1.06. The

retail price of codfish was extremely rigid at $.65 during the summer of

1967, but rose somewhat in the fall, and eventually reached a high of $.85

in the spring. Halibut had a much more rigid price structure. Its price

rose in the middle of August, 1967, but did not change again during the

study, with the obvious exception of price specials.

"''After trying several alternative adjustment procedures, and finding

only negligible differences in the results, it was decided to multiply

each frozen price by the ratio of the last fresh price observed in ^ the

fall of 1967 to the immediately following prozen price, and use this prod-

uct as the estimate of the fresh price.

27

The increase of prices in the spring were not particularly surpris-

ing in light of the findings of other fish demand studies [11, 24]. Most

all those conducted in the past, which were dealing with more than one

year's data, found a higher level of demand in the spring. In addition,

this is the time of the year when supplies tend to be short, as it is

difficult to fish during the months of January and February, While, ail

the species had their normal early slump, haddock was particularly in

short supply, since the landings at New England ports were down 38 per-

cent at mid-March of 1968 from the same time in 1967 [34, p. 19].

Special Promotions

Price specials, as was readily apparent from the data, were by far

the most important factor affecting sales for each of the five species.

As can be seen in Figure 5-3, the proportion of total sales accounted for

by the single, specialed species was quite considerable. Overall, these

single items accounted for 53 percent of the five-species, aggregate sales

(Table 5-3)- Broken down by individual species, there was a range from

43 percent for flounder to 63 percent for haddock.

Specials were determined with the wholesaler at least a week in ad-

vance, and the chain was given a lower wholesale price on the item to be

featured. A slightly lower markup than normal was then applied to the

lower wholesale price of the featured species, which resulted in a notice-

ably lower retail price. The relative change in price from nonspecial to

special weeks varied from species to species, as can be seen from '.ha

right-hand column of Table 5-4, but in general, the special price was

about 80 percent of the normal price.

28

cu

ucd

60 u•H ccj

<w a)mmO CD

CD

a

CD

l

CD

U

60*H

60C•HCO

-a

CD

*X3 CD

O MCD

CO cit

c

O

a)

>•H

oo o

1

29

Table. 5-3. Proportion of sales accounted for by thesingle featured species

.

Species Mean % of Aggregate3

Haddock 63Swordfish 62Halibut 44Flounder 43Codfish 44Overall 53

gj— 1 — — 1 " 1 .... —

,

These values are calculated by the following formula:

Mean % of Aggregate = Total Sales of Featured Specie sx 1Q0 ^

Five Species Aggregate Sales

They show the percent of total fish sales (for the five speciesaggregate) accounted for by the single featured species. Weeksin which no species was featured were omitted from the calcula-tions .

Table 5-4. Relative importance of special and

nonspecial prices by species.

Species

Mean specialPrice

$

Mean nonspecialPrice

$

Special Price as %

of Nonspecial Price

%

HaddockSwordfishHalibutFlounderCodfish

.56

.80

.68

.65

.59

.79

1.00.75

.83

.70

71

80

90

78

84

30

When price-quantity relationships were plotted, such as in Figure 5-4,

the importance of price specials became more obvious. For three of the

species, haddock, flounder, and cod, there was a clear break between the

special and nonspecial prices. With swordfish and halibut there was some

overlap between the two types of price. Even here though, there tended to

be two clumps of prices— one clump of high, unadvertised prices, and another

of low, advertised prices

.

With the exception of halibut, there was also a clear break quantity-

wise between the two clumps. Much larger quantities were sold when a spe-

cies was offered on special.

One thing to keep in mind when looking at these data is that the two

clumps do not show the same thing. Both are plotted as price-quantity

relationships, although the effects of other factors are also reflected in

the data. The variables from which most of these effects originate are

unknown, but it is known that the lower clump has the additional effects

of newspaper advertising and in-store promotion built into it, whereas

the higher clump does not.

Newspaper advertising for fish was merely a small part of a larger

store advertisement and informed the public that a certain species would

be sold at a lower price in the week of the advertisement. Although fish

was relatively unimportant compared to some other meats , the specials

might have drawn some customers from other stores. Likewise, in-store ad-

vertising was not expected to be a major demand shifter, but it too must

have had seme effect on attracting shoppers 1 attention to the lower price.

Promotion of this sort normally consisted of a poster above the fish dis-

play which stated which species was being featured and the price.

I

Figure 5-4.

Individual Price-Quantity Ordered Relationships

31

Retai]Price /Pound

C

100

90

80

70

60

50

40

A

Haddock

o c

©©

©© ©o ©

to €5© ©

© ©©

0 100 200 300 400 500 600

Quantity OrderedPounds

700 800 900 1000

RetailPrice /Pound

100

90

80

70

60

bO

40

© oc.'.'oo © o

© © ©c\:c:3&© ©

©o

B

Swordfish© ©

0 100 200 300 400 500 600Quantity Ordered

Pounds

'TK, 800 900 1000

Figure continued on next page

32

RetailPrice/Pound

C

J 00 L90

80

70

60

50

40

100

c

Halibut

300 400 500Quant i ty Ordered

Pounds

900 1000

RetailPrice/Pound

c Flounder

100

90

80

70

60

50 I

40

<j O CO

CO

4\ I- ,. -

0

>v

100 200- (i

300 A00 500 600 700


800 900 1000

Figure continued on next page

33

Re!tailPrice/Pound

<?

100 L90

806

~& OO Ci*

70

60

50

40

L.0 100

Flounder

200 300 400 500 600 700


800 900 1000

34

The effects of competitive species on the quantity of haddock sold

was also of some Interest in this study. It might be expected that when-

ever another species was offered on special, sales of haddock would suf-

fer. Apparently this did not occur. The figures in Table 5-5 show that,

of those observations when haddock was not offered on special3less was

ordered when no species was specialed than when one of the others was on

special. Thus, if specials on other species affected the sales of haddock

at all, it would appear that they increased them.

Table 5-5. Effect of specials of other species onpounds ordered of haddock.

Numberof weeks

Average Poundshaddock ordered

No Species on Special 15 231

Some Species on SpecialSwordfish 5 262

Halibut 9 224

Flounder 6 265

Cod 1 280

All 21 247

Summary

In summary, the primary item of importance noted in this chapter was

the strong effect of price specials on the sales of specific species of

fish. The effect of these price specials was by far the most important

factor affecting the quantity sold of any rpecies. Price fluctuations

within the normal range may have had some effect, but the exact nature

was difficult, if not impossible, to discern without using a more sophis-

ticated technique than that followed in this chapter.

35

CHAPTER VI

REGRESSION ANALYSIS OF FRESH FISH SALESFOR FIVE LEADING SPECIES

This chapter reports the theory and results of multiple regression

analysis used in an attempt to refine the relationships among the vari-

ables. Emphasis was placed on deriving a demand function for haddock.

Unlike the last chapter, separate functions were calculated for each

store. The dependent variable for these equations was expressed in ad-

justed pounds sold figures instead of the previously used pounds ordered

data.

Theoretical Considerations

Simultaneous equations . A multi-variate regression model can be ex-

pressed as either a single-equation model or a multi-equation model. While

consideration was given to the use of simultaneous equations in this study,

the single-equation least squares technique was finally adopted. Simul-

taneous equations are necessary when explaining a set of simultaneous oc-

currences . In terms of econometrics , this occurs when there is more than

one variable whose value is determined within the system, i.e., more than

one endogenous variable. There must then be a separate equation for each

of these mutually dependent variables, since each is a dependent variable.

If, as in the situation encountered here, the model can be specified with

just one ex. ^ ogenous variable there is no need for a simultaneous system

[10, p. 432].

Assumptions of regression . Certain assumptions must be recognized

when a regression model is used. First, it is assumed that the values

36

of the error term of the regression are randomly distributed with a mean

of zero. Second, it is assumed that the variance of the error term is

constant. This assumption of homoscedasticity can be stated differently

by saying that the values of the error term do not increase or decrease

as the value of any independent variable increases or decreases. A third

assumption is that the values of the error term are independent of each

other. If they are not, then there is a problem of autocorrelation.

Fourth, if linear regression is being used, it must be assumed that the

true relationship is linear.

Two additional assumptions are often made also. One of these is that

each of the independent variables and the values of the error term are in-

dependent of each other. This is most easily accomplished if the values

of the independent variables are constant from sample to sample [31, p. 26]

The second states that the error term is distributed normally. If

all the previous assumptions are met, the regression coefficients and the

standard error of estimate are efficient and unbiased estimators. This

final assumption assures the validity of the standard tests of signifi-

cance.

Demand equations are oftentimes expressed in logarithmic form, as

this greatly simplifies the task of calculating demand elasticities. When

expressed in this form, the coefficients of the variables are the elastic-

ities, so they can be read straight from the equations. Certain additional

assumptions must be made, however, to justify the use of logarithms. For

instance, it must be assumed that the true relationships of the variables

are multiplicative rather than additive. It must also be assumed that

the relationships are more stable when the variables are expressed in per-

centage terms rather than in absolute terms. In addition, the unexplained

37

residuals must be assumed to be more uniform over the range of independent

variables whan expressed in percents rather than in absolute terms [12,

p. 37].

Identification problem . A common problem with demand studies is the

identification of the demand function. Particularly in single equation

models, it is often impossible to be certain that the estimated curve is

a demand curve rather than a supply or a mongrel curve [36, p. 104]. If

it can be assumed that demand does not shift over the course of the study,

and it is known how supply shifts, then the estimated curve can be iden-

tified as a demand function.

The identification problem did not cause difficulties in this study.

Data were collected over a forty-two week period, too short to expect:

changes in tastes and preferences, population or other such demand shift-

ers to measurably affect demand. Thus, it has been assumed that demand

did not shift throughout the course of the study- In addition,, shifts

in supply were known. As described previously, the retail price was es-

tablished on a weekly basis by the head office and was not changed within

a week. Consequently, the slope of the supply curve equaled zero." indi-

cating that the weekly supply curves were horizontal straight lines

(S-l,S2, . . . ,85 in Figure 6-1) at the relevant prices. They do not extend

to infinity, however. At the established price each week, the meat man-

agers attempted to estimate the quantity that would be demanded and ordered

I

38

Figure 6-1. Theoretical representation of the supply- demand situation

Price

D

—— Quantity

39

that amount. This sum of the two weekly orders set an upper limit to the

quantity made available to consumers. Thus, as shown in Figure 6-1, there

is a cutoff point for each of the supply curves (Tj , T2 , . .. , T5)

.

For each week there is also a demand curve relating prices and quan-

tities. At the specific price established on that week, the quantity

which was demanded can be read off the demand schedule. If the manager

estimated correctly when ordering the speciessthe quantity demanded 00-

incided exactly to the quantity he ordered. This situation is illustrated

by the intersection of supply and demand at (P^Q^). If the actual quan-

tity demanded fell short of the manager's expectations, the demand curve

would intersect the supply curve at some point to the left of the quantity

ordered (P2 >C>2 Q/t

^5^5) • *f tne quantity demanded was greater than

the manager's expectations, the demand curve would intersect the hypo-

thetical extension of the supply curve to the right of the quantity or-

dered at (P1 ,Q1

)

.

Connecting all these intersection points of the individual supply

and demand curves yields the curve UD. Since the supply curves are per-

fectly elastic, the curve DD can be identified as a demand curve, even

when estimated 'by a single equation model.

The Model

Functional relationships. Variables considered important and capable

of being w isured were expressed in a function as follows:

Y - f(Xi,X2> X3P,X4 ,X5

,X6,X7

,X8,X

9,D

l5Sl9D2j S 2 )

Where:

Y = The quantity, in pounds, of haddock purchased by consumers.

X3 = TimeX? - Retail price/pound of fresh haddock fillets.

40

= Retail price/pound of fresh flounder fillets.X, = Retail price/pound of swordfish steaks.X^_ = Retail price/pound of halibut

= Retail price/pound of fresh codfish fillets.Xy = Total store sales.Xg - Quantity, in pounds, of shellfish sold.Xg = Quantity, in pounds, of other finned fish sold.

D-jl- Dummy variable for haddock price specials.

D-^ = 0; No price special.= 1; Price special.

S-j_ = Slope dummy variable for haddock price specials. It equals theprice of haddock that week (X2) times the dummy variable (D^)

.

S^ = 0; No price special.S-^ - X2; Price special.

T>2 - Dummy variable for a price special on any of the other fourmajor species.

D2 = 0; No price special.D2 = 1; Price special.

S2 = Slope dummy variable for price specials of any of the fourmajor species other than haddock.

S2 = 0; No price special,S2 " Percent deviation from the mean price for the past

four weeks; Price special.

Other variables that may be substitutes for fish in the market include

other meat items and prepared frozen, fish items . However, there was no

basis for determining which of these items to select and which to omit.

In addition, statistical problems arise as the number of variables ap-

proaches the number of observations.

Des cript ion of -variables . All variables were expressed as weekly

observations. The dependent variables were expressed in pounds sold,

and were adjusted from pounds ordered figures taken from store receipts.

Weekly store forms (See Appendix B) filled out by the meat managers were

used to determine how much of each species was left over each week, or

if the store ran out of a given species. On those occasions when fish

was left over, the excess quantity was subtracted from the amount or-

dered to obtain the quantity sold. When the store ran out, the time

that it ran out, taken from this form, was combined with information

about the normal intensity of sales from the manager questionnaires to

estimate the amount of sales that should have been made. These adjusted

quantities would fall on the weekly demand curves and are analogous to

the quantities Q1 ,...,Q5in Figure 6-1. For the relevant days of the

week, primarily Fridays, but also Wednesdays and Thursdays for some

stores, the rate of sales was broken down into three hour periods (see

Appendix A, part B3) . Within these three hour periods a constant rate

of sales was assumed. Although these rates of sale were only the man-

ager's estimates, it was felt that they would provide a more realistic

estimate than that which could be obtained by assuming the rate of sales

was constant throughout the week. With this information, only a simple

mathematical calculation was required to obtain the quantity sold. The

number and mean size of adjustments for each store were quite variable

as can be seen from Table 6-1.

Table '6-1. Haddock adjustments for five stores.

No. of Weeks AverageTotal Wjth Adjustments Net Adjustment

Stores No . Weeks Runout Surplus lbs .

A 36 4 6 13.0

B 24 8 11 13.1

C 27 1 20 11-2

D 30 0 13 9-5

E 25 . 3 19 5.9

Time was introduced into these equations simply to see if the higher

level of prices in the spring, noticed in the preliminary analysis, had

any significant effect. The variahle was given values by consecutively

numbering the weeks in which data was collected.

The retail prices used as independent variables in the equations were

either the price of the species under consideration, or were the prices of

close substitute products. Swordfish, halibut, flounder and codfish were

selected as substitutes of haddock because they were displayed next to

each other in the same meat case, and they all sold in relatively large

quantities. The prices for haddock, flounder and codfish were used di-

rectly as quoted from the chain. This could be done because the fresh

form of each of these species was sold throughout the year.

Such was not the case for swordfish, however. Fresh swordfish was

available from Ju]y through mid-November. For the remainder of the study

period- only the frozen form of the species were available. In order to

use all the data it was necessary, therefore, to adjust the frozen sword-

fish price to obtain a fresh price equivalent . The procedure fol lowed

was to multiply each frozen price by an index of the last observed fresh

price divided by the first observed frozen price. Since the index yielded

a value slightly greater than one, the fresh price equivalent was slightly

higher than the frozen price, as would be expected.

Adjustments were made to the halibut price a] so, but for a different

reason. Two forms of halibut were sold at the various stores included in

this study — fillets and steaks. Depending on the particular store,

either one or the other, or both taken together were important. To have

halibut included in the study, it was necessary to combine the two forms

43

and use just one price for both. This price was calculated by taking a

weighted average of the prices for the two forms each week. The weights

used were the mean pounds sold of each form over the course of the study.

Each store was weighted separately. On weeks when one or the other form

of halibut was not sold, the mean price for that species was weighted.

Other finned fish species were also sold, but either they were avail-

able on a sporadic schedule, or else they were not sold in all the stores.

They were accounted for by the finned fish variable in the equation. Since

the same species were not sold from week to week, it was felt to be im-

proper to construct a price index for this variable. Consequently, the

total quantity of all the other finned fish species was used as a vari-

able in the equation in the hopes of explaining some of the variation in

the dependent variable. A shellfish variable was constructed in a simi-

lar manner and for the same reasons.

Total store sales were included in the equation as an indicator of

customer volume and purchasing power. It seems logical that when more

customers are in the store, more fish is likely to be purchased. Since

variation in the dependent variable caused by this factor could not be

considered random, this variable was introduced into the equation.

Four dummy variables were used to distinguish between price special

and nonspecial observations. They were used to check for changes in both

the constant term and the structure of demand. If there had been enough

observations, the same information could have been obtained by running

separate equations for the special and nonspecial situations. However,

44

in this study, there were not enough observations to run separate equa-

tions for weeks when there were specials. Some stores had as few as •

four or five price special observations to explain eight variables,

which is impossible.

The first haddock dummy variable, Dj, was used to detect any change

in the constant term resulting from the effects of promotion in price

specials. In a simple regression model, the constant term is the Y-inter-

cept and it may be easier, conceptually, to think of it in this manner.

If the coefficient of this zero-one variable is not significant when tested

by the Student's t-test, then no change is indicated in the Y-intercept

as a result of price specials. If the coefficient is significant, then a

shift is indicated. This variable then, is useful only in detecting change

in the level of a regression line. It says nothing at all about the slope

of the line. Of necessity it assumes the structure of demand (slope of the

curve) to be constant.

In order to test for changes in the structure of demand, or in terms

of simple regression, the slope of the curve, a different type of dummy

variable was constructed. The one used in this study, S-^, was discussed

in Goldberger's book [15, pp. 224-225] and is in fairly common usage. It

was constructed by multiplying the price variable, in this case the price

of haddock, by either zero or one. In this study, an appropriate zero-one

variable was already available, D]_, so it was simplest to think of multi-

plying the haddock price by this dummy. The result of this process was a

dummy variable with the values of either zero or the price of haddock.

If the coefficient of this variable is significant, it indicates a struc-

tural change in demand; if the coefficient is not significant, no change

i

in the structure is apparent.

The other two dummies in the equations xêre based upon the same con-

cept, but were used to check for differences in either the constant term

or in the structure of demand resulting from price specials of any of the

other major four species. Ideally, two dummies would have been used for

each of these other prices, but this would have introduced too many vari-

ables into the equation. Therefore, one set of dummies was used to test

the general effects of price specials on competing species.

The only major difference in the construction of these two variables

occurred with the slope dummy. Since prices for four species, instead of

one, were involved, the variable had to be expressed in some sort of stand-

ardized units. To obtain the values for this variable, a mean price for

the species on special was calculated over the previous four weeks for

each store. Then the deviation of the current week's price from this mean

price was calculated. The actual value used as data was this deviation

expressed as a percent of the mean price. By using percentage deviations

the data were expressed relative to some base-- the general level of that

price. Its use, instead of the use of absolute deviations in cents, as-

sumed that consumers would respond more, strongly to a ten cent decrease

in price on a species that was normally priced at fifty cents a pound than

to the same decrease in price on a species that was normally priced at

eighty cents a pound.

Expected results . Some preconceptions could be formed about the re-

sults of the regressions before the equations were run on the computer.

The most: obvious was the expectation of a negative relationship between

the quantity of haddock consumed and its retail price. In addition, from

46

the results of previous studies, it was expected that demand would be

price elastic. Since the other species in the equation were competi-

tive with haddock, it was expected that their prices would be positively

related to the quantity of haddock consumed. As the price of one of

these competing items rose, consumers would be expected to switch to

relatively cheaper substitutes, such as haddock.

The signs of the shellfish and "other" finfish variables were ex-

pected to be negative, however, since these were quantity variables.

The species aggregated into these variables were also assumed to be com-

petitive with haddock, so as greater quantities of them were consumed,

less haddock was expected to be consumed.

A direct relationship was expected between total sales and the

quantity of haddock consumed, since this variable was a measure of the

volume of customers and their buying power. As either volume or buying

power increased, it seemed logical to assume that more haddock would be

purchased.

The two haddock dummy variables were expected to have positive signs

because of the. way they were expressed. Both had a zero value when there

was no price special, and either a one or greater value when there was a

special. Since their value was greater when there was a special, and the

quantity consumed was also greater when on special, a positive relation-

ship was expected. The other two dummies were just the opposite. Again,

the values were zero for the nonspecial situation, and one or greater for

the special situation, but this time the specials were for competitive

species. Consequently, when one of these species was offered on special

a greater amount of it was sold and it was expected that a smaller amount

of haddock would be sold. The sign on these dummies, then, was expected

to be negative.

Procedure of estimation. Until now, the analysis in this study has

been based on aggregate data. In this chapter, an attempt was made to

analyze each store separately and then test to see whether the separate

regressions were significantly different. The coefficients for the re-

gression equations were calculated by using a stepwise regression pro-

gram on a CDC 3600 computer at the University of Massachusetts Research

Computing Center. The particular program used was one of the Bio-Medical

programs, originally developed at UCLA, then adapted to the University of

Massachusetts facilities. With this program, independent variables are

added one at a time in a stepwise manner. At each step the variable with

the highest F-value of those variables not yet in the equation is entered.

No more are added when, of those variables left, none has an F-value above

a minimum value specified in the program. At each step the coefficients

of the regression equation are completely recalculated; they are not

merely modified from the previous step.

Since separate regressions were calculated for each store, some means

of statistically testing them for significant difference, or lack thereof,

was necessary. Chew's test for equality of sets of coefficients in two

linear regressions was selected for this purpose. Unlike other possible

tests, this one tests the whole regressions, rather than each individual

coefficient. It does, however, only test two equations at a time. Since

there are five stores, with an equation for each, a minimum of four com-

parison tests should be run to see if stores B, C, D, and £ are statis-

tically the same as store A. If one or more were not the same, it is

48

possible that the test would have to be run as many as ten times before

each store would be tested against each other store.

The compulations for the Chow test are fairly simple, and the nec-

essary information is easily obtainable from the computer output. For

the purposes of this study, the test can be described in the following

manner [18, p. 137]

:

Q2 /m+n-2k

where:

Q-j_= Sum of squared residuals from the pooled equation.

Q2~ Sum of squared residuals from two separately computed equa-

tions.

Q3 = Qx - Q2k = The number of independent variables.m = The number of observations in one sample.n = The number of observations in the other sample.

Once calculated, t?iese F-values can be compared to table values in the

normal manner to test for significance.

Equationa l f orms . Some preliminary work was done with the variables

in logarithmic form when the regressions were first run. There was some

doubt that the data fit the assumptions, however, and when it was found

that higher coefficients of determination were obtained with the data ex-

pressed in absolute terms, further experimentation with the logarithmic

foxms was discontinued.

Results

Several variations of the linear and additive form of che equations

were tried, although only a fexv- will be discussed here. They were: (1)

all variables allowed to enter the equation freely if they met the re-

quirements of the stepwise procedure., (2) price of haddock forced to

49

enter, and all the consistently insignificant variables omitted, (3) had-

dock slope dummy and all the consistently insignificant variables omitted,

(4) both haddock dummy variables plus the consistently insignificant vari-

ables omitted, and (5) only the nonspecial data used with the consistently

insignificant variables and dummies omitted. The remainder of this chap-

ter will be devoted to explaining each of these forms more fully.

Model number 1: All variables included . When all the variables were

allowed to enter the equation freely, high R !

s were obtained, as can be

seen from Table 6-2. These coefficients of determination were adjusted

for degrees of freedom and ranged from .70 to .84. They were also all

significant at a 90 percent confidence level, as measured by the F-test.

Thus, the explanatory power of the equations seems to be reasonably strong

While this is certainly of interest, the significance of individual vari-

ables is of even more importance when attempting to learn which of several

factors affect the dependent variable, and which do not.

Of the thirteen independent variables included in the equation for

store A, only the price of svordfish was significant at the 90 percent

level. Of the remaining species which were substitutes for haddock,

flounder and Halibut showed some importance, but their t-values were not

2When riot adjusted for degrees of freedom, R2 is biased upwards, i.e

it makes the equation appear to explain a greater amount of the variation

in the dependent variable than it actually does. Therefore, it was ad-

justed to tho unbiased estimator R2 , wher- R - l-(l-RZ ),(n-l) ;n = nu ,ber

n-k-1

of observations, k - number of independent variables [31, p. 80]. It was

particularly important that the adjusted coefficient of determination was

used because equations for the different stores were calculated from a

different number of observations. Therefore they had a different number

of degrees of freedom.

50

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52

significant at the 90 percent interval. The signs of the coefficients of

flounder, swordfish and halibut were all positive as expected.

The price of haddock was negatively related to the quantity of had-

dock, but its coefficient was not significant at even a 50 percent sig-

nificance level. Some blame for this lack of significance may lie with

a problem of multicollinearity among the variables. The simple correla-

tion coefficient of the haddock price with the haddock level dummy vari-

able was -.731, and its correlation coefficient with the haddock dummy

variable was -.705 for store A (see Appendix C, Table 1). Similar inter-

correlations were observed for the other stores. As a result of multi-

collinearity the standard error of each variable involved expanded. Since

the t-statistic was used to test each variable for significance, and

t- = Partial Regression Coefficient , , , . ,——— as the standard error increased, theStandard Error

t-value decreased, making it more difficult for the variable to show sig-

nificance.

The reason for this high level of correlation is not particularly

difficult to see either, if one looks at Figure 5-4A again (p. 31).

There is no overlap between the two distinct clumps of prices shown

there. Whenever the dummies have a value of zero, the haddock price

variable has a value from the higher clump, and whenever the dummies

have nonzero values, the haddock price variable has values from the

lower clump. Since this is true, and since the lowest of the high

prices is higher than the highest of the low prices, a high degree of

correlation must result. The variables are not perfectly correlated

because of the variation of prices within each of the two clumps.

53

None of the remaining variables were significant. It should be of

interest, however, to point out a recurring problem of multicollinearity

between the haddock dummy variables. The simple correlation coefficient

between them was consistently close to one, indicating almost perfect

correlation. The cause for confusion here is not particularly difficult

to see either. Both dummy variables had a value of zero when haddock

was not offered on special, and a value of either one or the special

price when it was on special. There were only four to eight observa-

tions of price specials, depending on the store, and these were the sole

basis for any variation that did occur. On those occasions x^hen the had-

dock level dummy took on a value of one, the haddock slope dummy took on

some value within a sixteen cent range about a fifty-seven cent mean. On

all the remaining observations the dummies were perfectly correlated with

each other, both having values of zero. Evidently the amount of variation

that did occur on the four to eight price special observations was not

sufficient to distinguish between these two variables.

In the regression for store B, three of the variables were signifi-

cant — the price of haddock, the price of swordfish, and the haddock

level dummy. The signs on each of these variables conformed to expecta-

tions, with the price of haddock being negatively related to the quantity

of haddock sold, and the other two variables being positively related.

The dummy variable, with a coefficient of 45.3 as compared to -1.8 for

the price of haddock and 1.3 for the price of swordfish, exerted the

greatest influence on the dependent variable.

Multicollinearity did not arise as an important problem in the data

for this store., as the simple correlation coefficient between the price

54

of haddock and the haddock level dummy at -.652 was somewhat lower than

for the other stores. There was no problem between the two haddock dum-

my variables because the slope dummy explained so little additional vari-

ation that it was not included in the equation by the stepwise procedure.

In store C, time was the only significant variable. Since this vari-

able was not significant in the equations for any of the other stores, its

importance in the equation for store C attracted some interest. The cause

lay in the data, however, as the quantities of haddock sold in the spring

were noticeably greater than the quantities sold previously from store C,

whereas there was not such a noticeable trend of this sort for the other

stores

.

Neither time nor the price of haddock were significant enough to

enter the equation for store D. Of the remaining variables which did

enter, only the haddock slope dummy variable was significant at the 90

percent significance level.

The equation for store E had similar results. Only the haddock level

dummy was significant, while the price of codfish failed to enter the equa-

tion at all.

It is apparent from Table 6-2 that some of the variables were not

significant in any of the equations. In order to salvage some degrees

of freedom these were omitted from the following models.

Jl^l!llJlHILbclLJ- : Significant variables only . This model differed

little from the previous one, except that the insignificant variable?

from that model were excluded from this one. Specifically, these were

the quantity of shellfish, the quantity of finned fish and both of the

"other" dummy variables. Time was omitted because it was not a variable

55

of major interest in this study, and with one exception had very little

explanatory power.

The remainder of the variables were retained and used in the equa-

tions of Table 6-3. These included the prices of the five major species,

which were of particular interest for the calculation of cross elastic-

ities, the haddock dummy variables, which were highly significant when

not upset by multicollinearity , and total store sales. This last vari-

able was retained because it had shown moderate importance in various

preliminary runs

.

All the equations of Table 6-3 were significant as measured by the

F-test for the whole equation at the 90 percent significance level. As

in the previous run, each of the equations showed a high level of explan-

atory power, with R2

1

s ranging from ,70 to .88. The significance of in-

dividual variables followed a similar pattern also, although not an iden-

tical one.

In store A, the price of swordfish was significant at the 90 per-

cent level again, but now it was joined by total store sales. The had-

dock slope dummy was close to being significant, but as a result of mul-

ticollinearity, was not quite.

Store B provided a much more interesting picture. In this model,

five of the variables were significant. Only the price of flounder, total

store, sales, _^d the haddock level dummy Tailed to show significance, 0re

last of which did not enter the equation. As expected, the price of had-

dock was negatively related to the quantity of haddock sold, while the

prices of swordfish, codfish and halibut were positively related. The

haddock slope dummy was also positively related.

56

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58

The equation for store C revealed only the haddock level dummy as

being significant. For store D, only the haddock slope dummy showed sig-

nificance. In the equation for store E, the haddock level dummy was

joined by total store sales, these two being the only significant vari-

ables.

Virtually no new information was gleaned from the model presented in

Table 6-3. The major issue was still that of a high level of multicol-

linearity among the haddock price and dummy variables. In an attempt to

circumvent this problem, the next model to be presented omitted one dummy

variable from those variables used in model number two.

Model number 3: Omit haddock slope dummy variable . In this model

(Table. 6-4),only the haddock level dummy was used to account for special

promotions of haddock. Either dummy could have been omitted, but the

haddock slope dummy was doing little more than describing shifts in the

level of the regression plane, so it was the one which was dropped.

The equations for all of the stores were significant, as measured

by the F-test, and all explained a relatively large portion of the vari-

ation in the dependent variable. The R f

s ranged from .70 to .83.

The haddock level dummy variable was highly significant for each of

the stores in this model, indicating that price specials had a strong

influence on increasing sales of haddock in all the stores. The remain-

ing variables used in this model reacted exactly the same as in model

number two. The variables which were significant for each of the stores

there were also significant here.

While the elimination of one dummy variable solved the greatest mul-

ticollinearxty problem, there still existed a problem of this nature betvecr

59

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61

the price of haddock and the haddock level dummy. When the haddock price

variable, was forced into the equation first, it was highly significant.

Upon the entrance of the haddock dummy variable, however, its coefficient

would diminish considerably while its standard error would diminish rela-

tively little, yielding a much smaller and sometimes insignificant t-valu

If the dummy entered first, and the price of haddock entered later, the

dummy's standard error would increase by two- or three-fold in many cases

While this was not enough to cause the dummy variable to become insignifi

cant, it did indicate a continuing problem of multicollinearity . Conse-

quently, both dummy variables xêre omitted from the following model.

Model number 4: Omit both dummy variables . With both dummy vari-

—

o

ables omitted, the R s for the equations dropped to the 50 percent range

but all of the regressions were still significant (see Table 6-5). For

the first time, the haddock price variable was significant in each of the

equations. This was to be expected, however, since this price variable,

also accounted for the effects of price specials in this model. By elim-

inating the dummy variables from the equation and fitting all the data,

the effects of promotion were completely ignored. Inherently, it was

assumed that trie large jump in quantity consumed, between special and non

special observations could be completely explained by the change in the

price level. Logically this argument is weak, but statistically it is

sound

.

For stores B and E the additional variables which were significant

at the 90 percent significance level in this model were the same as in

the previous two models, with the exception, of course, of the dummy

variables. In the equation for store A the price of halibut became

62

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64

significant in addition to the price of swordfish. The equations for

stores C and D were, the ones which changed the greatest. The prices of

flounder, swordfish and halibut were significant at store C, whereas pre-

viously none of these had shown significance. Onl^ the price of flounder

and the price cf swordfish were significant in store D, while previously

neither of these had been significant.

Since this model produced potentially useful results and did not have

any problems with multiccllinearity , it became necessary to test for auto-

correlation among the residuals. For this purpose the d-statistic was

calculated and tabulated in the last column of Table 6-5. This was used

in the Durbin-Watson test to check for autocorrelation. The results from

this test indicated positive autocorrelation did exist in each of the

equatd ons

.

The. presence of autocorrelation does not bias the least-squares esti-

mators, but it does cause their standard errors to be underestimated. Thus,

in equations with autocorrelated residuals, variables will appear to be

significant when in actuality, they are not. Consequently, it is quite

possible that some of the variables with the smaller acceptable t-values

in model number 4 were actually insignificant.

Despite this problem, both price and cross elasticities of demand

were estimated for each of the equations (see Table 6-5). In each case

the price elasticity for the price of haddock was both negative and

greater than one, indicating an elastic demand for haddock as expected.

The cross elasticities calculated for those substitutes which were sig-

nificant were always positive and greater than one. Thus, it would ap-

pear that for each one percent increase in price of a substitute species,

65

if there was any effect at all on the quantity of haddock consumed, it

would increase by an amount greater than one percent. Judging roughly

from the elasticities obtained here, changes in the price of halibut had

the greatest effect on haddock, while the effects of flounder, swordfish

and codfish all seemed to be about the same.

A theoretical problem existed with this model also, the objection

being that no account was taken of the effects of newspaper advertising

and in-store promotion separate from the effects of large price reduc-

tions. However, with the data which was available it was impossible to

separate these effects, since there were no observations of extremely

low prices without promotion, nor were there any observations of high

prices with promotion. Thus, while price specials were clearly the most

important factor affecting sales, no conclusion could be reached as to

whether this was due mainly to a price effect or a promotion effect. Be-

cause of the statistical problems all of these effects had to be gathered

into one variable, either a price variable or a special promotions vari-

able, In this model a price variable was selected.

Model numb er 5: Separate special observat ions. One way of c i rcum-

venting the problem with the dummy variables is to construct separate

equations for the special and nonspecial situations. As has been pre-

viously explained, there were not enough observations of the special

situation to do this, but there were enough nonspecial observations, by

the time some of the variables were dropped, to attempt fitting a curve

to them (Table 6-6). When this was done, only stores A, B , and C showed

any significant variables at the 90 percent level (Table 6-6). In store A

66

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68

the price of swordfish was the sole significant variable. In store B

,

the prices of haddock, swordfish, codfish, and halibut were all signifi-

cant, while in store C the prices of swordf ish and codfish showed signi-

ficance. As would be expected, the competitive species were positively

related to the quantity of haddock, and the price of haddock was nega-

tively related.

The equations as a whole for three of the stores were not signifi-

cant at the 90 percent level when tested by the F-statistic, The overall

regressions for stores B and C were significant at this level. It is in-

teresting to notice the range on the adjusted coefficients of determina-

tion for these equations too— from 0 for store E to . 82 for store B.

From this information it would appear that the prices of haddock and of

major competing species—swordfish, codfish, and halibut—were more capable

of explaining the variations in the quantity of haddock consumed in store B

than in any of the other stores.

The d-statistic was also calculated for each of the equations in

Table 6-6. At the five percent level, stores D and E showed no sign of

autocorrelation. Stores A, B, and C may have had positively correlated

residuals, but' the calculated d-statistic fell within the inconclusive

range of the test values.

Additional comments « While it was stated that the purpose of this

chapter was to analyze each of the stores separately, and then test them

for homogeneity by Chow's test, this became impossible by the lack of any

function common to all stores. Only store B showed any promise for ob-

taining a useful, multiple relationship. Several factors seemed to con-

tribute to this situation. The primary one was the problem of multicol-

linearity among some of the variables, most notably the haddock dummy

69

variables and the price of haddock. There were moderate levels of inter-

correlation between the prices of haddock and codfish in some of the stores

also. This relationship was true of store B too, however, so it does not

account for BT

s more desirable results..

Another one of the problems contributing to the general inconclusive-

ness of the regression analysis resulted from some species not being sold

during every week. For instance, in stores C and D, there were over forty

occasions when at least one of the four major competing species was not

sold (Table 6-7) . Ideally such weeks would be dropped from the analysis,

and the regressions would be run only on those weeks when data was avail-

able for each of the variables in the equations. Had this procedure been

followed, however, there would have been very few weeks of usable data for

many of the stores, and statistical analysis would have been impossible.

Table 6-7. Number of weeks particular species were not sold.

Total number Number of weeks the species was not sold

S tore observations Swordfish Flounder Codf ish Halibut

A 36 1 9 5 5

B 24 5 5 1 0

C 27 10 12 5 15

D 30 9 8 22 8

E 25 7 2 0 1

Sum. 32 36 33 29

70

An alternative method of handling the problem, and the one chosen

for this study was to use the mean price of a species whenever it was

not stocked. Since the least-squares technique works with deviations

from the mean, use of the mean price rather than any other price mini-

mized the bias introduced into the analysis. If the mean price was used

infrequently relative to the total number of observations, this technique

would have had little effect on the final outcome, beyond slightly reduc-

ing the explanatory power of the variables involved. On the other hand,

if it was used extensively, as it was for some stores in this study, this

technique could result in a crippling loss of explanatory power.

To be specific, it can be seen from Table 6-7 that of thirty observa-

tions for store D, only eight had any variation for codfish. During the

other twenty-two weeks no codfish was sold and the mean price was used.

Similarly for store C, many possible observations were lost because of

the frequent absence of three species in the meat case. While less crit-

ical, the same situation occurs for each of the other stores too. In

summary, uhe frequent absence of some species from the meat case must

stand as one of the major problems underlying the insignificance of some

of the variables.

It is possible, for stores D and E, that factors other than those

considered in the equations were important in affecting the sales of had-

dock. When all the dummies were dropped from the equations, the F-values

for these two stores dropped particularly low, indicating that the remain-

ing variables explained very little of the variation in the quantity of

haddock. This low level of F was even more noticeable in the equations

where only nenspecial prices were used. For the first time, the R s

71

became insignificant for these two stores. At no time were the R^ !

s in-

significant for any of the other stores.

Summary of Results of Regression Analysis

Overall the results of the regression analysis were disappointing.

The purpose of running the regressions was to isolate some of the important

variables affecting the sales of haddock and to construct a demand equa-

tion for this species* Such a demand equation, to be of any use, would

have to be general enough to apply to all five of the stores. This goal

of the research was impossible to attain, since no such general function

could be obtained. Different factors affected the sales of haddock in

different stores. However, some useful information was gleaned from the

regressions

.

The most important factor affecting sales of haddock was quite ob-

viously price specials. Whereas other factors might cause some fluctua-

tions in sales of the species, if it was not offered on special it sold

approximately some standard amount, and if it was featured as a special,

that amount increased considerably, possibly by six times. Part of this

great increase in sales resulted from the lower price, and part, it is

expected, resulted from promotion. The separate effects of these two

could not be established because of statistical difficulties.

When all of these effects were combined into the haddock price vari-

able it was found that, the relationship between the price and quantity ot

haddock was negative and price elastic for all the stores.

Of the species which were competitive with haddock, it appeared that

codfish was the least important. Swcrdfish was a fairly strong competi-

tor in most all of the stores, while halibut and flounder showed signs of

competitiveness in some of the stores.

Of the five stores, store B yielded the most useful information.

More of the variables were significant in regressions on data from this

store than from any of the others. Price specials, while highly signifi-

cant, were relatively less important for this store than for any of the

others. This point was emphasized when, in Model number 5, no price

special data were used, and the data still explained 82 percent of the

variation in the dependent variable. The explanation for these results

may derive from the large proportion of Jewish people in the store's

clientele* Since the Jewish diet includes more fish than the diets of

many other ethnic and religious groups, this store stocked more varieties

of fish on a regular basis than other stores. Consequently, the frequency

of using mean prices when fish was out of stock was reduced, thus mini-

mizing one of the most troublesome data problems. Also, since fish was

a regularly purchased item of the clientele in this store, it may be that

they v/ere more conscious of the fluctuations in price and wore more apt

to vary their purchases in response to price changes.

Another possible cause of the differences between this store and the

others might be the fact that fish was sold from the delicatessen counter

in store B. There is little evidence to support this contention, however,

since store E, which also sold fish from the delicatessen counter, yielded

extremely poor results.

In store B the prices of haddock, swordfish, codfish and halibut were

all significant, indicating that these latter three were substitutes for

haddock. Only halibut and swordfish were competitive with haddock in

store A. In store C, flounder, swordfish and halibut were competitive;

and in store D flounder and swordfish were competitive. Store E was the

other store which sold fish from the delicatessen case, but none of the

species appeared competitive with haddock-

Some work was done with both swordfish and flounder as dependent

variables, but the results were even less conclusive. The data prob-

lems discovered with haddock became even more difficult to handle with

the fewer observations available for the other species.

74

CHAPTER VII

SUMMARY AND CONCLUSIONS

The primary objective of this study was to improve the state of

knowledge about consumer demand for specific species of fresh fish. A

major part of this goal involved the construction of short-run demand

curves for these species and the derivation of elasticity estimates from

them. To a certain extent, the primary aim has been realized, but little

was accomplished in the way of constructing statistically and logically

sound demand functions.

Data were gathered on haddock, flounder, swordfish, codfish, and

halibut from five stores of a single, case study, food chain in western

Massachusetts. Other seafood items were also considered, but these were

aggregated into either a finfish or a shellfish variable. Some consid-

eration was also given to differences in sales when a species was offered

on special. Data were collected for forty-two weeks, from July 196?

through April 1968.

Overall, considering both sale and nonsale weeks for all species, it

was found that haddock was sold in the greatest quantities. On the aver-

age. it also provided the highest total revenues, although there was less

disparity here than with the quantity. A close second in both categories

was swordfish. When weeks of price specials only were considered, sword-

fish replace*! haddock as the sales leader. Following a few pounds and

many dollars behind swordfish were halibut and flounder. Fifth in both

pounds sold and revenue was codfish. Other species of fresh fish were

sold, both salt- and fresh-water, but there was a very distinct break

75

between even codfish and these species. At most stores they were sold

sporadically, and at two, not at all. Fresh-water species of fish were

particularly prominent at the store with a large Jewish clientele.

From a general type of analysis it was determined that price spe-

cials were highly important in affecting the sales of any species. When-

ever an item was featured, it sold at least three times as much, and up

to five or six times as much quantity as was sold in nonspecial weeks.

Data problems prevented a detailed breakdown of the factors causing this

large increase in sales. Factors that most likely had a major influence

were the lower price, newspaper advertising, and in-store promotion. Since

both newspaper advertising and in-store promotion were minimal, it is sus-

pected that much of the increase was caused by the lower price, but no

numerical value could be placed on any of these "factors.

A number of models were tested in an attempt to construct a haddock

demand equation. Some of these were logarithmic functions, but linear

functions were found to give better results and are the relationships

reported. Equations were constructed for individual stores, but , since

each one had a different combination of statistically significant inde-

pendent variables 3 they could not be combined to form a meaningful gen-

eral haddock demand function. In general, high R T

s were obtained for

these individual store equations as long as price special data were com-

bined with nonspecial data, and the regressions were run on these, con-

glomerate data. Attempts to separate the effects of promotion and low

price by the use of dummy variables failed because of severe multicol-

linearity problems. Regressions calculated on just the nonspecial data

had much lower R2,

s, and not always significant ones.

76

Only store B yielded acceptable results when all the independent var-

iables of the model were included in a single equation. Most importantly,

it was the only store for which both the price of haddock and the haddock

dummy variables (for price specials) were significant in the same equation.

In addition, it was the only store exhibiting significance between the

quantity of haddock sold and prices of both haddock and competing species

when no price special data was considered. Thus, it appears that the ex-

planatory power of the prices of haddock and competing species was consid-

erably more important at store B than for any of the other stores. It is

difficult to explain this result with the information available, but the

difference in clientele may be one explanation. Most of the stores served

a mixed religious and ethnic clientele, whereas 40 percent of store B's

clientele was Jewish. Another explanation may be that the data was better

from store B. A greater variety of the important species were carried at

all times in this store, which minimized the effect of rigidities built

in by more frequent data adjustments in the other stores.

In those few equations with more than one significant variable, the

signs of the coefficients were checked, and some elasticity estimates were

calculated. Whenever this was done, both the signs and the elasticities

agreed with the expected outcome. The price of haddock was negatively re-

lated to the quantity of haddock, and the prices of substitute species were

positively related.' Demand was found to have a price elasticity averaging

about -2.9, calculated at the mean price and quantity. This figure is

slightly smaller then, but compares favorably with, estimates from other

studies, which were in the -3.5 to -4.4 range.

77

The strongest competitor of haddock was swordfish. Only in store E

was this variable not important, and in store E none of the species were

significant (in Model number 4) . Halibut was competitive in three of the

stores, while flounder was competitive only in two stores. Codfish was

competitive only in store B.

Functions for the other species were not worked with extensively, as

they had greater data problems than did haddock. No results from these

equations, beyond the general importance of price, specials, were important

enough to include in the report of this study.

Recommendat ions for further study . There were two major data prob-

lems in this study. One was the lack of a sufficient number of observa-

tions to handle all the variables, particularly with the species other than

haddock. The other was an almost complete absence of overlap between spe-

cial and nonspecial prices. As a consequence of this latter problem, the

effects of promotion during price specials could not be separated from the

price effects.

The most obvious and perhaps the only way to correct these problems

is to run a controlled study where the researcher sets the price and chooses

the weeks for promotion. In this way the price could be promoted ac all

levels and the separate effects of price and promotion could be discerned.

A useful extension of the controlled study might be to run it on a

sample of stores randomly selected from the region, instead of on just a

case study chain. This, of course, will involve the close scrutiny of the.

different pricing and merchandising practices, but if properly constructed,

it could -yield a much more powerful model for understanding the factors

affecting demand.

78

It would be useful to examine, either as a part of these studies, or

perhaps as a separate study, the effects of other substitutes for fresh

fish. Of particular interest would be other meat items, if only by grou^

:

pork, chicken, beef, lamb, etc. Processed and frozen fish items might also

be interesting to survey.

This study, while not fully achieving its aim, has pointed out some

interesting relationships, and has uncovered some problems worthy of future

development. It is a start in a relatively new field of study. Hopefully,

further research will be undertaken to carry on this beginning.

APPENDIX A

MANAGER QUESTIONNAIRE

MANAGER Q^SSTIOWNAI RE80

Placement of Weekly Order -

1, What day of the week do you oraer fish?

a« For Tuesday deliveryFor Thursday delivery

2 0 At the time you place your order do you know both tike whole-sale and retail prices?

a* Wholesale Yes Nob„ Retail Yes No

How do you decide how much of each species ta order?

Factors Considered ( indicate order in which mentioned)

a. Wholesale priceb 0 Retail priceCo Margin

•

d a Quant* sold last weeke. Special

( given species}f* Special (other species)

g« Special HolidaySeanon

Lj» ~ „_

4. Do orders go through the head office or directly to

Quality Seafoods ?

5. If orders go through the head office are &ey ever modifiedthsre? Yes No

Diatribution of S^les During the Week

1 0 Wh»t are the peak sales periods. during the week? { Days of

the week and hours}]

2 C What are the unusually slack sales periods? (Days and hours

r

81

3. Breakdown of weekly sales

indicate

Store Hov.rcs

Percent of

Weekly SalesDistribution of

Monday9 1Z

3-6

6-9

Tuesday9-12

12.-3

3-6

6-9

Wednesday9-12

12-33-6

6=9

Thursday9-i2

12-3

3-6

6-9

Friday9-12

12-33-6

6-9

Saturday9-12

12-33-6

6-9

4 0 How much might the above vary from week to week and for

what reasons?

j's the pattern different this year from past years

Yes No

82

if the store is closed on a holiday,, are sates transferred Soanother day or lost?

3i tile holiday

iff .

on Trgtrij fferyed^

Lost.

Friday _Other Bays

A dditSonal Comments

C . Carry^Qy g?

1« 30 fish ever carried over and sold in the next w-êk?

tto Fresh fish sold next week as fry oh,. Yes NoHow often (no, of weeks in a yr c )

b, Fresh fish, sold &ext week as froaen= Yes N0How often (No, of weeks)

w .

c, Frozen fish Yes Noi §

How often (No* of weeks)

2 e. le fiah that ia carried over necessarily sold the folic wing week?

Yes No__

a* If aotp when would it by sold?

3„ What is the reason for carry-over, when, it is deliberate?

Wholesale- price,

Other

4, How much e;ct:«ra is ordered with a low price? (Two week's

supply instead of one? ) Fresh Froaen,

83

U Is fish del&rered pr„ -wrapped or i« it packaged inth$ store,. ?

If not pi^-v/rc\ppr.d, in what form is it delivered?

E. Digplay

1, Linear feet of meat case allocated to fish (normally)

2* Description of location within the meat case

If the above change, indicate how often and describe the change*

How often

( No, of Weeks) PesoripHon

Space More Less

Location

Reason for the changes

Spacet

Location

Within the total amount of space used by fisha is a given species

allowed more than usual when it is on special? Yes No

A P. P E N D I

STORE FORM

85

Store

Mgr.

Date

SPECIES

—

Lbs. at

Disposed 1

Of

end of weekCarriedOver

If you run out of stock during theweek indicate the hour below underthe appropriate day(s)

.

Haddock

Cooked•

Tues . Wed

.

Thurs

.

Fri . Sat.

DressedFresh filletstroên fillets

-—. ~ —

I

Halibut

Sword fish

FreshFrozen

—.

Cod

Fresh filletsFrozen fillets

Steaks

flounder

• Fresh filletsFrozen fillets

,

All She! IfishClamsCrab meatr 1Lo d s t er s

OystersSeal lops

-

LSchrimps LS q u i d

p i a 1

All Othe.r

finned Fish

Trout,

Butterf ishSole

m

r -

:——

RETURN TO OFFICE SATURDAY NIGHT

EACH WEEK.

ATTN. OF J. FERN

L V . ..r . C L . J

PerchSalmonSalt codfish i

SmeltsWhiting

!

tot a 7 r .

APPENDIX C

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Documents

Analysis of consumer demand for selected species of fresh