Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
INTERFUEL SUBSTITUTION AND THE INDUSTRIAL DEMAND
FOR ENERGY: AN INTERNATIONAL COPARISON
by
Robert S. PindyckMassachusetts Institute of Technology
August 1977Working Paper
#MIT EL 77-026WP
This work was supported by the RANN Division of the National Science Foundationunder Grant #GSF SIA 75-00739, and is part of a larger project to developanalytical models of the world oil market. The author is indepted toJacqueline Carson, Vinod Dar, Ross Heide and Kevin Lloyd for their excellentresearch assi-sance in many aspects nof this work, to the Comr;ter ResenrchCenter of The 't'ic.mna i Breau of Eccnr c Rsearch for assistance in the comru-taEional work, and to Ernst 1lerndlt, '."Klvyn Ftess, James Griffen, and LeonardWavezman for co-=aents and suggestions.
INTERFUEL SUBSTITIrON AI.D T'E ID1;ST.AIL DEMAND FOR ENERGY:
AN INTEl'NATIONAL COPARISON
I. Introduction
Until recently most studies of production concentrated on the substitutability
of capital and labor, assuming that in the underlying production function these
factors were separable from energy and raw material inputs. Dramatic increases
in the price of energy, together with the appearance of studies such as that of
Berndt and Wood [9] which indicated that energy and capital may in fact be complement;
rather than substitutes, resulted in an increased interest in the substitutability
of energy and other factors of production. In addition, rapid changes in the prices
of individual fuels raised the issue of how rapidly and to what extent the in-
dustrial sector could substitute among different fuels. Finally, there has been
an increased concern with the growth in energy demand brought about by growth
in industrial activity.
In this paper we report on results of an econometric study of the industrial
demand for energy in a number of industrialized countries. Our objectives are to
determine the extent to which capital, labor, and energy can be substituted for
one another, and vary across time. In addition, we will attempt to measure the
extent to which alternative fuels can be substituted for one another both in the
short-run and the long-run, and estimate the total elasticities of demand for
individual fuels.
We model industrial energy demand using a two-stage approach. In the first
stage total energy demand in the industrial sector is modelled as a derived factor
demand base on a translog cost function. Factor inputs include capital, labor,
and energy; a lack of data makes it impossible to include materials as an explicit
Griffen and Gregory [34] have alreadv fitted translog cost functions to pooledinternational dota in c;d'r to ->assure easticits of sustitution for capial,labor, and energy, but that work oes not explain inter-country diffcrences inelasticities since only four observations were used for each country, and does notdeal with interfuel substitution.
input, so we must assume separability of materials from the other factors in the
underlying structure of production. In the second stage expenditures on energy
are broken down into expenditures on oil, natural gas, coal and electricity.
Here translog cost functions are again used, but we have also experimented with the
use of a multinominal logit model to explain fuel shares. The use of this two-
stage approach requires certain additional assumptions about the underlying struc-
ture of production. In particular, we must assume that the production function
is homothetically separable in the capital, labor, and energy aggregates, i.e.
first, that expenditure shares for fuels are independent of the expenditure shares
for capital and labor, and second, that expenditure shares for fuels are independent
of total energy expenditures.
The use of the translog cost function has the advantage that it permits us to
obtain relatively unrestricted estimates of elasticities of substitution and demand
elasticities. We need not a piori assume that the cost function is homothetic
(at least in modelling the demand for capital, labor, and energy inputs), and we
need not assume that the elasticities of substitution between different inputs are
all the same. Of course there are other "generalized" cost and production functions
that could be used that also impose no a priori restrictions on elasticities of sub-
stitution, and we might find that these provide tighter estimates than does the
translog function. For the time being, however, we use only the translog function.
As one might expect,' in work like this one is continually bound by data limita-
tions. For many countries there is no good data available for some or allcf the
variables of interest to us. For other countries data exists, but obtaining that
2The necessity for these assumptions is shown by Berndt and Christensen [8] and
Denny and Fuss [26]. Note that this second ass~uption of homotheticity of fuel
shares will not be violated n the use of a logit model if total energy expendi-
tures is not an explanatory variable in that model.
-For example,. the . ont'f c n and te generalized Cobb-. outzlas
function, both of wich were introued by Di:;ert [27,28]. Lau and T-.lura [44]
used the generalized Leontief production function in estimating input substitu-
tion in petrochemical refining. ZLaSnus [46] used the generalized Cobb-Douglas
cost function in estimating substitution between capital, labor, and energy inputsin Dutch manufacturing.
-3-
data can be an extremely time consuming and laborious task. These data limitations
were one of the factors that helped define and delimit the modelling approaches
used here. In particular, it necessitated restricting this analysis of industrial
4demand to a set of only ten countries. Even for these countries, however, the
quality of the data varies, and compromises had .to occasionally be made. The
data used in this study is described briefly in this report; a much more detailed
description is provided in a separate report entitled "A User's Guide to the M.I.T.
World Energy Demand Data Base."5
In the next section we outline the specifications of alternative models of
industrial energy demand, and discuss the characteristics of each specification..
Section 3 discusses some methodological issues in the estimation of industrial
energy demand models using pooled data, and describes our estimation method.
Section 4 describes some of the characteristics and limitations of our data, and
Section 5 includes the statistical results.
2. Alternative Secifications for Models of Industrial Energy Demand… -=… ~-
- - --_…=…==-==-_-=…===---====---- 7---
As explained before, our industrial demand models are based on a two-stage
approach where energy demand is explained as a factor input share, and energy ex-
penditures are then broken down into expenditures on fuels. We begin here by sum-
marizing our assumptions about the structure of production. We then review the
properties of the static translog cost function, and discuss its application to
the industrial demand model. Next we describe some alternative dynamic specifi-
cations of the translog cost function; these specifications permit non-constant
returns to scale in the short-run, with an adjustment to constant returns in the
A much less detailed model of the demand for petroleum products is being con-structed for a number of countries for whnch only partial data is available;the results of this work will be described in a forthccring paper.
5Working Paper No. MIT EL 76-011WP, M.I.T. World Oil Project, May 1976. A re-vised version of this report will appear shortly.
long-run. Finally we discuss the use of the multinominal logit model as an al-
ternative means of describing fuel shares.
2.1' The Structure of Production.
Our approach involves certain assumptions about the structure of production.
First, we assume that capital, labor, and energy inputs are as a group weakly
separable from the fourth input, materials. 6 This assumption is made necessary
by the fact that we have no data from which to construct price indices of materials
inputs, and therefore we can only estimate unrestricted elasticities of substitu-
tion between capital, labor, and energy. Second, we assume that the production
function is weakly separable in the major categories of capital, labor, and energy.
This implies that the marginal rates of substitution between individual fuels is
independent of the quantities of capital and labor. The assumption permits us to
use aggregate price indices for capital, labor, and energy inputs; in particular
to construct an energy price index that aggregates the price of the four fuels,
and to construct a price index of capital services.that aggregates different types
of capital. Finally, we assume that the capital, labor, and energy aggregates
are homothetic in their components - in particular, that the energy aggregate is
homothetic in its oil, gas, coal, and electricity inputs.8 This last assumption
provides a necessary and sufficient condition for an underlying two-stage optimiza-
tion process, i.e. optimize the mix of fuels that make up the energy input, and
6Materials includes intermediate inputs as well as non-energy raw materials. Weak
separability here means that the marginal rate of substitution between any two of
the first three inputs is independent of the quantity of materials used as an input.
This is a necessary and sufficient condition for the production function to be of
the form Q = F[f(K,L,E);M]. For a proof and further discussion, see Berndt and
Christensen [8].
7Halvorsen and Ford [37] recently used translog cost functions to.test for separa-
bility of the energy agre-ate for each of eight individual two-digit industries
in the U.S. They found sparability to hold for four of the eight councries.
8The second and third assumptions together are referred to as homothetic separability
9then optimally choose quantities of capital, labor, and energy. Equivalently
we can express these three assumptions by writing the production function as:
Q = [(f(K,L,e(F1,F2,F3 F4));M]. (1)
where e is a homothetic function of the four fuels.
If the factor prices and output level are exogenously determined, the pro-
duction structure described by (1) can alternatively be described by a cost
function that is also weakly separable, i.e. a function of the form:l0
C =G[g(PK, PL,PE(PF'PF2'P3 ' P F4QQ );P'(2)C [g( K' L' E Fl' F2' F3' F4. (2)
Here PE is an aggregate price index of energy, i.e. a function that aggregates
the fuel prices PFi' This "aggregator function" is homothetic, and thus does not
include the total quantity of energy as one of its arguments.
2.2 Use of the Translog Cost Function
Our approach here is similar to that used recently by Fuss and Waverman [31]
in estimating the demand for energy in Canadian manufacturing. We first represent
the price of energy (which is the unit cost of energy to a producer choosing fuel
inputs) by a homothetic translog cost function with constant returns to scale.
Estimation of the share equations implied by this cost function gives us the own
and cross partial price elasticities for the four fuels. In addition, the cost
function itself provides an instrumental variable for the price of energy. The
second step is to represent the cost of industrial output by a non-homothetic
translog cost function. Estimation of the share equations implied by this cost
function gives us the elasticities of substitution and the own and cross price elas-
ticities for capital, labor, and energy.
See Denny and Fuss [26].
10This was shown by Shephard [54].
-6-
It is important to point out that we could have chosen to use translog pro-
duction functions rather than cost functions in estimating elasticities. Since the
translog cost and production functions are not self-dual, different elasticity es-
timates would result, and as Burgess [11] has recently shown, the difference could
be significant. However, we choose to use the cost function since it is more
appropriate to take prices as exogenous than quantities.
11We begin by reviewing the properties of the translog cost function. The
translog cost function is a second-order approximation to an arbitrary cost func-
tion, and has the form
logC - a + aQloSQ + EacloEPi + yQQ(1ogQ)2 + gEYi+logP logPj + EyQilgQlogPi (3)
where C is total cost, Q is output, and Pi are the factor prices. From Shephard's
Lemma [54], the derived demand functions are found by differentiating the cost
function with respect to the prices, i.e. Xi = C/aP i. Thus the share equations
are given by S alogC/alogP i a (PiXi)/C, or
Si i +Yqil to Q + Yl o imi, ..., n. (4)
Since the shares must add to 1, only n-l of the share equations need be estimated.
Note, however, that the parameters a0 , Q, and yQQ are not-identified unless the
cost function itself is estimated.l
The translog production function and cost function were introduced by Christensen,
Jorgenson, and Lau [21]. Applications of the translog cost function can be found
in the work of Berndt and Christensen [7], Berndt and Wood [9], Christensen and
Greene [34], Fuss and Waverman [31], Fuss [30], Griffen and Gregory [34], Halvorsen
[36], and Hudson and Jorgenson [38]. The translog production function has been
used by Humphrey and oroney [39] and oroney and Toevs (47,48].
1 2Corbo and Meller [23] recently estimated the ranslog production function directly
(instead of the derived share of equations) using capital and labor input data indi-
vidual firrms. This llc;:.d th;cn to cst '. hethar th ! lin .....rroduction functionis really translo,, and o test for cc:petitive bhavilor.
The cost function must be homogenous of degree 1 in prices, and mu§t satisfy
the conditions corresponding to a well-behaved production function. This implies
the following parameter restrictions that must be imposed:1 3
Ca -1 (5)i iy ~j 0 (6)
iYQi
yiJ Yi i j (7)
.EiJY i Ej 0. (8)
Note that the cost function as specified so far is non-homothetic, and may
have non-constant returns to-scale. The cost function would be homothetic if it
could be written as a separable function of output and factor prices. Thus the-
following parameter restrictions can be added to impose homotheticity:
YQi =0. (9)
The cost function is also homogenous if the elasticity of cost with respect to
output (logC/alogQ) is constant. This implies the additional restriction:
YQQ . (10)
Finally, we could impose the restriction that the elasticities of substitution be-
tween all factors are equal to 1 (so that the cost function corresponds to a
Cobb-Douglas production function). This implies the additional parameter restric-
tions: Y . (11)
1 3See Christensen, Jorgenson, and Lau [21].
14 Christensen and Greene [19] define the following index of scale economies:SCE - 1 - aloC/alogQ 1 - (lQ + yqrlOQ + ZYQioPi). Note that if
SCE is positiv> (n2c-ative), thoro is incrcasing (dacra3sin,) returns to scnle.
This is a useful . - an, d has a ntural it.rprctztion in prceltagea erms.However, it can only be computed if a and yg are known (which means estimating
the cost function) or are assumed to Qbe 1 and 0 respectively... . . _ . .. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,
Rather than impose these restrictions a priori, we can test them using a
simple chi-square test. The appropriate test statistic is
-2.logA = N(loglrI - loglIUl) (12)
where IRl and %1iuI are the determinants of the estimated error covariance
matrices for the restricted and unrestricted models respectively, and N is the-
number of observations. This statistic is distributed as chi-square with degrees
of freedom equal to the number of parameter restrictions being tested.
15Uzawa [56] showed that the Allen partial elasticities of substitution can
be computed from ij CCij/CiCj, so that for the translog cost function these
are given by
-ij =(Yij + SiSj)/SiSj, i j(13)
ii= [Yii + Si(Si-1)]/Si
It is easy to show that the own and cross price elasticities of demand are given
by ynii " algXal ogPi = (iisi
(14)
riJ - BlogXi/alogP Sj S
Note that these are partial price elasticities; when applied to fuels they account
only for substitution between fuels, under the constraint that the total quantity
of energy consumed remains constant. The total own price elasticity for each fuel
rii = d logXi/d logPi accounts for the effect of a change in the price of a fuel
on total energy consumption, and is given by
i ax1 + i +aE aE (15)iiXi PiE const E aPE aP
where E'is the total quantity of energy consumed, and PE is the price index for
energy. However, since the price of energy is given by the homothetic translog
cost function with constant returns to scale:
logPE a + logPi + CilogP + iyl1 g P '(16)
which implies the fuel share equations Si Yi + Zijl°gPj' we have
See Allen [3].
16Note that expenditures on energy will not remain constant.
-9-
PE PE
-i - S (17)
aE E.
· , aPE-a E E E (18)
where'nEE is the own price elasticity of energy, and, since the energy cost
function is homothetic,
ax ax xiX i ME Xi X i
a E ME.E E (19)
where M = PE E is total expenditures on energy. Then, by substituting (17),
(18), and (19) into (15), we have
tlij T ii + EESi (20)
Similarly, we can compute the total cross price elasticity nrj from
P ax ax aE aP
'i-|const. + E aP ap li + EE (21)Xi -J E cons. E
17aud the total output elasticity from
d logXi 2_ ....T)* = oX -. (22)iQ d logQ x a? aQ
Since the energy cost function is homothetic, this reduces to
niQ - nEQ (23)
where EQ is the elasticity of energy with respect to output changes. This
17 thi s
This assumes that the value of output is equal to the value (cost).of inputs.
This would be the case under perfect competition, or under oligopoly pricingba~.d on a : ' ;:rl,.: ov---I'"33r c:,;. Or-~7.e this elasticity would
be better referre d :o a a t~'~i cz.t zi;..2. thz c.t cr.e inthe dmand for fuel i corrcspondin to a 1 percent change in the total cost
of production.
-10-
elasticity can in turn be computed as follows:
d log E d lo E. a log CEQ d log Q d log C a log Q
logE _L__o_ +logQ aiogc aLogQ
gSE lo (24)logQ alogQ
Obtaining these derivatives from equations (3) and (4), we have
~QE+ I L E (25)nEQ = SE + aQ + QQlogQ + YQilogP i (25).E ~i= K,
Since the cost function is not estimated directly, we assume that aQ and yQQ
are 1 and 0 respectively.
We would like to calculate standard errors for our estimates of elasti-
cities, but since the elasticities are nonlinear functions of the estimated
parameters (since the shares are themselves functions of the parameters), there
is no straightforward way to do this without reverting to Monte Carlo simulation.
However, we can obtain approximate estimates of the standard errors. To do this
we follow Christensen and Greene [19] and calculate standard errors under the
assumption that the shares Si are constant and equal to the means (over the esti-
mation time bounds) of their estimated values. Under this assumption we have,
asympototically,
Var(8ij)- Var(Yij )/SiS
Var (ii) - Var(Yii/S (26)
Var(Tij) -Vcr('tj)/S2
Var (l) = ar (i) / S
Finally, it is useful to calculate the elasticity of the average cost
of production with respect to the price of energy, i.e. CE = log(AC)/3logPE
and the elasticities of the average cost of production with respect to the prices
of each fuel, i.e. Ci = alog(AC)/alogPi. This will enable us to calculate the
effect of a 1 percent change in the price of energy, or a 1 percent change in the
price of a single fuel, on the cost of industrial output. We follow Fuss(30] in
calculating point elasticities for nCE and nCi. From equation (3) we have
TCE + YEEl°gPE + YEKlogPK + YELlogPL + YQElogQ (Z)
We obtain qCi from
alog(AC) al EnCi alogPE !logP i CESi (28)
Let us now review the steps involved in estimating a translog model of energy
demand. First the fuel share equations
$ i ji + jijlgP J (29)
are estimated, and the estimated parameters are used to calculate partial price
elasticities. These equations are estimated subject to the parameter restrictions
Eac 1, Y , and Zy =Zy =0 We also test the additional restrictions
YiJ O. Next the estimated values of the ci and Yij are used in equation (16) to
obtain an aggregate price index for energy. To do this the parameter aO in
equation (16) is determined so that the price of energy is equal to 1 in the U.S.
in 1970. An energy price index is then calculated for each country.
Next we estimate the- factor share equations (4), with i and j equal to
capital, labor, and energy. In estimating these equations, we use our estimated
aggregate price index for energy as an instrumental variable; We estimate these
equations in stages, imposing additional parameter restrictions at each stage,
and testing each set of restrictions. In the first stage we impose only the
restrictions implied by neoclassical production theory, i.e. Ea = 1, YQi 0,
Yij - Yji' and 0ij s Yij . Next we add the homotheticity restrictions YQi= O.
Finally we test the restrictions that ij O, i.e. that the elasticities of
substitution between all three factors are equal to 1.ig
t
2.3 Dynamic Versions of the Translog Cost Function
A problem with the translog cost functions described above is that they
do not describe differences between short-run and long-run elasticities, or
how the adjustment to the long-run takes place. It is reasonable, for example,
to expect that in the long-run the aggregate production function exhibits
constant returns to scale, but that it exhibits non-constant returns in the
short-run. Our objective here is to specify a dynamic translog cost function
that permits adjustment to constant returns over time.
Constant returns requires that aQ P 1, YQQ 0, and YQi 0 ° in equation (3).
One way, then, to build in an adjustment to constant returns in the long-run is
to make these parameters functions of changes in output or prices. For example,
the parameters aQ and yQQ could be specified as:
K
a = exp[O l(AQt-k) (30)
Kand yQQ 02klX (AQtk) 03 (31)
Here the parameters 81, 2 and 03 are estimated. If 83 is not equal to zero,
then non-constant returns can exist even in the long-run. Thus if long-run
constant returns is taken as given a priori, the estimate of 83 (i.e. whether
it is significantly different from 0) provides a test of the correctness of the
kspecification of the lag distribution. The lag distribution parameters Xk and
Xk could be estimated if the data permitted or they could be specified a priori
We will also test restrictiocn: pertaiinc. to tea ch:ractcristics of inter-cot..try
diffrecnces in the cost functicn. This !..:o1vxs tha ue o du'.y vari'lcs th:'permit some of the parameters of the translog cost function to vary across countries.
This is discussed later.
(perhaps declining linearly). In either case K might be 3to 5 years. Of course
estimation of the parameters in (30) and (31) requires that the cost function (3)
be estimated simultaneously with the share equations (4).
The parameters of YQi can also be made to adjust to zero in long-run
equilibrium by making them functions of a distributed lag in changes in prices:
K
YQi = O kQi (AlogP )-k2 (32)
Thus if the data do not permit the simultaneous estimation of the cost function
with the share equations, aQ and' yQQ could be assumed equal to 1 and 0 respectively,
and adjustments could occur through the YQi. In this case the production structure
would be homothetic in the long-run.
An alternative approach is to introduce the dynamic adjustment directly into
the share equations. This can be done by assuming that the shares adjust to a set
of desired shares as follows:1 9
,t ' s + ES (s -s it Sit-l + i(Jtjt-1 (33)
where S is given by equation (4). Adding up requires that the sum of allj,t
changes in shares be zero:
s(S - 0 (34)i t Si, t -
so that
Z6 i(S* t Sj = *t (S* 't E - S X6t-s) = o.ij J ' j
Since the St and Sj sum to one, this equation implies the necessary condi-
tion that all of the columns of the matrix (6ij) sum to the same arbitrary
constant, i.e.' c 2 ' (36)
This approach was suggested by L. averman and M. Fuss.
where is a vector of l's (ones), 6 is a matrix (6ij), and is an arbitrary con-
20stant. Note that if the number of shares is greater than two, there are alterna-
tive constraints on the ij that can be imposed to satisfy (36).
2.4 Multinomial Logit Models for Fuel Choice
Multinomial logit models have already been used to study the breakdown
of energy consumption into demands for fuels in the residential sectors of
the United States and other countries2 1 and in the industrial sector of the
22United States. Although the logit model is not based on assumptions of cost
minimization, it has properties that make it appealing for this work. The
model is consistent in terms of shares adding to one, and shares respond to
price changes in a way that is intuitively appealing; as the share of, say,
natural gas becomes small, it requires increasingly large price changes to
make it still smaller. Finally the logit model is easy to estimate and permits
us to easily introduce alternative dynamic specifications.
We follow our recent work in applying the logit model to the estimation
of residential fuel demands [53 . The logit model for four fuels can be written
as
Qi efi(xS)
Qe 4 f(37)J-1
where Qi is the quantity (in tcals) of fuel i, QT ZQi, and the fi are functions
of a vector of attributes x and vector of parameters . Given this model, the
relative shares of any two fuels can be represented as
log(Q1/Qj) = og(Si/Sj) = f(x) - f(x4). (38)
Only three equations are estimated, since the parameters of the fourth equation
are determined from the adding up constraint.
For a disc ussio n z :d .- Ir: -;i " c.s 1foe .. ore ui.era lag structures, seeWall [ ] and iernLit nd Savln [ j.
21See Baughman and Joskow t ], Fuss and Waverman [31], and Pindyck [53].22See Joskow and Baug.man [421.
-15-
In estimating fuel shares we include as attributes the relative price of
each fuel. The relative oil price, for example, is the ratio of the real price
of oil to the real price of energy, the latter being measured by the energy
price index described earlier. We do not include total energy expenditures of
industrial output as attributes since we a priori impose homotheticity on the
fuel share model. Other attributes, however, can include lagged quantity or
share variables that allow shares to adjust dynamically to changes in price.
Functional forms for the fi are somewhat arbitrary, but in the simplest model
they might be linear functions of the relative fuel prices Pi = Pi/PE, where
PE is the aggregate price of energy, and output Q:
fi(x ) = ai + biPi + ciQ .(39)
This yields the three estimating equations
log(Si/S 4) = (a i-a4) + bi b4 + (i-c 4)Q, i = 1,2,3. (40)
Note that these three equations must be estimated simultaneously, with b4
constrained to be the same in each equation.
The simplest means by which the preference functions can be made dynamic
(e.g. to account for stock adjustments) is to include the lagged share:
fi(xB) = ai + biP i + iSi,t-l' (41)
The three estimating equations are then
og(Si/S4) = .(ai-a4) + ib4P 4+ CiSi t-l 4 4t-1 2
(42)
Note that two lagged shares appear in each equation. The three equations must
again be estimated simultaneously, with both b4 and c4 constrained to be the
same in each equation.
-16-
3. Some Methodological Issues in Model Estimation.
There are a number of issues that must be resolved before the model pre-
sented in the last section can be estimated. Some of these issues have already
been dealt with in some detail in an earlier paper by this author [53]. For
example, purchasing power parity indices, rather than official exchange rates,
are used to convert data measured in local currency units into U.S. dollars.2 3
Secondly, we followed the approach used in our residential energy demand study
in measuring energy consumption in "gross" rather than "net" terms.2 4
There are two other issues, however, that must be treated. The first has
to do with the identification of inter-country differences in the structure of
production. The second important issue is the choice of estimation method. We
deal with these in turn.
3.1 Identifying Inter-country Differences in Production Structure
One of our objectives in estimating energy demand models is to determine the
extent to which elasticities vary across countries, and the possible reasons for
such variations. To identify regional variations in elasticities, we must specify
alternative ways of allowing for regional parameter variation when our models are
estimated with pooled data.
At the one extreme, we could assume that the parameters of our models are the
same for all countries (the resulting elasticities could still vary across countries
since relative prices and total output levels are different in different countries).
At the other extreme we could estimate our models for each country separately;
23As before we use a Fisher "ideal" index (a geometric mean of a Laspeyre andPaasche index numbers) as a single index of relative purchasing power. Ourpurchasing power parities are binary index numbers with the U.S. as base country.
2 4Thpt i, we do not adjust fua! qu.ntities or prices by thermal efficiencies ofutilization. Thrn, a.~re t-o r-o-n for this; first, thr e no gocod cinmatesof thezal afficigr.zcs a;vl iae., and second, there ara ochier economic' effi-ciency measures that could be equally important in affecting consumer demand. Fora further discussion of this issue, see Pindyck [ ], pages 25 to 28.
-17-
this would be infeasible, however, due to insufficient data. Instead we use a
compromise approach that we followed in our earlier work in residential energy
demand [53]. The countries are pooled, but regional dummy variables are intro-
duced that allow a subset of a model's parameters to vary across countries. In
the translog models this could be done by assuming that the coefficients a i of
the first-order terms in the Taylor series approximation can vary across countries,
while the coefficients ?Qi and Yij are the same for each country. This would mean
estimating the following share equations:
Si a D. + QilgQ + Yi :(43)k ikk Qi k lo P
where Dk are country dummy variables (Dk = 1 for country k and 0 otherwise).
Note that the usual restrictions on the yij and the YQi apply, but Eaik = 1
for each country k. Note that an advantage of this method is that it partially deals
with heteroscedasticity of the error terms within each equation; it is essentially
the covariance method for estimation with pooled data.
Alternatively, we could assume that the coefficients Yij or YQi of the second-
order terms can vary across countries, while the ai's are the same for each country.
For example, we could estimate share equations of the form
Si i + YilogQ + .DlogP j. 44)kj I ksk
Note that the restrictions on the yijk's are now that Yijk Yjik for each country
k, and that Yik Yi = 0 for every country k.i ijk - ijk
There is no a riori reason for preferring either specification (other than
the econometric convenience of the first specification). However, for either
specification, the null hypothesis that the corresponding coefficients are the
same across countries can be tested using the straightforward chi-square test.
3.2 Estimation Methods.
The choice of estimation methods involves a trade-off between the richness
of the stochastic specification (and hopefully a resulting gain in efficiency) and
computational expense. This trade-off is particularly severe given that all of
our models involve systems with equations. Ideally one would like to estimate a
stochastic specification for which the error terms are heteroscedastic and auto-
correlated both across time and across countries within each equation, and are
correlated across equations in the system. Estimating such a specification (which
amounts to full generalized least squares) however, would be unreasonably costly
given the computer software available to us. We must therefore settle for a more
restrictive stochastic specification that would still capture the more important
characteristics of the error terms.
When estimating our models we ignore error term autocorrelation within equa-
tions, but account for error correlations across equations. In particular, we
use iterative Zellner estimation which (under the assumption of no heteroscedasti-
city or autocorrelation within equations) is equivalent to full-information maximum-
likelihood estimation. However, we limit the number of iterations on the error
covariance matrix to five; this reduces computational expense while still capturing
at least 90% of the added efficiency that results from accounting for cross-equation
error correlations.
We will attempt to account for within-equation heteroscedasticity (at
least as far as we can given the ccnstraints on our computer budget). This
-19-
is done using the following procedure. First each equation in the system is
estimated using ordinary least squares. The resulting regression residuals,
which we can label Ukt, are then used to obtain consistent estimates of the
regional (country) error variances oF 21c , .
Ok T-m- Ukt) (45)
where T is the number of annual observations for country k and m is the number
of independent variables in the equation. Different estimates of these error
variances will of course be obtained for each equation in the system. We then
transform the data by dividing each observation by the appropriate estimatedA
error term standard deviation aok , and then re-estimate the entire system of
equations using iterative Zellner estimation. At this point, new estimates of
the regional error variances can be computed, again using equation 43. Iterative
.,Zellner estimation can then be repeated. Ideally this process should be iterated
until convergence occurs; because of computational expense, however, we limit
.A:the process to one iteration.
Our estimation work has been carried out at the computer research center of
the National Bureau of Economic Research, using the GRELIN experimental non-
linear estimation package on the TROLL Econometric software system. Some work
was also done using the new version of TSP at M.I.T.'s Information Processing
Center.
4. Characteristics.of the Data
Estimation of the models described in Section 2 requires data for capital,
labor, and energy price indices and expenditure shares of manufacturing output,
and for the prices and quantities of petrolemi, natural gas, coal and electricity
used in the industrial sector. In so-me cases data was available from standard
sources such as the UN Statistical Office or OECD publications, in other cases
-20-
we relied on the data collection efforts of the International Studies Division
of the Federal Energy Administration. Finally, in some cases it was necessary
to turn to the national statistical yearbook of individual countries.
Ten countries are included in our sample: Canada, France, Italy, Japan,
The Netherlands, Norway, Sweden, U.K., U.S.A. and West Germany. The data col-
lected for these countries are described briefly below.2 5
Expenditures on Labor: Expenditures on labor include wages and salaries
plus supplements paid to the manufacturing sector. For some countries,
Canada, Italy, The Netherlands, Norway and West Germany, this was avail-
able from the United Nations' Growth of World Industry. For other countries,
where the UN publication lacked data on supplements for all years, it was
necessary to extend supplements by using the national percentages of supple-
ments indicated by GWI, UN National Accounts or the International Labor Or-
ganization's Statistical Yearbook. For Sweden and the United Kingdom it
was necessary to determine what percentage of total national compensation
went to manufacturing, using data from UN National Accounts and ILO Statis-
tics. Finally, for the U.S., Japan and France, national statistical year-
books were used. Data is in local currency units and is converted to U.S.
dollars using the purchasing power parity numbers for GDP.
Price of Labor: The price of labor was determined implicitly by dividing
labor expenditures by total manhours of employees. Manhours of employees
was calculated for 1967 by multiplying manhours of operatives by the ratio
2 5The data used here are part of a larger international energy data base assembledfor use in this and several related studies. For a more detailed description ofthat data base, see "A User's Guide to the M.I.T. World Energy Demand Data Base'.'(M.I.T. Energy Laboratory Workin, Paper). Other researchers wishing to replicateor extend this stu-:dy or .ror; st:-es of -hir can cn ccess te data dircct lythrough the TROLL computer svste-i of the 'N"B.
-21-
of numbers of employees to number of operatives, for Canada, Italy, Japan,
Norway, Sweden, U.S.A. and W. Germany. Data is from the UN Growth of World
Industry. Where GWI did not have information, manhours were calculated
from UN data on number of employees and ILO data on average working hours.
Then, for every country except Norway, a wage index (1967 = 100) from the
U.S. Bureau of Labor Statistics, which includes wages and supplements,
was used to convert our price/hour for 1967 to a time series, 1955 to 1974.
The time series for Norway was available directly from Growth of World In-
dustry. (Note that the resulting index is not quality adjusted.)
Price of Capital Services: We compute a capital service price index sepa-
rately for non-residential structures (PNR) and producers durables (PD),
and aggregate these two series into a final price of capital services
using a Divisia index, where the investment shares of non-residential struc-
tures and durables serve as the Divisia weights. The computation of the
price of capital services of each component is based on Christensen and
Jorgenson [20], i.e. we assume that the investment price of an asset q is
equal to the present value of its future services evaluated at the ser-
vice price P (which is the price we wish to ascertain). We aiso assume
that the service from an asset declines geometrically over time. Then,
disregarding taxes, the asset price is related to the service price by
j+l 1
qt = jJt [(l-d) tpj+l n +rs (46)
where d is the depreciation rate and r is the appropriate interest rate.
From this we can obtain the equations that relate the price index for each
type of capital service to the corresponding asset price index:
2 6See also Hall and Jorgenson [35] and Coen' [22].
P R(t) = R(t)qNR(t-1) + dRq(t) - (qNR(t) - qNR(t-1) )NR N RN RN (47)
PD(t) = R(t)qD(t-l) + dDqD(t) - ( qD(t) - qD(t-) ) (48)
Here R is a long-term government bond interest rate (source: International
Finance Statistics of the IMF), and qNR and qD are the asset price indices
for non-residential structures and durables.27
:For some countries (Canada, France, Italy, The Netherlands, U.K.
and U.S.) asset price indices and depreciation rates were obtained from
Christensen et al. [12,13,14,15,16,17,18]. For the remaining countries it
was necessary to compute implicit asset price indices from gross fixed capi-
tal formation in current and constant units using national statisical year-
books, the U.N. or OECD National Accounts. Remaining depreciation rates
were obtained from life of capital figures in Denison [25], or implicit
rates from OECD National Accounts were used. Asset price indices were de-
flated and then converted into indices relative to the U.S. using the ap-
propriate purchasing parity indices. Data on the investment shares (gross
fixed capital formation for producer durables and non-residential structures)
used to compute the Divisia index were obtained from national statistical
yearbooks, or UN or OECD National Accounts. Note that this method of compu-
ting the price of capital does not take into account differences in corporate
tax structures across countries; we simply did not have access to the data
needed to take taxes into account. This means, however, that our price
index for capital services must be viewed as approximate.
Expenditures on Capital Services: Expenditures on capital services were
determined by subtracting labor expenditures from value added. Data on
value added at factor cost was obtained from the United Nations' Growth of
World Inr.:strv or Annral Ycar:boo"k Value added for France and Germany was
2 7For West Germany the discount rate was used as the interest rate, since thegoveriument bond yield was unavailable.
-23-
available only at producer costs, and value added tax data obtained from the
EEC Tax Yearbook was used to arrive at a factor cost figure. All of this
data is measured in local currency, was deflated using the local GDP price
deflator, -and converted to U.S. dollars using the purchasing power parity
for GDP. Note that this does not include depreciation. Since the concept of
depreciation varies between countries and comparable data is not available,
the gross figures are used.
Fuel Quantities: Quantities of fuels used in the industrial sector (ex-
eluding energy conversion) are all obtained from OECD energy publications.
Two different publications were used, Energy Balances of OECD Countries:
1960-1974, Paris, 1976, and Energy Statitics of OECD Countries. The 1976
publication is used for 1960-1974 since it contains the most recent and re-
vised data and clearly excludes chemical feedstocks. These data series are
related to those in the earlier OECD publications via simple linear regres-
sions, together with the earlier data, are then used to extrapolate our
1960-1974 series back to 1955. The U.S. was treated differently from other
countries in that the 1976 publication showed a large amount of "crude and
NGL" consumed by industry. Investigations into other publications and con-
sultations with the Paris office of the OECD and the International Studies
Division of the FEA have led us to conclude that this category probably er-
roneously contains some petroleum products used for petrochemical feedstocks,
non-petroleum hydrocarbons and other refinery.gas. To keep our accounting
consistent with other countries, this category was not included in our petro-
leum total.
Fuel Prices: Industrial price of heavy fuel oil, natural gas, coal and elec-
tricity were obtained from EEC publications and the OECD statistical office.
These data are measured in local currency units, and converted to U.S. dollars
using the appropriate purchasing power parities. Final units are U.S.
dollars/tcal.
Purchasing Power Parities: Purchasing power parities for gross domestic
product, producers durables, and non-residential structures were obtained
from Gilbert and Kravis 58], Gilbert et al. [59], and Kravis et al. [60],
and are all bilateral indices with the U.S. base country.
Our basic models require cost shares and price indices for capital, labor.
and energy, expenditure shares and prices for the four fuels, and the value of
output. The available range of our data is shown in Table 1. Note that for
France and the U.K., factor share data is not available for some of the early
years. It is useful to examine some of the share and price data before turning
to the estimation results. Data for 1962 and 1970 are shown in Table 2. (Note
that the energy price index is computed from a "preferred" translog fuel share
model; this model is presented and discussed in the next section.) We see from
this table that there is considerable variation in fuel expenditure shares across
countries, and through time in any one country. Fuel prices also vary considerably
across countries, and have generally decreased over time. Factor shares and prices
show much more variation across countries than across time, so that our capital,
labor and energy elasticity estimates should probably be viewed as long-term.
5. Statistical Resultsa==_=.__=- -====------
In this section we present the results of the estimation of the models set
forth in Section 2. We have estimated static translog models of fuel shares and
factor shares, and static and dynamic logit models of fuel shares. At this point
we have not yet estimated dynamic versions of the translog model. We begin with
the two stages of the transicg rlodel - first the fuel share model, which in turn
is used to generate a price index for energy, and then the factor share model.
I N Pi lit
in Lf ,)1001
N
I
10
NNr I -
I I I I10 r) Ln V
I I In I I In IU ) U In U) Ln U 4U1rl Lu u ut in t n n M In1010U1u1 1U1gf.1 u
It In Iii I I IrI rI c_ ri r- I II I
ri I' t In. 1 , in !~.l t li lt in u) n i iU in i
i i i t In tu) In In tn in In In nL n t r) n rn INLn u) Ln n u Ln n
r NN rN N4 Nr -
*n u I ur in U' un c Ci
u- I u x I
en M - (*
_0 _0._. _,_
1= I. o co
VsN N 00 0 0
~~O C ~ %O n a
10 10 0 CO i o t l : I n I I I coci. I I 1iC
10 o 1 1rrr co co\o i
CO Ln NO InPI. P 1 0gn %OLn11( Ln r
Ln Nm In
co ' 0CO % 1I C I CI I h I I
10 Q 0 0 13 4 ri ri 10, '10 '10 ch h II~~~~C
O~~jI ~~r~~ II re II cj 00~~~~~~i
(C3 IL_' ~·I j
o'I
IT> 11rz.
I x,1o !!%D 11
C':
I
P2cr
Cl
4
0
zIrl
H
NU
H
.t ira., in !tI I I In LI) Vr) L __UE l tn tn
I 0I I Ln I I I
..Lt)L tnU I I I I
U) In In I
t I I Iu n Ln urf r rLn U Ln U)
a .
N 10 rw r110101010
liii§10101010U101' U) Un
*10101010r
Cd
0
0
i,0
E4,rq-.2
I_ ~ ~ ~ 7 _ _ I _ _ I '- -- -- --
_
1r- f
Ln
I
x
Cl
Ua Cp" rjpa
P 0
*atUC)
-ri
: XU.74p4h4)$4Cd,CoI
N
4)
90coH
v-fC-)
Co
I
CtG
N-
to0'-40)u-Hp
C)4
rI4W
a,ma)
Cd
C4
I04)
0xH-rl
100(14
w
r-4
FZ4
orqC)
t)C,,
0
04a)
'H
O z
00
-r
C t
Vn
H OC
H
N CN- U)
08 o0h Co
N N000 N
co coU) 0O'IO -ItH- H
-ItCO
0\'DCT)
Co
-1
riCY
tN
r-
N- NLn U)
N- N
CN CN
0
N 0\0 r-0o On
Cd'0·CrdcoL)
tV) CV)H (
C) aC
V.0 COH Ho
co N
H C
O.r
\0-r-IcC1
m
00C)HN-
mN,-
coa\)N-
'0%ON-
C4N
cn
LnCY),CO
C',Ct
u)CHcn
O %OH 0
CY)N
0r-e'Ht
)U
rdS-;:1
-z:CY)
N%OONHe
c\ CN
r-f.
\0CV)C)
1~%D-A
ON
rcV)CN
CI) COCf) U)
co co
'I 00C N
CO Ct
cos clCV) Hb H
N -1rH5 CC'O )
* *
£ U)
0 1 0
O O
NC CN)NV N
CY) CNH. H
*
cJG00INH-
0O
r-
rdAiH
N Hr-'. N-N- C
C14 C
o~Na'LI)
CV
Cf)
CVV.0-Zr
N- N
o NO Ct)W muN 0
N-
N- LV)rs o\
*e oN '.C) c
o a.C C)
0 %0r( LaP-4 1CT CC]
N- LVU) 'IC
CO
e)
C0)0
0H N
o0Hi
cN OD H
a% Cs
Nh -:t NLV) CV
-Z H* N-
C) o0
C) Coin c~lc% r-co N
Co
N
HN-00Co
CY)
Nr-CX
00OCD-T
-
OC)0
cO
0o
CN
coCoCV
C0%0
0
H 0
C,,
('3ch
HIV)
ori4.)
)4)z
O0'
L) C0\ 0)
N14 N
\D V)OOD m
C)
UnNC)OO-
en
Ct)N-'00
H
'. 08
Hl CY)
CN O0' CY)N~ C')
oN-
-Yr)cV)
D.
O O
0 0
Hl Ct)
0\ OCO H,-~
N*\1
1--a!~H
C)
of-0OH
NC')C4LI)N~
-
co 1O0cc 1o
NJ Hl
LV) H4cJsr-. N-so u'O LnNi r
~fO' 0cn -Zrrt uncl\ L)O \D
03 c)l '.0
C.o
N CV
C) Co
O Nrs LnC)e NCt HO O-t C)
0
0
LV)r
0
-q0hHn
dra)
3-cna)'I.
.D\o
O0
-4H1
N\0H(
HNI'DC14
a00.o
C14
tn N
O <N -1
-r N0' -VN C
N- N
C\ %t
aZ NH- LVr)
rs u
-. H
rl- coCY) Co4
C)
LrC)
%D
r-4LV)C
H \
CV) -
N 0
,- -(
C\I. .adc~
0Hl
00 Cn)
C3~U') LV)N C)-z H
-T r-4
N- H
Lr)N- Hr
%O -11
CV) C
Nl HH- C)H-- H-
* -
CO r-OC) O
0H 0
-h
Li). D
H ul
Co CC
o LPCO C-
CIA
OD %N- cnN3 riC_ C.) cN N
o uC 0-- t'0 v-Ct) (N. ,n
n ¢0' CV)
o o. .
Co 'zt00 LV) '.0
.
CV)O m03 OC LV)C) 0 I. j
H U) IH I
'
H LVCiCY r-
N\.0
,--q0'CH
0C.
IC
0)uI n
c0
z
_C I�C w -
__ __I _ · __ _�' - R-
_ _
-- _ __ -_ _- --
__ - � II |- ____
- - - - - - - - - --
I'll4-i00.v
'-I
04-ia0C)
POn4
10
a0
4)Iz
N0Ek
to
.
X X
co
n
¢-
0p*
050lri
x Q
U)
U') H
-4 ,4
t o'CO 0-4H 0
r-Co
CY) e l uI
H',.0 N I
l r- .'. ,0 .
H U')
N CN
o o
C.
N oH H
N I)£ m
N o'0\ ,H H
00
:3;
.0
4i:30O :(L)azH
r-4I,
00 ~NC)
r.
I-
H 0N
H 0o 0
OI
O O%
CN
. 0%
%$ ClC CO
4j Cn
Cd060 o
a ~U) C"r- P-* NH H
Cd Ori Ln-. 0
C5'
0 CN- N
. -Ita ,
C)l cf* 0
N -40% Cl
eX n
o o
'0 0
C)O C
VI) Ln)
-o0O
cl -4
c% -
Cl '.
tn mD*c N
0 OLI) Cl0% 0%
* O
-4un vo o
LI') N-
*; TN*c N
N 0
H
Li' H-4 -
CN ea C
N N
O OC C
,4 ,4mn U
C) H
N '0* Vm Ul
N 0l r-
CN ChH H
H
4-i
0% NH LI)
*4 NN CN-It C4C14 CI)U) C
H
N HI_ CN* NN N4
c0
O- O
N 0%
-41 -It
H Hb\
4 NU-) Ln'
N' 0CD r-cri c7'.0 N-
z(3
cbII-)
00 Nu
.CO
0 0
C N
.. 0
4 0
d H
. c
.
rH H
Ncr
o H) Cr"
NV C
C%
O 0
HO Ho 0* 0
4 ,
r< <
*1 \O
N 0.0 rN
oH H
Cd-H 04co
v ,
0uC)
Pc
.4)
p4.0
0D0H
N
Hl
0 N
H
00%H
0H-
N0D
Hmnr-q
co10
0UI
I)
0r-NH
a)C)00
'-4FX
oI'NZ.
Ch
0z
rtoci
Pa
ZQ,z
7
_
From these we determine partial and total elasticities for fuel demand, and elas-
ticities of substitution and demand for capital, labor and energy. Finally, we
describe the results (which were less successful) of estimating the logit models.
5.1 Fuel Share Model
In estimating the fuel share equations (29) a number of choices must be made
regarding the pooling of data and the choice of time bounds. First, regional
dummy variables can be used to allow the intercept terms of the share equations
to vary across countries as in equation (43), or to allow the ij parameters to
vary across countries as in equation (44). We found the latter alternative to
involve a considerable reduction in degrees of freedom, and the resulting elas-
ticities had large standard errors, so in our "preferred" model we use regional
dummy variables for the intercept terms. We also consider using no dummy vari-
ables at all, and we use the standard chi-square test to determine the need for
intercept dummies. Second, since fuel prices in Canada and the U.S. have been
significantly lower than in the other eight countries in our sample, this might
have resulted in a production structure different enough to suggest pooling
these countries separately. We therefore estimate models in which all ten coun-
tries are pooled together, and in which Canada and the U.S. are pooled separately.
Third, although our data span the period 1959-1974, there is a question as to
whether the 1974 data should be considered to have come from the same popula-
tion as the 1959-1973 data, i.e. whether the 1974 data point lies on the same
long-run cost function. We therefore estimate models both including and excluding
the 1974 data. Finally, it is useful to test whether we are indeed estimating
a long-run cost function. To do this we estimate one of the models using data at
three-year intervals, and compare it to the same model estimated with annual
data. If the resulting estimates are nearly the same, we can conclude that we have
estimated a long-run cost function.
-29-
Estimated parameters for the various versions of the model are shown in
Table 3. (Standard errors are in parentheses.) In the first version all ten
countries are pooled and the 1959-1973 data are used, but the model is restric-
ted in that no intercept dummy variables are included. We can test this re-
striction by comparing the model to the equivalent unrestricted model of column
6. The value of the chi-square statistic is 628, and given that there are nine
parameter restrictions, this is well above the critical 1% level of 27.8. We
therefore include intercept dummy variables in all other versions of the model.
(A model is also estimated using regional dummy variables for the second-order
terms, but we do not report the estimated parameters here. The resulting own
price elasticities, however, are shown in Table 6, and as can be seen from that
table, many of the elasticities are statistically insignificant.)
In columns 2, 3, 4 and 5 Canada and the U.S. are pooled separately, and
in columns 6 and 7 they are pooled together with the European countries and
Japan. Also, the effects of including the 1974 data can be seen by comparing
columns 2 and 3, columns 4 and 5, and columns 6 and 7. Note that in all cases
the ij estimates change considerably when the additional data is added, leading
us to believe that it should not be included.with the 1959-1973 sample. Also
note by comparing columns 2, 4 and 6 that the Bij parameter estimates for Canada
and the U.S. are quite different from those for Europe when these countries are
pooled separately. In addition, the parameter estimates for Canada and the U.S.
are still statistically significant when the pooling is separate. This is an
indication that it is probably preferable to pool Canada and the U.S. separately.
By comparing columns 8 to column 4 we see that using data at three-year inter-
vals results in little change in the estimated parameters. The resulting price
elasticities also do not change much (compare Tables 4 and 7), so that we conclude
that we are indeed estimating long-run elasticities.
J "O r- - CD r- O -4 I- C C, . r- -- t' 0 00 00 0 ,c0a u . o , *:~ 4J .- - c~ u'~ c'.lO s t; s .- C, ¢. t'-. -.r ,~ ) . C r-) { O -" O -T t r, C o 3 co e'n f ; ¢f40 JS- l o c-,i 0 O O O - 0 - .- ¢ C') O , ' - ,I " ' Gq r ' ;. " . °- ;IO r-- .I4 . ... o .-I 0 OCt H UIr & I J c0'i 0 C-~l 0 C'j 0 0 0 ' 'I 0 0 .) 0 C) 0 e5 0 O 0 O - -T-4~~c: o uc 6oc
OLOnO OOOxoOoOo HOoOooOoOooood -o~ ~~~~~~~~~~~~ oI
0 C - -r -4 V rJ " V) D rD al a w c- to r- - M aq \a n 0 M O n M X) o \ -' · , , , 0 0 0 0 00 00 00 0O n 0 ,,
o o4 I-H I i P C C t O C C C O O C O 0U C -- C� C C '-14 O~ a ~ S4 *r1 .' I'-. 1 . . . - O,0 ..T o r-O1 \ 4J OO OO O'l OO O O O, CO O 0 Lt) ,- O O O O O * co *o ' ' 'M "~~~~~~~~~~~~~~~0 r-- -i o50-. C5 u5 C n'qL nc CN-T"~ N" O " r- V~
%O O 4C
9-4~~~ c~ dcd ~dddc ~ddddod6co o >----.. -- i , iI_ i.
S~~~~~~~~c M C o -a r- 0 4 r- \o M m :r r- co cr 0c N C1 1 n C" QN f
r-U > CO C1 O 1 O 1 O -q C. O H O H 0 Cl 0 Cy C) -' O e <On O -t O 'I~ (0 P * . . . . . . . . . . . . . -O ..4r co~ r1 . ', O- C O O O O O ,O ,O O O O 0O O -
I~~~~~~~ ~ ~ ~ ~ ~ ~ ~~ ~ ~ ~~ N
~Ow CN c4 P C; ;c; C; C; C;C C ;C C C;A0 0 0
0 frj Q . 0 . H Ln C. n 0n
t-~~~~~C co n cn co t-^ %O H Ow St £<t nmno<NnN
0 *0~ 4 ~ 4 . . -vl #. Cs) ' , ,..O'C ) :D 0 C O< 43 %tv' N O sO c - O^C JO , Oo -
0 I 3S j .i. . 0 0 4. 6 4 0 4
HO U '. I -
1 0 N _V%~~~~~~- -a %S < n f 'J£ OH - ~ ' LrN d1rI 4 N O H O NO HO
0a 8 O4 J 3 . . . . . . .....,- b-, ~ ~, O Oq O ,-tOO O -O- ~iO eO-~ O O~O,~Oe qO' Ut 0 0 0 0 0 0 0 0 0
*' O~o, C; _~ , . ...ddcdc d'd'< o'~~ ~ ~ ~ d o do.c
I Bn El w I
004 ,O L f L N OC4 H i "N H~.~ C4X LI Om oW' 00O~N NO C0 O i 0 0
0H O '- O ,-,I S
p2 U
o co
0CP%~~ ~ ~ Ic C; C:')1 ~ ~ C CI C ~ _6V4 -~~~~ ~, eq i', ,I' , ' .. ,,,O 0 C4 O H
C) rH O C) i oa 0 0 0 aH 'S--S
0 0 0 0 0 J 0 0 _ 0 9 ¢ -4 0 0 4 0 s 0 0 ->
H H H H H v-4 H H4 H H H Ns N> N q C Nc ('4 js
. ~ ~~~ ~ ~ ~~ _S _S .S ,S 'S .S _S C S C S S C
to
10
0z6410
rz4
0
f4Qo
13.4
04)
'-4
0
E-4
.)
Hu
*-HPv
, JC.)
II
cow
n
0
o
tIH
4.-
'.0 Nc H C- l t- HUtt in U) - -I F-- C1:) Hr4 C CIJ % C2 I\o CI Us NC4
C) r O 4 CN 0- r-4 C)G0 0 0 0 0 0
V. V - V0 V
n -It , Y
C1 C1 In) CAr- em H c)C;. C .m..t tcl
0 O H .:tr r-..'0J H '. ," _ c.> Ci H-4 U) Cot
H,- O O 0000'0
,n ° tO 0 0 C O .' .o,-t C 4 ,- o ¢- -- O q CO -T ID O , -H O' c . n ,- n C4 O C4 T CN O %D CN Cf M 00 C1 L) -. 10 %D cs4 N T M -4 L) M 1, T T %O r-- r4 °° 1- 0% m CZ a - U_ C. CX 4
O C1l TJ C1 M CI C) *1q m~ 1- --T * r- 1- lz r1 co 'A cn _4- ITJ-l rs 1- T ^; * r- - T _1q %D -4 xD 04 tM " 0 rr O -0 ) O . u O'1,-i ,C) 0 0o O Oq O c O r9 O,.o O4 c O C)9 C) o O C> C O cO u1 C D O '
O O c O O O O , O- O -O O r-40 O O O O O O O O '0 -40 4 o c o -'
D0C) 0 0 0O 00000000 00 0 0 00 0 00 000 0 0 ) 0 0o o o o 0 C C
co at rs a- C- 0 C x ) %O 1 r- M m r r r 1 r r-I 00 m, T Lf) 40¢, C,4 C7, r-q 0 cs ~l(- 4 C-4
M~~~~ ~ ~~~~~~~~~~~ (3J r- 0 H 0 r- 0 N C) 0C r-4 C 4sH qo4 ) r- o C oa .z 0 Cn u
en O- -1 O- %D O) csO O Cf O- a, cc C) O OO H O LA O cn O %D O H 'd- O 0 % HO °. . . % . * . .. . . . p . . .p. .. p . .% . . .% . . . .% . . . .V C14 ON , ,-T D , H -4 co ,-4 or1 ,-i 0 N , -4 4 ,- 0 Cl0 '40 CI zt L C0cn H ' ')0 C)OH O H O H O C 0 0 00 H 0 CC) )0--40 H O C0 C 0 C-4 O-0 C' O O OO-OO.O,-O,-OOOOOOOOOOOOOOOO O O O O,-t O(%10~ -IO,-40 O~ OO O O O G
,' 0 0 . 0 0 0 0 0 00' I'~ ~D t?'l 0 0 0 t' ~. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0D HoLof oc.J, e0l C r HO In. rO. C .,0* 0 .4 0 C14 10 en M co
u~eq ~,-!-.T ,-4 ~O ,- ,- 00 0 0 0 0 0 0~~,~. -~ 0 0 0 0 0 0 0 -~ 4 O ,-4 0 0 0 0 00C~ 0 , - tO,-0O OC'q 0 O O OC' O- O C,-0OC" 0CN C" O' 0 C)O H-
C0 .i i
C; C; C; C;~~~~~~~~~n H '6' e ' ml0i -01
N I,0 000O c 0 c 1 00_ 0 0 1
p., p., p.. p L..oO n f cr. co O N , N H xD e *H n ;r D 00 , bb s~t co v i,H < ^ < vD N n m H ('11~ oo~ t[ ('~ ( cq O¢,") D Hr
I'%0Lrl~~~r~ o~c',eo'.rrl0 0 0 - 0~~~ ~ ~ ~~~ ~ ~ ~~~ ~ ~ ~~~ ~ ~ ~~~ ~ ~ ~~~ ~ ~ ~~~ ~ ~ ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0 0 ' m O O a 00 0000
gg_
0* -q *s s *.*~. J * 0 ib F
,- ¢'qnC Ha) 'v0
o-,t, O -t
g (.1 I"> 0 LfC * H.00 0
.C ( C
\o0 I-I t-o H0o 0;%ggo
I o,) ( O C. i-:7C,i r-.oe l(D c-
--
, .
o d .,.A
0)1
C)
-H0
Vci0)010k
40-I
5.40
4-,0
CE,
.00
r-
0%d
0p4
- -
>~~~~~~~~~c C'4 0) tol O , rQl m< t r ) C-4 4 CqN rt4 0 M r - 1-4 M CN N fo 'T 0 Cf .nC14 MI CfU C C) Cl N C) t- .' C) C-W , ) r "- - (cc CIA r- N c V) CN CO Cr r- .- q cn YM - (P
It C) 1 t'- VI -) C') r' -4 CI #r' - 1 ()M l r-4 r- O_ -4 V1 fq rH t- *-t r - 1^ C:)C) r - C ) r-4 rsV 0 C0 C 0 0- C) O C) C) C) rO 0 I r r O O O O O C) O C) O r4 O C) O ~ C: C
I **C) . . . . . . . . .. . . . I .~10 *,I C:O C10 O C O O-- O O O O O C) O O O O OC C) O C; O O O O O C; O O O O C C; qO~ OOI C | -4000OIOI OOOOOI IQ~r .40I I)OCNIC
-40~~~~~~~~~~~~~~~~~~~~~~~~~~~-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r r.
' \ 0 f I-4 0 -T 0 cn c -o 0 , Cl) w LrI in ot o In ar ) 0 N X i'J if) 0 o o-'n oor\ 4 V) :T "O ' -)@ t VN, r- 4- C:i t 1 ).:) %O r-i re "". C:o 4_ t-q r- CO P., r- L') k) V*1 P, V,: I V)VIf
N C C C f- C4 C, CA* - C4 :D r -4 ,-- C) 4 C'-) CD C,. " r ) ) C 0 D 0 ) W- 01 t) 0 %Ov C O _°;
~~~~~~~~~~~~~~~~~~~~~~~~~ '0H 0 0 H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00
O o - OH ' C" 0 0 O 0 i '0 0 O ON O'O C\5 O O 0 ONON O0 iC 1O - 1-O cO Czt
v I '_ I .v _- I '_ I v _ I v i v v i ''I v I' - I v i ~ - _-'H O 'r 0 "_ 4 0 -. 0 ,, N C 0 N C)0 00 C -- .¢ N C C .0 C H N C0 ' 0" N C 'CNI ~! " O C O C;. O C; O 1 C C; O C; C; C; l C; O C 8) C; O C) OOI r' C; G
°o O14 co°C-4 o T- O O O e O O O O O -O O O C) O O C M) O OC O O O OOO O O v , I # vE v vEs_ I _ v_ vJ I ' I v ~-~ _ v I I - I i I v INCClrJH(NC'lHC4..~~H1r4HNHCNC) ell.0C f0%HH0lu- _ .
co %D cn 04 cDOe t ) 0 T a<r 0 fl .r m rl C 0 0 It n . o rvo m h N o- co u- ) 4 m rq'O esq -N C) r- C-3 - GT 0 ffi a) 0 o (,'I <N T r-- c- 0 k o U'
°:' ~1 0 C 0I " H - - r- O -- C C H C", r'q e O 'IO CO N O C o %'~ ~ o O r~-HoC; o o, o o Co O o O O o O O o o o O O o o o o o C oI v v ~' I v ~ v I v I v v I ~ .~ v I ~ I v~~~~ I I i - ~
i ,i i i i at~~~~~~~~ C14 in - c el 0D N) i n 1-4 r- %( O 19 t C) 0 Le C 0 1 - 04 0%\o ~ ~ ~~ ~~D e a 4 i LI) - INS 00 C4 _ o V- o, -t - C-- ko -( C:T r- ¢ M c: Lr v-o3 M r- O T- MC toC4 r-" .N N - O cs o cs H H 8 c4 6 ( oC; C; C; cs 8 8 8 ; 8 C; cs 8 coG8 sH ;Vx
N~~~~~~~r O t O O rH) O- C3- O1 OD O en O O , O- O' T c O~ O c O -O .O i O .O 11 O- O c OHO **
O1 O O O O O O O O O O O O O O- O O ON O O O O O O C) O O O COv O~~I I \/ 'I v v I v _s I I v I I v _- I ,.)I v ~._ ~,~~~~~~ ~ im ~
V- O c On r- co C 0i 0 Un , o o o o o o 0 ro c o 0 ar 04 O C-C C; C; C; .8 C; c; C; C; ~o o c C, o o rsr nc <nca o ;
C1 C\ 0% Cbl V) C r L4 N C) -zq N CI I V , LI) CO N Lj N %O U- \ - Cq %D %O VI %O C? HO O O NO O O G O O O O O O O O O OCO O O O-O O O O OO O O OO O*- a- 4 -8 L% -- : 0 0 * S S L N C 0 r C C ) _ N r \* > O F-4 0 q
ggC C; C4' O', O C C; C O O O OOO O O O O C O'
' C,e <) uEo cst < < uE c uN 0> ̂ t N < C vt M 04 < ,t t Nc clb <s
.' .X ,. ,. ~ ,.q %'t N \4 V o U'q e' {,I ev > ) r
C'~ (N LI H Cl Cl'0 N 1'~ tH H '< ') 00 u;) C Cl '00 N H L~ NO '0 N 0 - f N (. _t . 2
C c n C C = ca ca ca ea ea Cc e in C°COl* (N H *N C( N'* .- . .. : . , @ H. . , . , , . . HC. , , O . , . .OO H O O OOOHQOOO: > ^^>;O 0 vO' O O OO CO clC> O c.I I _OOOOOOOOOOOIOOOOOOOOOOOOOOOCOOs_
* _1 co} r~~~~~~*
n~~~~~ a~ a' % eJ -X _% S f _ F_ eqcCJ1
, ~ ~ ~ ~ v .. . i N.~' . f)C )~.~ - ) . .1- N C . lH , .-4. --% -l H 7
X
I%O
.-.--
jv
C4
A
0
0
0
IH
.
.-44.1
4
4-I
1
P
41
00
0
4,0
f-4
:-: I I �- 4'. .
i
Estimated elasticities are shown in Tables 4, 5, 6 and 7, (again, with stan-
dard errors in parentheses). Table 4 shows partial own and cross price elasticities
for Canada and the U.S. pooled separately, for both the 1959-1973 and 1959-1974
time bounds. The same elasticities are shown in Table 5 for all ten countries
pooled together. Note that while elasticities for solid fuel and electricity
are more or less the same for the four different versions of the model, elas-
ticities for liquid fuel (largely residual fuel oil) and natural gas vary across
the four versions. In Table 5 we see that pooling all ten countries results in
own price elasticities for liquid fuel (Nl2) and natural gas ( 3 3) that vary
little across countries. We see in Table 4 that pooling Canada and the U.S.
separately results in the oil elasticity becoming much larger for these two
countries and smaller for the other countries, while the opposite is true for the
natural gas elasticity. In addition the own and cross price elasticities for oil
are statistically significant for Canada and the U.S. in Table 4, whereas many
of them are insignificant in Table 5. This is a further indication that Canada
and the U.S. should be pooled separately.
Note in Table 4 that including the 1974 data results in a large change
in the price elasticities for oil, and in particular these elasticities become
smaller and in many cases insignificant. This is not surprising. Oil prices
rose considerably in that year, but demand can adjust to these higher prices
only slowly. The 1974 data thus lies on the short-run cost function, and in-
cluding this data gives us demand elasticities for oil that are somewhere be-
tween the short- and long-run. This, however, is of little value given that
we are estimating a static cost function. By leaving out the 1974 data we
can safely assume that our estimates represent long-run elasticities. (As
mentioned before, this assumption is supported by the elasticity estimates of
Table 7.) We therefore choose as our "preferred" model version (a) in Table 4 -
i.e. Canada and the U.S. pooled separately, and estimation over the 1959-1973
time bounds.
TABLE 4 - PARTTAI, FUEL PRICE FLA:TICITISS ·
(US & Canada Estimated Separately,
*(a) 1959 - 1973
Count:rv Durrama Variables)*
(b) 1959 -. 1974
0 0 -4 4
HOO Cd O 0000 r %
I~ %. I C) cn rl ~ rlL o lqr 7 3c
-, 0 oc; ` ;,~ o o o
O Ln \ C\0 ( %o cq
* *
O. Ltn ~o -1~t0~00000
%.T %v
r a) a\ tC 00 C4 r-.n-4 H O H-4,0000 , 0-o ,
`3cJ`3` c;`3 ~Nc
-% ~-% -'% --
co C)y4 0.. C V- -1 n
I I
o co tn Ln-4 NO0 C1
0c`3`3`31 -..O I--
C M oN N - CIN Cr 0 ,HC.J- I H e4 O -4
_- %- I - I
Do 0D 0 r,- VIO O O O O O H` O
I - I - I %.
6 e n CN 45 O \ Ln 1n M LtN H- rI -I C H , O UL O 0bl O
I %- I . _ %. %,
O r-.c,I r- 00 -1-0 N , , H
It C S ` cC c3 C" `8 8 ( 86 8
-1% 1% ,-% -%r- .* . C4 -It cn O 04cn q C"4 4 m r(y-4my 4
0000 HOHO "9- '9
r( 1 45 yC r rq r-
-99'8 000000C Ln coa\ o o' oC; C; 8
r- %O co
v r -, -%
co r qHO00 0 0'9- 9'- r-99 d9Cvt4H
9 co mI
-(o 0 000008 C;
'99, 9999
c 0 0 0 000 I . * * . I v
* .'l . % ..-- .-
r---4 r H r-I 0 P-
-, - %-
0 r-l -'i d JI
.99- -%9 -9% -9'
e-(V-h r r 04U') \0 ON84H '3%00000 000
`N r4C c;-400 0 0
%, o o o
`_. c;`0000 -4\.,*-i C) T C
I-_. H3 a oC .' coc c co C Co c o
_ ` ̀
0 u c"O - N o4 co C, o D c v- )
(' c1 _ -d i000 0000V
00 l cn c - 0 0 00C* r-i 0 . .r ., 0 6668 86861 - - %-
-9% 0-% -9% -9%0 C9 r .4 '%0 .r- Oq o o 0 0 o
*dd * *H ** Ivoo Ivlv
,'9 -%
co -so I - i --X o <
* . *
Or-0 0000
-l -%- i*% -9% -9% ,-% -9 '- -99% ,- -% 0- -9% 0-0 .0 0 .0 co .0 0 .0 0 .0 co .0 co ,0%.O %-,- %. I %..I - %.. , , %..
C'9.4
Cc494
C7
0a:
e r' 1-i0I".-4 9-I14 814
cc o\ cc o
coO -o o
I' I a C) O c
I % I
H c c3
0000'9.0 99-d
N O _ co
1 _( I -. O0000
00 0 DO 9 cO '-*O* * oooo3`
*1 -. I . .LA O )O
_ _
0 ' tLO L'Cf) e O0c0 c;
v '9
CN -- r- r-
0000i, I 'v
z
:E
.- % i0'900 cn -I r-O Cn 00 c
"940 -I O-
r C r4\ C- 99 %C3
1r 4 (l
b Ds t Nfi- 40w- I1%il--
-9l% -%
r-i V) _4 U)H-f'iHU ,-IOHO0000
o0
11) Ln rn000000
0 '99
JJ
)
0wa
c.9
0r4.
CI
-,
c.
r i
1I I
0C,
r-4
0c;
c ̀ 3 c
- D 000"d3 - l9 - %
N rn r-4 nCn H N rt40H0 "'%-I'--
-% ,-%
v-4 r-4 c0 14 614 1 %, I%-H
%O VC 0 e
00o00s 8 8 (d
v .
000O'
* * I
C14 - 0 -4i .. i I1%- ,
O 0 o 0"N 9-I' r-.-- .
` o `3`I v !
%c0
-99% -%
Co 0 C O 000000000I -I
000000 O om Ln CI _
.- I 0 . O* * * .
H o o Il l
-9. -C) O .;, "co c cn1 C 8r- Id
I--
` o `* *' * .-
0000'9-i %9
,_4 c :T 0\-99%QN 'C-H
* * * 80000o
,- u r - tL
,-I d . .
- 09`O `3 -I c;I C) ; C)
% o 9o
*%9c r.
i d --rv C
09.0
-rq14
4-,
rHl
C) t- 0O
0000* . .-
.- % o o
% 0 0OH i
O
-1
0 clC'9 4t
t ·.-.
-4
I. CO L)
r
Z
r.rN 0*99 '
es
,,�,,,,,�--�cllc-�-.�--�--r�---------�·l
_ I ------ � --- -------- -- ---- c�--C --- II�-C---LI---L·-C C I
m
M
TABLE 4 - PARTIAL FUEL PI:ICE EL,.ASTICITIES
(US & Cananda Estimated Separately,
(a) 1959 - 1973
Country Dummy Variables)*
(b) 1959 - 1974
oo% , -
v v.11 . . -cO o co oq1 I -JHOd
cc-v cc'
0 00 0 0 00 c c-I r H H C H Ov . In *~ . * * *
v % O O I v O vvv- l
F ; 4 C;4
N o 01 _ I -r f~%_ccc a10c'J0L(' o t'o
0000* o o o -
N Ln c 4cnc cr4 e n owO 0 00 a 0
el% - e%- '-I
Iv %- ( v gdggI gdgc;
co LH - " m o' cOc r n H c 0 C O
4I C O O OI I v ? v
0000I ~ Iv
-4C " C
0 0 0 dv v
0e% .c ,-% .1
c'q o , I c -o IoC40CN 0 0 0 0
0o N % O oK - * C Kc K * ' . O 4 H O0
-x * * C ) * K O
C K * C *K K 4 K * K 00 00* *r ·0 00 0
%.O -.
% \0 0ulCD r-I 0 r410' 10
t o HHOHO
C C 4 0
0 ri I
HOY0 -4 0
r -I r O r DI. .V .
4 O 'HH O
L r %C r(
cM LO Cl O
U r \0 0 C .C4 c* )
HOHO4 0 10
rH O T
ddI Iv vC, c O,4 CS* * i vI0 % I
CV G r CO(4 O C' OC0 00
Ivi r- v % CY It u) H O o ac r CNH 1 * ;t- 1-T r-i _ rt H J O
I I - I I - I I
0dd0r'S-I C r-
.* *1%N 'JH 04,.
I'SO I C)I . I %-,
o O O 0 tn 0 0
-IH rA n 4 n 0r ) < C) H 0 0 0 '
IvIv I vIv
0 0 0 0 0 0 0 * *
-I C4N W-400000 000
v0% 0
' C 0C
c N co c4 0o eN 0000 0000c;d c;d c;c;d cvv v v %O N 4 Itr( ( N N
H-O H O 0000
0 00 0 0000 Oc cr)O C c c cnHO 0 c 0000
0 ) . M co .M ,
0 (' Q O 0 0 0
0000 o 00 0 0 0 ; c ; c; 0
co r( o ro* a a 0
I 1 I03000
enN cn C4000000 0v _
tn W-f L r-000000 001'-I'--I %-, I %.
OH
00000
C) O O CJ0dd
I O -i 0000
I I v
l HO 10 N co C_IO O _I O O C0 -I0 I0 0 0
0000H N H00 000000
00 00C-4 C r-q0000. . .
0000
1 - I
O0 CO4 O C0000O 00'd
, Cs ' C
I-'.
-CI 0 C
CV ,- . , ~ ~ Od rVN C -4 en 4 's C '40000 H 000Iv- I v I v- I -
0000i * Iv
0000c-I c; Sdd d * * *
,- 0 VA C)
I - I,%0 10-; ; c;
t M rl V)
Oo r-iO. 9 .* * * C)I %-. I %-
V ,0 0 .0 V V V 0 - 0, 0 co ' 0%..O - %.., %.." %.e %., %.., %-, %-ol %.O el %.., %-O %-., %..O %-, ..,
onC
C-*
.)e4
O9:
.ttO
O*.0
(CON'T. )
C-,
R
0U
zE-4:x:
EHH
.00
44
cnU)
rq0
0O)
4.
0
o4-i
0)
r4U4a)
4jc :
o
0
0 O04 a
-4
Jl,.J
,4 t4qC )
! H
-4ti )
v-I- *OII·~'K4
_ I __ � ____ __
m _
_ ____ ___ __ __
I
TABLE 5 - PARTIAT FUEL , 'T1C 2TASTICITIES
O10 Countries Pooled, Country D:..y' Vriablce)*,. __ 4. _ _ou
(a) 1959 - 1973 (b) 1959 - 1974
'.., O (13 \D Ln c) VI enC 0 --0 --T 0 -. 00000 0000
%-.. %*1 %_1 %V-p
%-t0 i0NT 0 -
i r- r
· %*cN -H O r q 0 N 00 I I I Iv l o oo Oo
.- 1% 1-% -% -41
L~tVH~-~t CH0CIr-i 1 0 14 4 4V 4 c r4
0000 00006 ; ;C;C;8C;a
0O r,- O o Ln V-4000 o c - --oC4 -
00 ,-4 VI 0 0 r n
000 '0 0000
co u)co c'oCcl0*f 'O -o O -I on
0000 000066.c ; 6. 4-
1- ffi< o-4 m 0 m 0
% . .00004- 44
0 00e 000
6 o6 I66 I ,,~ i ,-i- I 'I J
In r u c 0 o c CI - I - %V n -V r
I vI
,H C U H r(N I
.-. ' I 4- '-' 4--
.I CO 1-,00044 HO ...' O -I
c; H 6 C;4 v
O N O -4c; r- c; r
%4.- %4.I
- 4 uM , r4 .n )I-HH -0 Hv0 1 I I I I % O
LA C! ' rC, r Cq rH
I v I
in r-t rlAH-~2HOHO
, O 0 O c CO Ln CO ui000 0 00 00c;-p 8 c; 4c-
45-M r m f-8 8 8 C;r
%..' %-.
O O O \0
O O6 00%.., 4-1
-4£D \D <- \O
000 04 ,-4
0 0 n 0
co co " -N O O
* .('0 NI C 0000_ 4
M-4 -
-4 -
ai C3 WI co" OCq 00000
4- 44-p
CO r- o H- Cn L)o'l,-4 o4,-- 0,- 0
I v I I v
m P5
4 d-4C.- 0 ct, C
Cj 0 O* * * 00004-I O -C; C CI - I
-v 0 - 00 0 0 06
0f l C t, c? -1 0 :en o 0co ot O of0 0 0 0 4- -.-
. o ,- co r, ,-4 co oN o N0 r- H H
*~r~ * ** **Ho Vo Voo
P d -. 4 -4t P-4 .1
t -. 0 H O C% v
c 0 -I
i . I I
N f- Co %O It r- Ln VON OH O i m C0
0 0 0 I -0 00 000I % I ,-' I·dd · ·'vl cv~~ o
.- % e-, .-. ,-4 e-% -% J% -% -% -%
U 40 c , - X ,0 0 o 3 45- 44-p 4- p %41f %-1 % _v 4-p %- I % -I 4- I
.- 4-4cr dr~9 m.4
* eq('I
0 0
C* '%.I -
N
,.41 41- -l% - 40 .0 0 40
%4.- 4- -I 45-p %4.o
9,
Ca.1'$
C7
0 co c oo
r-4 0 04
5·
-4C/)
r O l 00C,4-.O NC4 6 C4 1 -" I -.
o -
*6 . * 8 o; o o1- _1
rl N C-I r.- 4 '-4'
4- r 441 v v
(7 m 00 f--00 0. . .; 8 l - I ,
_
H o 04 -4 H...
c( o 1 I O
\I O ;%-4 p%e.JO'J
-It --t 4LIC I 00000
* * -
c 0 o
4 v
dr c I\ O
I v_/ I vrdcJOd
0 r 0 "~ r r-
O'dHOOI %-. 'IH
044 -4cn 0 r-%o-- r c 0- C ;00000
4 v
01% 0 %O C7M -- i4 -40 80 0O'
cvHe4I00000
04
-4 -%
Cw,00a
HO,-LO14. 4-'~
- -I %C
O 4 O 4O, i 8 l ;
H -4* - 8
-4-o00
44
rI
r-4 ,-4 4
% 4-I I
-4
I O O4O O O Oit r-'0 .- 4tct,
-0 0I C; CI O I I
l . 4o 0 c000
-4
004-,
HH'
C N U i0-00c~c~c
044-
o0~
-4 -4\.O Ln Ln0004
o 4-8
oP544r oO Or-0000H O H O dI'-, I -
.-. I-.
H- 0 r-lO0%-"I --
%O O M L V
-. 4 %-.
0%1 -. 40'%. H-TLOHi-d
0D0044.- 4-
HO 0 rH 0O O O _tC,HOH
0"4m
.4
0
U)
0HJw
3.
c-)
4,-
0H0@1
aC-
I
I'I
0
C
44-
I-
I - - -.---
TABLE 5 - PARTIAL FUEL PRP.ICE ELASTICITIES (CONT.)
(10 Countries Pooled, Country Dunmy Variables)*
(a) 1959 - 1973 (b) 1959 - 1974
1 o t D Co aD It n CO CJ \0 0 H -- H O C% Cn -- e H--I O O O e O q
v v Iv I v I I I v I I
* . *
A A·- O yL . lc~ c5 PI c
r~ u asm-t . -I O 5O OO O 0 o ooI 0 I v I v I
Oc0 c )c(n C>cn 00000 C O
- ,-%Ccli C140 CV OD 0
0000d %.'9.v
-0oO HOH - 0 o00 000 o o
I - I v
**% *. .% -%cV O V %O % V- q0000 0000
I %
-4 C14 c -· K Ke 'K K( ~K K 'K 'K lH O HOc K K * *
C; C C; c;
-% dei
9 'K K K 'K c K; O K* " c * * c* 0000
4~ ~ '54 5
D M (y NC4 H C') H
15 I %ANi C') Hddd"5-I"-
-d,%d %dddu lH HH-. 9.- '- I' .5, - I
-
HO cIS,-l
-51%
c HO o
I
eq% %(4 cr' 00 N
-5% d %
cs o c oI I
O CY oo n b N rqI c0000 0 0 0 o0
I I v v
O 0 oO (n 4 r C"L( rHt r rH 0 H 0o0000 0000
cN r O r CO N O C4(0 O(0O 00000000 0000
% .-
00000v
L c Hue N c
dddd
; _
I _ Iv
or4 CH oH
ddd
l . I v0000
en -I'
; * oo oo
CO L f) ( C 4 c)0C N
0000 H0 HI v i v, Iv Iv
0000 O r0 Cy) 000%O ct r s rq N r-q 8888 68881 -. I %-, , %-
O03
c'q N r H cOH r tc - C O A000 O O O O H0H000 0000 0000v Iv I I Iv I v
.~ 3 - ¢', c4 (c- * %O * c .%D .-t * "4
I 0 000 I -" I -, - %Il
H4N Oc c c c14 C c H000 0000%-' '5, I _5- I '-
0 0 t0 ,10 .0 10 , c .0 1 0 0 .0 0 ,0
.4 N t . N 0, tinIn In 09 &t a & .
C' r-7 C'
Cd
w0
U)c
-A C A
-ooo
d c cn c3
Iv I v
-4 c4 r400I - I
,O rc Ca~ H
v v
0O
0000v vo o o o
o -o
0 I c I -
dddt-irii C-1"d -I'14 ; 1 C
-% -5%,
00000 _ Cl o ? c
t CrqO _4-O r-0I 0 I
00 t,O
0 C
,-4H0
00S
$40z
HE
*M -4 Ch r0
v v.
VH % CV Ln54 ' V 9.-
; _
I .v I
0000
OO Co
I I _
,-0 o o
tS% 5%
-I Ol ,I
_c;%c'.5 9.4
0C')0 0 O
v-4 I _ -14 ; 4
O -0 0oO
00 00I %_4
H c; c;IvNI
030
N4
r-40
-Wr4
p-Wc)u00
(5)
sO39
5-4
H'tCcowI(n'0H
H
IK
O,4r-4
IH:0
C4 O CO4
v
- ---
- --
F = 97
Lf r 0 -.zr o( T,N C ' - A. CO I' 0 D CN
*,i 00 ( r VHI -.. I -
03 O *H t- .C
O,- 00 00%- I I -_
o' H o - l 'DOC N O C C) H
I - I I
c;I
CeC3)
O
4:
0i
..- I'I
, hC)O CO Y I P-
_, % I
O cO
I,H O
l O
.-. 'I 0
-,c; jr
CN o ' V)
q3 co . t
0 00
Coo ) o0 0 0 0
I , .
I'- Is-
H0(0
H
I
oq('4oq
I
oq
I
H
H c'4 Cr
P
O4
0:3U
0
Pde
,aWvo
0di
a,C)0.-444
II1-U
-H
to0
r-..
H,toUdHv
4-.O-
U4I
,IH4)0
04.-
C)44,-I
14CdoCc
a)
0ol30U
.o0
0)
m
CdC)44r3HN
CdC)CU)'P4
CdCd440~
C,)C)
co
.3.
0¢Z
)4
H
GO
O OI .
C' r- o O O400 '0 00
+I- I- I
O H Hr-
I %_ I
C 3-' o3-00 v;? r4H 00
I I ~
00 i N -
I I%
'n C14 CO nU) ' O O
HO 00I'- I _-
0
-K 0O
I
0c;0.4
00
.4
7CO w 00 (3 0% 0 C 0 N-j , O CN Ul " 0 0
Ho dd H 0
NH OCN D CJ O O
* * . . .Ho 00 HO 00
Ch HH - H O O* * . . * C)H 00 HO 00
I I I' Ij_
0'H OC ' N O O0
-('4%ir:d ~ :C7 C -
. .'
C' 00C;c;dd dd~.4
7
C,
(/
Q
W:3U)0z
to
Hr;
E.
Ki-.
C)
coC,C)
Hco
0Cd4i-
N
C)
:30
a)0H
f,C)
44
V
P44C)Cd
H".
~0
C)He'al03H
-It-l
0,%
o)c
ONC)
PT,Eq
V)
gk
10
C)
U
:,'Ci
44
44'U
:3rC5U)
O
X'V
U
U
ClJ
C,N'_
C;
tO
:C)
r
'4a
C .Hc
r:Cd'
Nl
4
C ··
-:3.4
m BII - -
- --- ----- - -
i -- _
Note that, except for electricity, the elasticities of our "preferred"
model are large in magnitude. (Remember that these are partial price elastici-
ties, i.e. based on constant energy consumption, so that the total own price
elasticities will be even larger in magnitude.) Own price elasticities for
coal range from -1 in France and West Germany to about -2 in Norway, Canada,
and the U.S. (where coal has had a smaller share of industrial energy con-
sumption). Own price elasticities for natural gas are less than -1 in the
European countries and Japan, but -.33 in Canada and -.52 in the U.S. This is
reasonable given that natural gas prices have been much lower in Canada and the
U.S. than in the rest of the world. One the other hand, Canada and the U.S.
have the largest own price elasticities for oil, even though they had relative-
ly low prices. We can only explain this on the basis of a greater availability
:of alternative fuels at low prices (notably natural gas), so that producers
chose technologies allowing for greater interful substitution possibility.
Finally, note that the own price elasticities for electricity are all quite
small in magnitude. This is not surprising; since electricity is a much more
expensive fuel on a tcal basis, we expect it to be used only where there is no
possibility of using an alternative fuel.
Our "preferred" model can now be used to generate the aggregate price
index for energy. This is done by applying the estimated parameters to equa-
tion 16) (note that the first-order parameters i will vary across countries),
and choosing go, the unobservable parameter of the equation, so that the price
of energy PE is equal to 1.0 in the U.S. in 1970. Then using the data on fuel
prices, we can generate the relative energy price index over time for each country.
The resulting energy price indices are shown in Table 8. These indices will
in turn serve as the instrument variable for the price of energy in the estimation
of our factor share model..
Table 8 - Enery Price Indico, Dr tw d Frr:m "Preferred" Fuel Cice Model(U.S. n 1 7 i 0)
00 r - C O 1-) (I ) 0 Cr a) C1 CC % -J 4 O r - £ ; U O N r C c 1 O: n CM Cf- r( a % 3 ° to ¢<) -o4 o0 ro o C) r O r- ON - O C -t.T 9 O C) NN
Z CY ° D r- \ <r 00 (I r C C I' r - C,% ¢) M C X N s o q N Ci c O n P C% ur N. O In 00 ) .¢ r" ' U c o "3 r. C, c. C3u 3 .. oC) 'n .N CN.,I ¢O O. Co c .-'c
V; c4 c4 c4 c4 C-4' c4 c4 c4 ' H ,, c _I c _I c r.. -;-z ,. O -.:- ,- .C) Ci C, C,
N O rW O rU I n < % n t m U N m U n O O . N N l OC M M N 1 0 C r N O '3 MOZ· · · '. · · ·1C"'Ci 0C 0 CO r ° " " O " c~ C" N ¢-4 % 0 0 C- O r- 0 vT % ) V N N t 7 r! ¢ C-4 _0 * U N .l 0 .-t ...............................
0 c O H 4D M t- - -Ln coMC HN H H H H H H H O I o O H C -')
(0D u ) m CT 0 0 oO I ~ s m M C co n .- r-1 c4 N H C H r H o C C.r C cW W 0 -0
HI C) ) 7 43e t~ C CcV CI~ (~ C CS N tl N r( 1i _( _ - N ~cMl N tn N -,- N C N N C , C"oa cl en H C"
C!. Z C r "s " --I c. o N .' N Cor N NO O ..-I ar r HN..
n i cq u O - , 04, o u O O. t r C L - ,-4 V1 00 r- r4 O o on , - ,- o T H 0O Go 3.. r-s ,- n T,,-4 O O' o o o r-. % o %o o r- r r - O %O . . . . ..
c . . . .. en * C m N C C b N C CO > yJ 4 L" H - ,< , co co -- O q o o c/D c . co co o t- o cO O - . .< rs uN r_ tn - C C s £ u n C,- ' I t VD 1 4 O C C1 C H Y) - 0 0` )O C4 4 - -i H ,- i C O CO O C O O ON 0 ; CO ° O 4 '.-I . C L -T C, CO O-T c. N O c4 ,') 0 -T C.'
./I U'~ u'N u"N , _ l.O r.-'3 O O ) OC O- O' C, CO O C'' ,- O * .- c
Inl D r t0 0 O en 'T If) vA t.9 t_ 00 O1 "l T i n "" tP " O O .O ". I, ', .n co ON co .:o = N m tt) n n Ln L 1- \3 vO \3 3 \ D .-_ %:! · , 1 ) . r- ( -, LeN U L L t Ics ) ',0 ',-') I k O .I Z t- - - . -
0 O 0N i7 O 0 C C . C7N N CTN t C! J C OO Ch ON C,% CJ C'% C C cC O CA QN -1% Ch Oh N IN N N H H ,, -r H H H q H H , 4 H H H H H H H H H H H
-41-
5.2 Factor Share Model
We turn now to the model of capital, labor, and energy shares. Once again,
choices must be made regarding the use of dummy variables and the pooling of
28data. In addition, we cannot assume homotheticity, but must test this as a
possible restriction on the model.
Parameter estimates for several forms of the model are given in Table 9,
although other forms were estimated as well. In columns 1 and 2 the share
equations have been estimated without regional dummy variables. In column 1
the cost function is homothetic (Qi 0, i = K,L,E), and in column 2 it is non-
homothetic. These two models can be used as a first test for homotheticity;
the value of the test statistic is 68.4, and this is significant at the 1% level,
indicating that homotheticity cannot be accepted. In column 3 the cost function
is non-homothetic, and intercept dummy variables are added to the share equations.
A comparison of this model with that in column 2 allows us to test for constan-
-cy of the first-order parameters across countries, The test statistic is
.359.8, which is significant at the 1% level (9 degrees of freedom), so that
intercept dummy variables are retained in the share equations.
In columns 4 and 5 a non-homothetic cost function is again estimated
with intercept dummy variables in the share equations, but now Canada and the
U.S. are pooled separately. Note that the yij parameter values change con-
siderably, with the values in column 3 generally midway between those in columns
4 and 5. In addition, the parameter estimates generally become more significant
for Europe and Japan, but less significant for. Canada and the U.S. This pro-
vides us with no firm indication of whether Canada and the U.S. should be pooled
separately.
28Inclusion of 1974 data is not a question here; our derived capital price dataextends only through 1973.
, -4 t~~~~~~~~~~~
o I. [ ' ' '*;.0 4 ) W )k, D S , (I (
%D i4e M4
C) cl r-5 -H > > " ezO p -,-I
o o 1 ~C00 U ' ,z __ .: __ I'Hp n
i T (DI ,,
c >
a) cXi S C
n n HE. >-. ao i S
la: " -i4
0 P 1 .-I0 ¢ Dt. '
( cO 4 0 'D 0 0 C' COuf) 0) N r- '0 C\ U) r ) C)
c .. . '. . C. . * crl ,Crl C -1- N- c'.i c'4 cl -~r -.1'
N ;r 0 r " C N H C H H N ' 0 HHCO a " C *. -r- \D r- - H-
0 0 0 O O O O0 H H
O') C`4 - -7? 0 z-
0 f C) -Z ' C i C4 H C tr 0 -- - r- - N 0o r -- -,-
CF C l C;' N C N -<
-K . -t '. I. . . . ' 0 COO~~~~~~~~O C) C) o C) o- o so
..'2 ~ ~ L'3 c- o o' o '
Ni ' N .) CO 0 nC '4'.0 -1' -< CD co . CO cn Cl C70 o o C .H N H H H -
I I I I. . .. . . . . . .~~~~~~~~~~~~~~~~~~~~
r ' 0 o E tr) CO N N" H o ¥r o H aC )O U C C- \0 CO C C' N " r-
Lr) n C Co co -4 co 1 C %t- ' --0 0 T O '.oN N N H H * N N N N *H H H N N
0000,00 L-0 00000000' ~~ * * ~ * *~ * . . . ._
0 O O C.) r--C t % o r-, Co , o,C; C' '. C ' C;'. CO 0 N N O H CO H
*0 *) vC) H < C~l o n U b t) < C ) O0 0 0 0 0 0 I 0 0 . 0 0 0 0 0 0 0
0 Q ^ ' ,o .a0 oel co a--ia4c 00'n% Cl L n U
rI ftcl N C .0· ,- ,I D ,,~ o~ o' co
o o C4J
v 4
Z R v v v0i~r > ' r -I, 0 eN
h~ ?q H 00 000 0
~ 0 ~ o~ o o o o o o c:J o o o od o o o o o o o o0 ,- C;O r O H 0 0_
. > 4 O H - O , 000 ( , (H - , -4 O 0 N H H N
1~ ~ ~ ~ ~~~~~~~~o V4 No U. 00 Ln :I 0 m e < m V) m r- r- fl m < 4) W CO '' H N &r CO < Ot Cl COm Cl L" N H N Cl N H
C NO iu \o N '. N N - N HO'. m Lf N in H in CZ o . N -- H N .N., HN H4 _ .C)N _
ro ~ , -t 0 CO 'T -T -t 0 -..C ) . - C CO N C' N r-, C'. C) CO co C.o C) ?C N N C N Cl N O Cl Ln' ''D Ln" \.0 if' 'D N- u -It-
V HJ o co
C)~~~~~~~~~~~~~~~~~~~~~~~~CCl C
C1 4 :) 0 00r N 0 o r H
I .m Cl N
0OH H 0
zZ; *- .....0 0
O C) Oj: r
00 H
O
o 0 0 E U \ DCO 0 -4
H 4 )rs O OO
I0
fJ Ci _ c' n -n Q C I: oa n - -° c' '- * n .. t- °N s e_ n
I
_ _ _ 'e
r *4 a)
0
0)
0e
P4lo)
XU)pa
C)4-iU
0'o
E4mwl
ks
. (X-
AX
E4
C)0I'
,0
r4
-q
pi)niHr
I
- I
I
0 4 I
4. D v h
'd O H d:.r v ) I10H I0i c .0)U'0 co on . ci
01 -W 4 m CI4 Q X. >.f! -,> US ~0 p X Ae -. !>s L
0 0% -
t; C)I '"r
CO CO N. , O -I0 -. 0 -z O N0 N. r- O0 0 -
O O O O sO OC; c C; o C;0000001- %, -
cO N
o-' %n I-0 C)C C;
Cl VN -7 m -. 7 C N 0w C1 C, O v) O CO: f-
0 0 0 C 0 0 CO 0 C 0 C0 0 0 0¥O jO - -- 0 - CO 0
00000000_ E a
C- N H co O C OO rN N. CY) N. '. O'Lu n Ln c') N M %" r' In -z CO - Un0O cO 0 0 N- CO cl 0' cO co C' .-T 000 H H 000 0 0 0 0 0 0 CO O O O- O O O CD O O O O Oo o o C; o o oC; o C; o C; c;
I I
-T 0
0 00 0
O) O to U1l U~O- O O O *LoI N. o NC -0 00 LI L0 0 0 00;c~-c0 0 0 0 0 I- %., -
C)¢0
O00
H a H 0 H H o'-7T LnIT '00 t- '.00 0 0H N. r. 00 o o 0 0 o oO O O O oI * * I ! * 8To To To 1o To T,-- . v v
c,,a N
0 ~0 ~X O.4i1· 0
4dO c~ cUrOz 42oi 0 HI 0c
oi eo .-a > :O 102IC Ca oenI o. '1 0,041U C) C',
0 m Ir
coiei.1
0 I en
m' 0'0 HH I
0 0 MOH, i ,o SHY o
1 4 .i.1 N
0 0 '.0z a
O %H
OH
00 Q
0
0) 4.1CU '.
O 0 a'lOH
c o
4H=211-4s- 4.1
N- o OH V N co 0 - cN4 c a' N a H0 o i) - 7 0 0 0 % --T C" -7 co N. L' cn tn -7 cM cM c' c' '.C '.0 IT It i C'l N n -. { -T N NO 0 NO 0 0 0 C l M 0 00 00 O . 0 0 0 0 O O 0 . .
·' '. ~ % ' %.' .~ . .~..' ..o~ % . ~ . ... ..- .. '- o 'O O O O O O O O O O O O O O O O ° ° ° i
,- 0, . On CY) O m 00 C O C C I % -O 4 0 n
,- ,-~ o ,-~ w- q a- ,-~ O O O OD O O O O O) O H H Ns H H H H H 000 0o 0 000 0 0
* 0 0 0 0 0 0 0 O. . *. . . . . . ' i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...
O I C- O CO O N O N. r N N H
O e N O N O O CO m N O aO
N. - l .,-0- -.- . -. .
a'I a' 0 00 0 co 0- - 0 0 0 -q0 0 0 00000000 0 \_- HO s_ _ ~a'j
CJ N N. N. '. m C NO -r -I COO CO L *0 'O CL I 0'\c H CO IT H N C H C N - N N H o m N H Ln
. . m - m N N -*- NION N * . * 0o o; ' o o o o; o o; o o; o o~ o oI I. t........ ! I I,_ I ....I. ..,N~ .,l .0 , 0 H 0 0 0 H N 0 C
Hi \ H 0 N N a' CO H O ,--I H -u H N H L o H '0 H 0
H H l m 0 H N N H -7 -T 0 -4 -I 0 0 0 0 N H HH H H H H q H H HH 0 0 0 0 0 0 0 0 0 0 0n < -e <~~~ ^ CS CS < < < N~ Ch O CY% N CO O CO %O % n
II~ ~ ~ ~ ~ ~~~~c I-- q !- I- I I4 I ,,,,i - I. ·. '! '
O~~~~~~~~~~~~~~~~- :- O I~ q 4 ~ ~l ~l ~l 0 ~o ~0 0 000000 0 000 0 00 0000O O O O O O OO ,-% , -O O ,- -O O O O O O OO O OD O1 O O O O O O O O O O O O O 0 °. ° ° o 0 0' rs ^ o H o o n N tn N. H 0 H H '.0 00
o o o o H o o o o o o · H n n O O H N N H < < O < O O O O NC 0 L
HI N '. 1_ I {_ 0 0 0 0 . 0 0 '0 0 0 ·o c; ~ ~~~~~~~~~~~~~~~ ~~; ; c; c; c; c;
.. . . . . . . . . . . . . . . .I I .I I I I
N4 H - 0 0 -4 '.' '-7 -4O -OOO O O O O O O O O' ON H' O ON CO N Cl N NO OH 0 0 0 0O 000000000~~~~~~~~~~~~~~~~~~~~~~~~~~~~0ILO O O O LO cO H O O Co CO 0' H m N. N H N '00~ ''D .O 0 .0 N. 0000c; ~~~~~~~~~~~~~~~~c c ;Jc c; J c O 0 0 0 0 0 0 0 0O 0 0 0 0 0 0 0 00O O O O
O I I ~ · I I I I I I I I I I -
4 0) t g-. w a .- HH
* .4 Ncr '-4 N ) .-4 N en c(
C" 0 0n I" m m en m 4 C I 04 N lN 0 )4 n c co Y C (D6e * 6o 6s 64 6 6 r6 6o 6
• o 'I:IC i
·N.
I
0-% 1-1 -% 1-1 -% 0-1 -% .11% 1-1 e-, 0-1 0- 1-11 -% I-N -%
A second test for homotheticity is perfomned by estimating homothetic ver-
sions of the cost functions in columns 4 and 5 (the resulting parameter estimates
are not reported here). These models can then be compared to the corresponding
non-homothetic model. For Europe and Japan the test statistic is 8.58, and
this is significant at the 2.5% level, so that homotheticity cannot be accepted
here. For Canada and the U.S. the test statistic is 1.25, which is not signifi-
cant at the 10% level, so that homotheticity could be accepted. However, if the
regional dunmmy variables are eliminated, the same test for homotheticity gives
a test statistic of 32.4, which is significant at the 1% level. In addition,
testing constancy of the first-order terms in the non-homothetic model gives a
test statistic of 2.35 which is not significant at the 10% level. We therefore
consider the test for homotheticity to be inconclusive, and retain a non-homothetic
29 model.
In column 6 the non-homothetic cost function is estimated, with all ten
countries pooled, using data at 3-year intervals. Comparing columns 3 and 6 we
see that many of the estimated parameter values do change considerably. We are
thus less confident that we have estimated a long-run cost function than we are
for the fuel share model.
The resulting elasticities of substitution and price elasticities of demand
are shown in Table 10a and 10b for the model in which all ten countries are pooled
together, and the model in which Canada and the U.S. are pooled separately. Note
that the choice of pooling method has little effect on the elasticities of the
European countries and Japan, but almost all of the elasticities for Canada and
the U.S. are larger in magnitude when these countries are pooled separately.
29We also tested the hl-uethsee.s that the y,. are all zero, i.e. that the rouzticn
function is Cobb--Dv.I. ' . I'm ., t st at _s cs are significant at the 1% level,so that this hypotr.:ses c be rejected.
-44-
f--"- r 0 HH -4N ; NC' IO v 1 IVI O, C T C) C-tO (OH 00 V-i t-A -#H
00.00 00 00 00 0 IO
co tO -4 C-% "Oo4o' r~ ~ c-~ ~0C -4 , r-4 C CV4 0O
HO HO HO rL('%. v v wIY
L -- ~o r o40 r -I r- ( HH N cO c-400 'O CC O LtO r-4 m -4 LI00 HOq m 0 r4 0 IM D N h 00 HO C0 4O 00HO 0 -CN C
IVIv v v I v Ivv v v o N ~ vI I
cor C O H f- n * Lr) 'CO '0aO co tr -tr N co 0C0 0 0 i co-( C r- --T -( O ,' O -( CH Cq r -( Oq O HO h fO O , -
C'C 0 O C N . H....L~r. o,. i!oc oo~ i-,JCO O 0 0 m N 4 5 S 6 0 S 0 co 0 %O 00 5 r- 00 oq
% 4- N c 0 r- '-0 H O -OC O OT o -. 1 Lt5I C Co J'
I v v v v v v I v '1 v v,-i,-I'
HH ONH (OHc0 ..4 co CN N O. NnO N O IOND HHq C LnN00 C OHO. rO 0 c C 0 000 00 00l O OHO 0 OO o
Iv Iv v v v u Iv Iv v ~' ,.-v t-I '. . . .I i
Lr-4 'OCD HH OCD N CN C; LrCO OCO NON8 rH t ri OIo "O 0 0- r- 0 0 0 0 , C l 00 O ' NO ON O- t,- I .
; ; c;~ cdc c;J jc; cdc cc ~; ; c;d ;i V Iv v v v v I v I v v ,-iv r-. v-I I rI
COCO NON -H- ON 'O ..- o c NLt' N '-,f. i" rn, fNH,-I 0o'O0 r'O o H r- H 0O O 0 - NH ON.H HH H- L- (4 L
, c; c; J ;d c; c; do; O' ;0 d ; d 4 ; 8 d 8 c;Iv Iv v v v v I ~ I v v ,.-V ,-iVI
*.' 0 0 r 0 O 0 O a% Oa r6 . 0 ,-0 ,0 0 S , '• , -r- O , 00 o 0 H -O H O 0 C 0 -O r- ON l O VI; C; c; d C;d c; ; c; ; c; 4 c; d ;Iv I v ,~ v v v I ~' I "- v v ,.-v r~vI I
r -q OO HH0 ON NON cNO ON0ON cOn 4 LNN Hnf- O00 '3'cq
H NH H O COOi 'O,1H NhO o H ON.... .0Lf' *
C* 09 O 0 0 , l 5 6 0 ~ , ( S 0 S 6 0 0 00'l 0 0 0
ON- r- 00 r-i ,- rIl . -- 00 -4 c c O r,,' -4 I - 04O a .? 4
Iv v v v v v I v I v v v rciV ,-.vI Ii4 i .0 i .% -i i 4 i!% m 4 -4 i % i 4 -4
0 ' H N (OH (4 N - COO CN ON -; COO Op -4*0 ) O 00 O S 0 O .S to I n00 HO 00 HO 00 HO 00 HO 0 'OHv- I v -o v 4 v o v~ v I I v v H H-i , -I I
_ - ! J · ! i · . i4% i m ·
b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
VIr
o
I
-4
'-.
U;C',
tI
0
zI-,
Hpr
H
C4C4
0
4
0
A
10
O
Ho·4J0
.0
to0.4,4i
4-6
touC4000-rq
4-i
.41-H
4im
go
0H4)H
90
IHww
co
r-IIV
W-4.2
0)
0.0
Hao)
0-p:34
10 4
0 4sHO
0)
p 4'
4iCda ma)
O0) r-
90'4O Cd
laOdecoa
CJ
t;
.0
-- - I·-- - -- -- --- ·
--- ·-c·-·- --- ·- ··- ·
'I - ON In ' T- (n < H e 4 N t- C- %0 r-- f, I r- %O ?-) o C mO CN o o 0 0 o o -tO t In -t o o o o o0' c' c; C c; ' ' cc c. cc... . . . . . .. .11. . . . . . . .O O o o o O 00 0 o 00 o o o C O o o 0oI , I ~, ~ ~ v ~~ v I ~. I '. _ _-
0 %0 rs O uN t N 4 CY) S m 0 5 0 0 o
I T 0 4L 00 00000 C)00C0 00 )- 0C1 0000 C 0 0 0000 %DO ; C'J O ..... i i 8 i' i i Fri Ci j' ii i H
c- O ri I C o r% o o o oI Ot o or 'D .' O Co r-t O O O OO0 o.- ot ori 00 00 o-J o -o ooo S oo oo 0000o I I Y ) o 0 . Iv 0 v 0
C0 00 0 0 0000 0 0000 C ) C 0000C C' O HoD O 1N - O , inH , H O -I I D -t <L t r- t- rNHTo u O r-t O O O O ('O1 el)O -tO COq O 0 0OB . . . . . . . . . . . .
.-II~. O90 ~. ~ ~lD 0 0000000 00 00 000 0 C000 0-'-O'9 O ' O O O O O O O C- O rO O O0 O O O O O O OI V I ~ _ J * v _ _ v i I v _ v
i.5 i 5 i .5 i~ ii5 i 5 % -% 5 H'N ,-IN ,i u ,O f'l,-H -'H 0'' ' 'C)- ' r '5..u 0H 0H -
el9 CY C)9 0 ~ 0 0' 0 0 0 O0 'oI 0 ¢0 0 .V'0 o 0 0 0 C 0:;c; c~c~ c; c; C &c cc dccc; c ; cc; dc; c; c; 00 ' t O '-tO cO 00 00 ~ , C'J Cl C O OO O 0 O 00 0* i i 11 B ·i i Si
n .n . .. % .n .f . . - . ' . - co .n . - .n . T . LI . . . . .- AO O O.; O O 0 0 00 0 0 0n0 0 00 0 0 0. ,
In In co 00 r., il 0 i. ii co i . in . i T %0 - i, rI o -oo cH 0 0 0 00 -'tO C9O H IT 0 . O'u 0 0 0 0~ O ' O HL' O O O O O O o' O o40 u O H-'O O O O O:'co -'co .cto do 00c 00c coo; cic -'o coo; 00c 00c. . . . .. . . .. .0 0 0O O O O O O O 0 00 000 0 0 0 00 0
I05~ -5- -% s_ -5E I 5% -5% ~ S5% -5%,6' .' .OC . - , . 9 .' -. .9'- -. 0 . " . . . ., .' ., ... u.~ . g -- . N . .,O ", o, ooo, O rO o O o o oo o o O O o oI
vI v v vv v I
v
I _ v v
v vH vt NH 0 O v v H v v O 0000
. .0 . . .0 . J . . .ii i iE · i o i _ i i i i I '14 14~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
_s~~~~~1 - 4 1
140
la
la
1.40d
,0.0to
0
4-)'.406Cs
.04,10r4
4IU
44-
0Ho
0
U*-I4.4
400*H-04H)
.0
.0H
pi
00to
0I404.4
0N"-4
H
0:4w
00
041
ocd
Hto00
0
0H0
4
U
-%
'5-
r0H0
04
co4
axA -I.-U
0
coUa
cI o % 0'3 % ' r- Lr 03 (4 u
00 0 00 00 C 0C, o oo "- CC) 0 - o C) o~; c^o c;~ cc c ;
-5Ln oco o0 01 .- ,
coo C r- r- .N e ,u a O ,Ci H- 00C1 -,-I o0C' r-.0 c o H
1 o o o o o o o o oo
Oes -. f) .. U, LI -. , .T.C 0 l0 0 V0 D 0 0 0 0
co c o oo ; o o o o;ON -' CO .. O ') -. Lt .' -' ,c0 C0 N 0 IfO D O 0 0 00 00
~-~v . t ' -' IJ I', u. u U% O ,--{ -. c' r-.co
* C) 0 C) C; 0 0 0 C ;
a--~t 0 N u ) *4.1f - b., (i-0 -0 C V0 -* co coo
c< o co l o co co O co oC! .. IV I
' o c o U) o ' o o o O cO o.
*7 5 5Dx O 0 0 0 C C 0 0 O
O 'oD o O c Cv O 0O
dd dd ddX dv v v
h h h
WQ
¢vt
zw
v,
CO
0U)
H
H
wC999
u- -
aii0P.C*
Ca
a)o0
o,0:3'N0
4-4
o.ea)
,-I4o
0C)
Pdcoto0
v-I
00
0.
10co0
Hu,.505-i00a)-H
o,op
I',-0.2N
5I
,o4.
o.4
0C)
0-4iPd
4
0U0E-4rC
,0* 0
'-I0(
* -900Hl
- -
-48-
Pooling Canada and the U.S. separately, however, also results in elasticities with
larger standard errors, so we are inclined to choose as a "preferred" model
that for which all of the countries are pooled.
Let us now consider the implications of these elasticities for energy
demand and the substitutability of energy with other factors of production. First
we see that the elasticity of substitution for energy and capital ( KE) is posi-
tive, although small (0.61 to 0..86). We thus find that energy and capital are
substitutes, and not complements as earlier studies for the U.S. had indicated.
We find that labor and energy are also substitutes (with elasticities of substi-
tution close to 1); this is not surprising, and is supported by most other work.
Similarly, we find that capital and labor are substitutes, as expected. The own
price elasticities of demand for capital and labor are around -0.3 to -0.5,
which is in agreement with most earlier work. The own price elasticities for
energy, however, are larger in magnitude than most of those obtained earlier by
others. We find this elasticity to be about -0.8, whereas most earlier estimates
were around -0.4 to -0.5. Most earlier work, however, was based on data for a
single country, so that it is more likely that we have estimated the long-term
31elasticity. Finally, note from the cross-price elasticities of energy and capi-
tal that over the long-run a doubling in the price of energy should result in a
5% increase in the demand for capital and a 6% or 7% increase in the demand for
labor as substitution away from energy takes place.
Since our model is non-homothetic, it is also interesting to note that what
our results imply about economies of scale in aggregate production, and about
3 0Berndt and Wood [9], for example, found strong complementarity between energyand capital. Griffen and Gregory [34], using pooled international data atfour-year intervals, obtain results ver silar to ours.
31Our estimate is close to that found by Griff`tn and Gregory [34], who also usedinternational data.
the elasticity of energy demand with respect to output changes (EQ). In Table
11 we show the index of scale (SCE) introduced by Christensen and Greene [19] (see
footnote 14), and the elasticitiy of energy demand with respect to output changes,
as given by equation (25). (The indices and elasticities for each country are calcu-
lated at the point of means.) Note that the index of scale economies is insignifi-
cantly different from zero for each country, so that the aggregate cost functions
exhibit nearly constant returns to scale. The output elasticity of energy demand,
however, is significantly less than unity. Thus, even if energy prices remain con-
stant relative to other prices, as output increases there will be substitution
32away from energy.
We can now examine the total price elasticities for the individual fuel
demands. These elasticities are computed using equations (20) and (21), and are
shown in Table 12. The own price elasticities of energy are obtained from Table
10b based on all ten countries pooled together. Note that these total elas-
ticities are larger than the partial elasticities of Tables 4 and 5, since they
account for decreased use of energy as well as interfuel substitution. We find
that coal has the largest own price elasticities, ranging from -1.29 to -2.24.
For Europe and Japan, own price elasticities for natural gas are large (-1.37
to -2.34), while those for oil are small (-0.6 to -.56). We attribute this to
the fact that for two countries (Netherlands and W. Germany), as oil and gas prices
fell, there was a large increase in the share of natural gas (from almost zero)
as supplies became available for the first time. This might have tended to bias
the natural gas elasticities upwards. It is more difficult to explain the low
oil price elasticities; oil prices on a tcal basis were generally the lowest of
any fuel, but oil did not gain a dominant share in Europe. For Canada and the
U.S. (which was pooled separately in the fuel choice model) the situation is re-
versed - the price elasticities for oil are larger than those for natural gas.
Here natural gas prices were lower than oil prices, and the share of oil was small
(in the U.S.) and roughly constant over time.
3 2This result is not surprising given the data. Note from Table 2 that forlarge-output countries like to U.S., the share of energy is smaller than for
low-output countries.
Table 11 - Index of Scale Economies and
Output Elasticity of Energy Demand
(all ten countries pooled)
Standard errors are computed based on constancy of shares and
prices at their mean values. The standard error of SCE is thus
computed from:
Var(SCE) =L,M
i(igP i) Var(YQi) + I logPilogPjCovar (QiyQ )i=K, Q~ j
and the standard error of Q is computed from:
VarOlEQ) = Var(SCE) + [2logPE/SE + 1/SE]Var(YE Q )
+ (2/SE)logPKCovar(QEYQK) + (2/SE)logPLCovar (QEyQL)
Country SCE 1EQ
Canada .0015 (.0080) 0.785 (0.108)
France .0086 (.0383) 0.783 (0.113)
Italy .0032 (.0335) 0.855 (0.078)
Japan .0105 (.0487) 0.849 (0.087)
Netherlands -.0124 (.0170) 0.818 (0.093)
Norway .0056 (.0172) 0.807 (0.097)
Sweden . 0019 (.0205) 0.864 (0,'070)
UK .0041 (.0327) 0.778 (0.113)
U.S.A. .0003 (.0037) 0.624 (0.188)
W. Germany .0012 (.0316) 0.761 (0.122)
. q
in rH rH m 0 0 00 t 0 H 0 N f-.C;ooocjcjcj
Cfl Cl It 0%
0 0 4 0
J o N NI I I
H r O 0%0 ,-I , 0-; C; 0 0
1 . *
I I I I I I I I I--T C4 O' cn o rs co o Ln 0 e n 45 c Cl Q\ %) 0 Hn Cl Hn 3 o r 0 H H* * * 0 0 * * * 0 0 * 0 V O *
H 0 0 0 0 0 0 0 H 0 H 0 0 0 0 0C'~ O O ,- o t C; ON N , .
IT 0 Ln 0 0 ST H Cl H en 0 0o o o o o o O, , , , , , , , , , .,
,-IN~ Ic IK M 0 0% -,,I I I c i% In O D 0 0 O
I I I I I
co ON (4 C 0% N %O cn cn co PN c H co m
* C0 0 o 0 % 0 0 0 0 0 4 0 6 0O% N 0 o oo cu %o 0% H P 0,
< 0 O 0 0 C H < a pC UC Co O H 0 ;* 0 . * C.% 0. . . * t * . ' 0
H O O O O 0 0 0 0 0 0 0I I I I I I Il ;% c; ; c; c ; c o < C H H C C; o'0 0 N 0 O H C C l N Cl 0 O 0 H 1 U,0 %D 0 H CN 0 0 n0 I I N I N -I
< U, H . . .. . H
H H H H N N N . i,. , .. j j.
i i , , , F . ......
r-
I
'..
:31
a
C)
m
9
-,r
0z
z04Cfi21
4QCHw
8
1W
- -
1
0Cb-4r441
hU)0-H
0C4
H04)
H:30r-I
410
H0H,001I-
41
laco
0.41000
.
V
.ato0440
CO
0
"4
C;
rr:
:-
tC
.0U O
C!' '~-
(:·OC
u
·H 4-'0kOC
II .-'
CJi
Cdco 0t3
H C
h'.
il FNC
'y c'
t} r -Q C!
U fr' d
3 -)·
re Qk
cu rw3 ̂
o
H HO CJ·
h~g
r O
- - -
_
I
C
In Table 13 we show the elasticities of average cost of output with respect
to the price of energy and the prices of the individual fuels. These elasticities
are based on equations (27) and (28), and are shown for two versions of the factor
share model - Canada and the U.S. pooled separately, and. all ten countries pooled
together. These elasticities give us the effects of increases in energy prices
on the cost of output, assuning the level of output stays: fixed. They thus pro-
vide information about the inflationary impact of.an energy price rise, but they
do not provide information about the effect o the level of GNP. Note that in the
United States a 10% increase in the cost of energy.would result in about a 0.3%
increase in the cost of output, whereas for Italy, Japan, and Sweden the cost of
output would rise about 0.7%.
5.3 Logit Models of Fuel Shares
We estimate a number of static and dynamic logit models to describe the de-
pendence of fuel shares on prices and the level of output. The "decision functions"
in these models are linear or logarithmic functions of relative fuel prices Pi
(the price of fuel i divided by the price of energy), the level of output, and in
the case of the dynamic models, lagged shares. Recall from equations (40) and (42)
that this leads to a set of three equations that must be estimated simultaneously
34since certain coefficients are constrained to be the same across equations. We
therefore use iterative Zellner estimation to estimate all of the models.
Our static logit models are of the general form
10
1 (i/s4) klai4kDk + biPi - b4P4 + ci4Q, i=-1,2,3 (49)i 4 i 4
3In comparing these elasticities across countries, remember that they are dependenton the shares of enerv,y. and the fuel sh.ares. Thus Italy, apan and Sed;len hv-:the largest valu.s oz 1C _ in part bucause they have the largest shares of er ervin the cost of cutout.
3 4Even without cross-equation coefficient constraints, simultaneous equation esti-mation is desirable in that insofar as errors are correlated across equations,it yields more efficient par;eter stim.ateS.
It
O oo0 o*) 0
o oCC)
o co
o o
CON 4 oC N ' Lf )D ' OC4i 0 0 H N00 0 0 C) 0 C)0 g CC CC CC Co Co
Io VrO O
,- coC)
* O
O D y IL C) Hr r- OC -, CCO0 0 00
. . _ . . .
c O LI C C'lI r C rr - C 0 0,- 4 H C0 0
04 0 CO
o o o +%O ~1O0 0CC CCo
O O * * * C)0 0 O
-O0 O) 000 00
CC Cl C CC 4t %0 Cr O r O -H -4 O 00 00 00 00
O -O
r OO O
)0 C Y )O0 0* o o *
- r-4O O
Ln -I r 0 Ce rOt O C H00 00 00Lf1..O OO O
CO
*
L O OO OO O C O - O- V) 0 0H C) C c
;>~) a a car cli C C C( O, - 4 r- r-4 r- HH r-
i Ci CU u t u
0)
00P64
0C)0-4
4-,
0U0HH)
-f-iHC
z
>-4:4n,0
zw
Atn
Cz
EW04H
'
IZ
" T - Io o o-Cl Ot Oq C C)
* 0 r- 0 * * -0*0 0 0 0 0oo Cb CC C\ o C*0 Q X *
Cl, C 00 Co C C) 1
ro ,>
%D %1 cq 00'o,~o C'Co,
L) 0 Ot* *1 *
I'D0 H- r (\I H -0o 00 0 0 ,0 0*~ * ,- ,- ,- ,- O * -* -~
C CD Co D0o o O O - 0OO OO O O o
O O-It c
O O
O O O t cn T O rl O r-HfD O0 O O - O r -
CC M c t c %D CC CN Ot- D O HO G OHt O 0 O 0 00 0 0 00
O c O r o Pr- o oH H- H -4 00 00 00 0 0
* * * * * *
LI-< H CC CC C CC*0 0 0
* *' I* .·
CCOO OO*? .j *
C, Ol
O O
CO C C c' -.4
0 0 05 00
H O O OO00 L0 040* H C C * * *
mC C"J m CN "c C14J T -1NvO H H HD H ND H- _ ,O CN C". C, LI Cn ON
-P F- rp -P p
UL) -C.)
i-
JtpiU
V;
zw
V)
z
H
.¢
R14u
PL
O4i
4i04
04-i
0
0o'4
0)
4J0O
4.
M
C0
,43I
,U0U0N0
U
U
HlIzd
* k~
H
0c-H,0H
%D OHC00 00
i -
LI ---
V U t Ujk-) .
i
pc;
-54-
where ai4k = aika 4 k, and ci4 = ci-c4, as in equation (40). The Dk are country
dummy variables (countries are ordered alphabetically), and the fuels are ordered
(1) solid, (2) liquid, (3) gas, and (4) electricity.
The dynamic models are based on the assumption that .the choice of fuels this
period depends on the relative shares last period, as well as this period 's rela-
tive prices and output. The dependence on past shares is intended to incorporate
partial adjustment of the captJal stock. It leads- to equations of the form
10
log(Si/S4) klai4kDk i b i b4 4 i4
+ dS dS 112,3 (50)iSi,t- d 4 ,t1' =1,2,3
Note that this is not a Koyck adjustment model. The coefficients di can be greater
than 1 (although we would expect them to be positive), and in general a change in
price will not lead to geometrically declining changes in shares over time.
The results of estimating various versions of these models are shown in
Table 14. Unfortunately, the results are disappointing. In all of the models that
we have estimated, the own price elasticities are positive for both solid and
liquid fuel (note that b and b2 are positive for all of the models). In addition
the coefficients b3 and b4 are insignificant or positive for some of the models.
The logit models provides essentially an ad hot description of fuel choice by
industrial consumers of energy, and that description is not consistent with the
data and our a priori expectations regarding the characteristics of fuel demands.
6. Comparison of Results ith Other Studies.
In Table 15 we present a survey of recent estimates by others of industrial
energy demand elasticities. ],e can compare these estimates with our results to
get an idea of what "concensus" elasticities would be, and how and why our esti-
mates might differ from these.
C) 1.4 U) m (,) 1
H-4 t? >.O " iP 0
- 'l O 1 '4 -
" ~ Cv P" o 4
' 41 ) U) U 4
0 0t n .H, 44, -' 0 4 ;:U) , r- 0.0
ri) Ca0) C) )
.
U) 0 .
H . 4)D 0
C*4 ZUW r 4aRu U *
w4,304
- ^J O 0..;cC U)
'4 a C4v
-'H 0 r wd I Iu , 0) Uv 4-i
* - ) U 4 -i 4j -44j l*v- i "-
44 1-4 C i) -4Vw Hi & O ; F,
I 0IV4 ¢)VI C)
0 o
r* r41-_
C) r"3
n )'(N
I Iv
"4 - M - O ,-, O'..t -, C .r-4 r- r--Lra t r- L r) C, " Or- H C- a C)0 0a 0 4- ' -. "-. . I · ' · * H -
I- I I I I T iv
rC )N- C))
.I I
v
\ C) COi nOC)n ( N Co
· 1 I I_- '-
,O-0'H1
I Q-1-i C'0
0'.. -1
(NI --
0 .* .-
0: -c C O C OO ,h, C0 /" , ' , 0 CO n 0 r Co -H ,. c'O zcO o 0-CO N0 - nre) o U C ' .'C CO -C fn 00 m * <
I'D ' CO '- co .- * 00 '-z oC r0,0 a, C C '). * ..%0 . . . . 00 . C- . C .'3u. c r . co . .o , O .CO31.( I ' v v .v ov - - I 00 H C4I I I
I " I ,-4
r I_ mC o co r - r- L 0 oD N- O 7- nC C u1 uL) I 0C co o0 CN JN ( ) O t-O N- HC) , ~ .r- H - tH- O- H C) ,t CO u rl O
. .C . C . C . : . · , . I . CC . .
C ,. ~ fn , ' 3 N 0 TO N C4 ' / 0 , -- .In -. " - o I o c - u" - r. ,,--I , CLt) i- Vf C 'D Lf( C4 0 N cn -. .O. H 0. 0 ) a r)( cg CO oLn H 4L)I ,D - ooH aCN M N -- C (N 0t o r) -T l - -H r- -,
. H -b a . 0 *. H . eD . o . L) . L) -.:I . 0 C ) * C:)*L) *- '(N 'In M- C Mi *.0n rq . 'I
0 4 ct CO t H V. Lt N- _ - Ht- -I H v , v VH t I I I I CIv v(N(n m cx c ot n < h4 o H s O CO O e ) r o e \D O n H h r
HI I _ * ' I II
,. . ..
I 'C ' '-~ I "." '
!~ , , .,J · , ,, ., ,, .0002- Co l
I iIvI -I -
H N Cm : Ln % - CO Cy%- -IT It -I -T -t -+ T - "-H4 v- H- H4 H- H- H- H- H- H-0o l co 0 co 0 0 to to co
-:1 - A * -9*,P CON0 0 U 4 1 t
04.1X
-)'H0
0
44
0
01
43V4'i-f
bO01.
04-
0)04i04
co
;."14
4-i0
0H
4H
,0'A
Al
rr c
-- - - - - -- · -- -
r--'. '.0 Q<- ... ' r-4$' 0 a~ C"' rs vi &) '.0'N '." HN f'wo C O O c'. ir >_ ,<N e tr t- ** e c , tr,° cs r-.- co % C c a' .o.L 00" 'O*C\ <)H ~ ~ ~ ~ ·o o,- ,0 r00 r-. . *~-* '3* iC.' - 0 i * o a C1 -- , O N ° C' °, ',,1' 0 * ,N o '.D C. 3*-
*" ' t*r- " *r) AH C*~
* * ^ ; < 9c's'. - r_°<O> ^ru sU col U'I tt't-N.O CN C - C', m. C" l CO C. Ut'" C. ) a? ,. I O -',." O C] t C .- kid 0 'O 'a, C'0N--I. 0~ 0O u- N <"4 o' ,- -,O.·0 '~ 04,-.~ O% ,-t '00 O0 -~ rD. · Ntri %7%?''.0 ' ,.. J , I' ·5c vc O " ' .,.o ," N -. r oCIc) c o C .
coIN CO * CO , * . ~H C) . H ' 'O r t -'. L ."I I I I NI I' I NI I .-- N , HC( O '-' Ij.4 I.'IA 0 II II " N * t 00 .
H *,- '.0 H N. a'. e(',,IC.or-v a'.'r o,. ., C(V 0%A N , a , -''. rO- N) H r- O N.ON
OH * . , * O 4 ,oi , I ' * , -. O ' ." , . u kO.,,.~' I "S (",I u"3 .o. r_ , o · , .N0 NH Co , .. , o-.t -n. .N VI -.NI I corI rc -.. c4 OO co I , N- vCO I
II I I' I '.L I .0 lN00 0 coN ! ,,, , , .N -T ' .O'.O r-.n o H ' .O e H XLO '.o- ^ e ~'.o Q'.O c'4 ^ Ln r / * N * O * *O , D *ON A *- H , I* * : - -. N H-*N I ;v ·CO * CO * C. * N * C cO CH o I i NI
v I v I v -· t', I NI I N v I vI Ig,N ,N .00a. m C
* N * so * *' ~~.~ * ,. CH N o~, * a.*-- '. o ''. ,.N-
I I ' N .,H H.',, N - I H 3 ,- O IC IN vN I v i. vN IH N
O% C
.~f, ,d a% t-~,, o,, ,.,, or , , , .A 0 ,- o -- ONr- ooz UONc o o ',, co m r-. o 'q 'qo C' C)u m ~r C- d cn C? r-..U ~ 1~U~O~90
· ~ ~~~~r N.'\O 0 - - .1 o.i .. . I ~ -Iv c,
C' ., ) , ·C'q "
J.1
o· 0 r, %0 eq 'i "D -T Ln r-. ·7\ ,, , -4 MD ON 0 C14 Ln
' Ln'.0 re co ON aX H*. - -T .r ' -3 -:T -:TN4 N N N N . CO
0 0 0 C 0 0 I * C-
N ce -T u) '. r- o
I cy) CO Cn C e O C-tco d co d l co co
4
-Kw
0
0
5:4t4
0
H0)10
0
'Hbt00
0
40
054
0
C-)
Hi0)H*0to
'.0
N~
H~
I
pCp4-
cnCO4N
ad
--
e~~~r- C ~~~~r- -- -4~r L( ,C 7-4C ON &CO C,) o ~-Mic 'ti O'- o 0 CO CO ,-4 CO In irne Ln cV- 'rr- CrN Lc) CO --T 0C') -;j (1) LI) N -. C\- Lr r-C4' (N-z1 Co( CON -.1 ~ ( -,-· 0 coIr- ) Q ',.O .--. I CO'. - C ,- .' 'CO r-3 oo OD 0 -I O
o cl Ln ,o ,o r- u)I " ''' ,-,O ·c~ q ~~~ ~~-.. ~,o O' , · O · . 0 O M re) c,~ o'h C 4 co 0
O ,. 0 . u. Lf-. 1'-.- -i-cO0 u ~ .OCO C"1--, '.C -J-1 ., el,-,, CO,.-..-,- '.0.?O,- . ~ ~ e'Iir c..i 00C ~ o.co cor I - 0-4 CH o-co Ooo 0 I eq - CO z O' - oo I COO' u'3 (N N r'O-.)00 C. U) -- * t (. O V) - CO. *f CNH 01 * 1 0 0C0 :J, * - 0 *o00CN oN- o-, 001 .1 C0 0 C C4 *c ro4 · 0 o C) o00 m C., * *
o\Lf~ tIO.' C-J1..' COO Lr~i-~ J COO.' '.0 Or-. 0I.t I~ oc H' - · · ·
%~CO NL ON. HN-(,1 C) O,) N 00 C OO.' -i- 0-- 00'n 0'o c-- -*~u .~ CO *~ '.0 CO 0 * '.1 CO *.~0 0 I 0 * 0 *~ 0.C0j COI- r-I C", r- - O0 oM (~ 0 %[ 'D CO C~ - - C) ,T 0 0 u~LnI .....~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1 % 4· O~ .O, I ~l'. v t"l~ ',D I ~ O CO IN I'
Cv I r-. I v~ ~ ~ ~ ~~~ ~~~~~~~~~~ Iv I v' '. ·I
-' -.. r-q O'N -N .,
C4 . P- -4 "~4 o P- o- o) o0 · n r ,oCM cf) H C% m - " 1-4 Ln C)-Z 0 0% C 1" h N- N-4'.0.-- i n .'.... 0 H 0 N- N
11.O.'0~~~ r-~~0.' r C7r- (NJCN OD IL! 04 00. ON- f-. N- '.0 L r-
* 19- C.4 *r Co ) o( " ·- -o{ C · ' co -o C .o·- N-N 'C ·4( .0, , · OC -40 O O('( ·f,- O.0 O0~- 01Cl c-~~ 'CO Ct-)N- .Lt~~ *~ N- aD v- v -- ~-I I I I I uI II Lu r-I · C .. v--l CO CI v ', v I -v v -4 .~. T ' c '
eq4 00- H-.. · CO C). (N. · -C 0 .· -
H CN(N CO * * N-H OH 0 * 0.~~~~~~~~~~C C1 C0) _z H * * * H * -i * - 'e..I- v ' I I I I I IIiI~~~~~ -I,- c~ 0
C) :' . N- H i i -ii
C'-
C
C
H
10
41
0
1~4. 04J
I (0
14itj4.1
4
-4
II
9
-k
Tab] 1 5 (ont.)
Elas. Country Estimate Source
Price Elas.
(cont.) Canada K 0'.76, LL -0.49,
nEE -0.49, KE = -0.05,g
nLE 0.55
NetherlandsKK = 0.05, nL -026,
nEE -0.90
9 industrialized
countries KK = -0.18 to -0.38,r LL =-0.12 to -0.27,LEE = -0.79 to -0.80
KE 0.13, XE 0.11
six-countrycomposite XleE = -0.30 (h)composite - EE
Fuels -
own price U.S. elec: -0.66, oil: -2.75 (i)
elastici- gas: -1.30, coal: -1.46
ties, partialU.S. elec., S.R.: -0.14
elec., L.R.: -1.20
U.S. elec., S.R.: -0.06(k)
elec., L.R.: -0.52
own priceelastici- U.S. elec: -0.92, oil: -2.82,
(i)ties, total gas: -1.47, coal: -1.52
Canada elec: -0.74, oil:. -1.30, (ggas: -1.30, coal: -0.48
Sources:
(a)(b)(c)(d)(e)(f)(g)
(h)(i)(j)(k)
Berndt and Wood [9]Halvorsen and Ford [37]Fuss and Waverman [31], translog
Fuss and W-averman [31], generalized LeontiefMagnus [46]
Gr.i,cn a-c Grcory [34]
Fruss 3)]
No rdhuo [50]Halvorsen [36]
Mount, Chapman, and Tyrrell [49]
Griffcn [33]
Table 15 - Al.ternative E'stimates of Idustrfal Demand Elasticities
Elas. Country Estimate Source
Factor In- a 1.01, a = -3.25,puts - U.S. KL KE (a)elasticities CLE 0.64of substitu-tion tion U.S. (2-digit a = -1.03 to 2.02,
industries) aKE = .48 to 2.88 (prod. workers), (b)
ilE = -2.02 to 5.59 (non-prod.LE workers)
Canada KL = 0.72, aKE = 0.42, (c)
OLE = 1.70
Canada aKL = 5.46, aKE = -11.91, (d)
aLE =4.89
Netherlands OKL = 0.30, KE -4.50, (e)
aLE = 3.80
9 industrialized .KL = 0206 to 1 07.52,countriLes = 0.72 to 0.87
Factor Inputs price elastici- U.S. K 0.44, L -0.45,a)ties T1EE = -0.49, KE = -0.15,
)LE = 0.03
U.S. (2-digit -0.67 to -1.16,.industries) nKK -0.67 to -1.16,
nLL -0.28 to -1.55, (b)nEE = -0.66 to -2.56
Canada nKK = -0.79, LL = -0.45, (c)
.]EE -0.36
Canada nKK -0.31, nLL = 0.77,
TEE = -0.59! ,., ,,, , , ! i , . , , . ,E
4.
Note that there is mixed evidence on the substitutability of energy and capi-
tal. Berndt and Wood [9], Fuss [30], and agnus [46] find energy and capital to
be strong complements, but they worked with time series data for a single country,
and might have estimated a short-run cost or production function. Halvorsen and
Ford [37] and Fuss and Waverman [31] obtain mixed results on energy-capital sub-
stitutability, depending on the particular disaggregated industry or the particular
form of the cost function. Only Griffen and Gregory [34] find strong evidence of
capital-energy substitutability, and their estimate of the Allen elasticity of
substitution is close to ours (1.01 compared to about 0.8). This is reassuring
since both their study and ours use international data and presume to estimate
long-run elasticities. As for elasticities of substitution between other factors,
our results are close to Griffen and Gregory for labor and energy, but we find
greater substitution of capital and labor.
The own price elasticity of aggregate energy use is an important parameter
to any energy policy debate. Our estimate (about -0.8), together with those
of Magnus (-0.9) and Griffen and Gregory (also -0.8) are larger than most other
estimates, which fall in the.range of -0.3 to -0.6. Again, most other estimates
are based on time series data for a single country, and may be short-run.
It is more difficult to find a concensus on partial and total fuel price
elasticities. Although most would agree that electricity demand is less elastic
than the demands for other fuels, partial long-run elasticities for the U.S. range
from -0.5 ,to -1.2. Our study finds electricity demand to be even less elastic;
we found partial own price elasticities to range from -.08 to -.16. Our total
own price elasticity estimates, however, are closer to the estimates of others
(largely because of our higher estimate of the own price elasticity of energy).
We find this elasticity to rane from -0.54 to -0.63, here !Halvorsen [36] ob-
tained an estimate of -0.92 and Fuss [30)] -0.74. Our own price elasticity estim.,te
(total) for oil is also well below the estimates of others; -.22 to -1.17 as com-
-61-
pared to Halvorsen's estimate of -2.82 and Fuss's of -1.30. An explanation for
this discrepancy will probably require further work. There is less disagreement
over the elasticities for coal and natural gas. Our estimates of the total own
price elasticities for coal (-1.29 to -2.24) and natural gas (-0.41 to -2.34) are
generally in line with other estimates.
7. Summary
We have seen that the use of a "two-stage" weakly separable cost function pro-
vides means of estimating demand elasticities for aggregate energy use and for in-
dividual fuels. In addition, by pooling international time series-cross-section
data we can obtain a sample large enough to provide low-variance estimates of es-
sentially long-run elasticities.
We have found that the'own-price elasticity of aggregate industrial energy
demand is larger than had been thought previously, and that energy and capital ap-
pear to be substitutes, rather than complements. We attribute these results to
the long-run nature of our estimates. We found the:total own-price elasticities
of coal and natural gas to be large, as expected, but we found the total own-price
elasticities of oil and electricity to be below 1 in magnitude. While we expect
the small elasticity for electricity (there is little flexibility in its use), it
is harder to justify the-elasticities for oil.
We also found that the aggregate cost functions are mildly, but significantly.
non-homothetic, so that the elasticity of aggregate energy use with respect to out-
out changes is below l (generally around .7 or .8). This is not due to economies
of scale in the long-run (we found cost functions to exhiboit constant returns to
scale), but rather to substitution away from eergy as output increases. Finally
we found that further increases in the price of energy would have only a small im-
pact on the total cost of production. This is due in part to cnergy's small s ihare i:
production, and in part to substitution possibilities.
-62-
REFERENCES
[13 Adams, F.G. and J.M. Griffin, "Energy and Fuel Substitution Elasticities:Results from an International Cross Section Study," unpublished, Oct. 1974.
[2] Adams, F.G., and P. Miovic, "On Relative Fuel Efficiency and the OutputElasticity of Energy Consumption in Western Europe," Journal of IndustrialEconomics, November 1968.
[3] Allen, R.G.D., Mathematical Analysis for Economists, Macmillan, London,1938.
[4] Barnett, H., and C. Morse, Scarcity and Growth, Johns Hopkins Press,Baltimore, 1963.
[5] Baxter, R.E., and R. Rees, "Analysis of the Industrial Demand forElectricity," Economic Journal, June 1968.
[6] Belsley, D.A., "Estimation of Systems of Simultaneous Equations andComputational Specifications of GREMLIN," Annals of Economic and Social
Measurement, October 1974.
[7] Berndt, E.R., and L.R. Christensen, "The Translog Function and the Sub-stitution of Equipment, Structures, and Labor in U.S. Manufacturing1929 - 68," Journal of Econometrics, March 1973.
[8] Berndt, E.R., and L.R. Christensen, "The Internal Structure of FunctionalRelationships: Separability, Substitution, and Aggregation," Review ofEconomic Studies, Vol. 40, July 1973.
[9] Berndt, E.R., and D. Wood, "Technology Prices, and the' Desired Demandfor Energy," Review of Economics and Statistics, August 1975.
[10] Berndt, E.R., and D.O. Wood, "Consistent Projections of Energy Demandand Economic Growth: A Review of Issues and Empirical Studies," M.I.T.Energy Laboratory Working Paper # 77-024W1, June 1977.
[11] Burgess, D.F., "Duality Theory and Pitfalls in the Specification ofTechnologies," Journal of Econometrics, Vol. 3, 1975.
[12] Christensen, L.R., D. Cummings, and D.W. Jorgenson, "An InternationalComparison of Growth in Productivity, 1947-1973," Working Paper 7531,Social Systems Research Institute, University of Wisconsin, October 1975.
[13] Christensen, L.R. D. Cummings, and P. Schoech, "Real Product, Real FactorInput, and Productivity in the Netherlands, 1951-1973," orking Paper7529, Social Systems Research Institute, University of Wisconsin,October 1975.
-63-
[14) Christensen, L.R., D. Cummings, and K. Singleton, "Real Product, RealFactor Input, and Productivity in the United Kingdom, 1955-1973,"Working Paper 7530, Social Systems Research Institute, University ofWisconsin, October 1975.
[15] Christensen, L.R., D. Cummings, and B. Norton, "Real Product, RealFactor Input, and Productivity in Italy, 1952-1973," Working Paper 7528,Social Systems Research Institute, University of Wisconsin, October 1975.
[16] Christensen, L.R., D.W. Brazell, and D. Cummings, "Real Product, RealFactor Input, and Productivity in France, 1951-1973," Working Paper 7527,Social Systems Research Institute, University of Wisconsin, October 1975.
[17] Christensen, L.R., and D. Cummings, "Korean Real Product, Real FactorInput, and Productivity, 1960-1973," Working Paper 7507, Social SystemsResearch Institute, University of Wisconsin, December 1974.
[18] Christensen, L.R., and D. Cummings, "Real Product, Real Factor Input,and Productivity in Canada, 1947-1973," Working Paper 7532, SocialSystems Research Institute, University of Wisconsin, October 1975.
[19] Christensen, L.R., and W.H. Greene, "Economies of Scale in U.S. ElectricPower Generation," Journal of Political Economy, August 1976.
[20] Christensen, L.R., and D.W. Jorgenson, "The Measurement of U.S. RealCapital Input, 1929-1967," Review of Income and Wealth, Series 15,1969, pps. 23-320.
[21] Christensen, L.R., D.W. Jorgenson, and L.J. Lau, "Transcendental Loga-rithmic Production Frontiers," Review of Economics and Statistics,Vol. 55, No. 1, February 1973.
[22] Coen, R.M., "Effects of Tax Policy on Investment in Manufacturing,"American Economic Review, March 1968.
[23] Corbo, V., and P. Meller, "The Translog Production Function: SomeEvidence from Establishment Data," unpublished, July 1977.
[24] Darmstadter, J., J. Dunkerley, and J. Alterman, How Industrial SocietiesUse Energy, Johns Hopkins University Press, 1977.
[25] Denison, EF., WThy Growth Rates Differ, The Brookings Institution,Washington, 1967.
[26] Denny, M., and M. Fuss, "The Use of Approximation Analysis to Test forSeparability and the Existence of Consistent Aggregates," Working PaperNo, 7506, Institute for the Quantitative Analysis of Social and Economic
@ Policy, University of Toronto, August 1975.
[27] Dics rt, W.E., "n ApDiicaticn of the SheGpard Duality Thcorcm: A Gner-
alized Lontiaf Product ion Function," Jcuri1 of olitical Econor.',, Vol..79, No. 3, Miay 1971.
[28] Diewart, W.E., "Separability and a Generalization of the Cobb-DouglasCost, Production, and Indirect Utility Functions," Working Paper,University of British Coluwbia, 1973.
[29] Dieward, W.E., "Homogenous Weak Separability and Exact Index Numbers,"Technical Report No. 122, Institute for Mathematical Studies in theSocial Sciences, Stanford University, Jan. 1974.
[30] Fuss, M.A., "The Demand for Energy in Canadian Manufacturing," Journalof Econometrics, Vol. 5, 1977.
[31] Fuss, M.A. and L. Waverman, "The Demand for Energy in Canada," WorkingPaper, Institute for Policy Analysis, University of Toronto, 1975.
[32] Gallant, W.R., "Seemingly Unrelated Nonlinear Regressions," Journal ofEconometrics, February 1975.
[33] Griffen, J.M., "The Effects of Higher Prices on Electricity Consumption,"The Bell Journal of Economics and Management Science, Autumn, 1974.
[34) Griffen, J.M. and' P.R. Gregory, "An Intercountry Translong Model of EnergySubstitution Responses," American Economic Review, December 1976.
[35] Hall, R.E. and D.W. Jorgenson, "Tax Policy and Investment Behavior,"American Economic Review, June 1967.
[36] Halvorsen, R., "Energy Substitution in U.S. Manufacturing," unpublished,
1976.
[37) Halvorsen, R., and J. Ford, "Substitution Among Energy, Capital, andLabor Inputs in U.S. Manufacturing," in R.S. Pindyck, editor, Advancesin the Economics of Energy and Resources," Vol. , JAI Press, Greenwich,Conn, 1978.
[38] Hudson, E.A. and D.W. Jorgenson, "U.S. Energy Policy and Economic Growth,1975-2000," The Bell Journal of Economics and Management Science, Autumn,1974.
[39] Humphrey, D.B., and J.R. Moroney, "Substitution Among Capital, Labor, andNatural Resource Products in American Manufacturing," Journal of PoliticalEconomy, February, 1975.
[40] Jorgenson, D.W. and Z. Griliches, "The Explanation of Productivity Change,"Revie: ,of Economic Studies, Vol. 34, July 1967.
[41] Jorgenson, D.W., and Z. Griliches, "Issues in Growth Accounting: A Replyto Edward F. Denison," Survey of Current Business, May, 1972, pps. 65-94.
[42] Joskow, P.L., and M.L. Baughman, "The Future of the U.S. Nuclear EnergyIndustry," Bell Journal of Economics, Vol. 7, No. 1, Spring 1976.
[43] Kmenta, J., ndi R. Gilbert, "S:il Sar:le Prnertics of Alternative Es-timntes of i ournal of te A-:ericanStatistical Association, December 1968.
[44] Lau, L.J., and S. Tura, "Economies of Scale, Technical Progress, and theNonhomothetic Leontif Production Function: An Application to the JapanesePetrochemical Processing Industry," Journal of Political Economy,November 1972.
[45] MacAvoy, P.W., and R.S. Pindyck, The Economics of the Natural Gas Shortage,1960-1980, North-Holland Publishing Co., Amsterdam, 1975.
(46] Magnus, J.R., "Substitution Between Energy and Non-Energy Inputs in theNetherlands: 1950-1974," unpublished working paper, University of Amster-dam, November 1975.
[47.] Moroney, J.R., and A. Toevs, "Factor Costs and Factor Use: An Analysis ofLabor, Capital, and Natural Resource Inputs," Southern Economic Journal,October 1977.
[48] Moroney, J.R., and A.L. Toevs, "Input Prices, Substitution, and ProductInflation," in R.S. Pindyck, editor, Advances in the Economics of Energyand Resources, Vol. I, JAI Press, Greenwich, Conn. 1978.
[49] Mount, T.D., L.D. Chapman, and T.J. Tyrrell, "Electricity Demand in theUnited States: An Economic Analysis," Oak Ridge National Laboratory,Technical Report, June 1973.
[50] Nordhaus, W.D., "The Demand for Energy: An International Perspective,"Unpublished, Sept. 1975.
[51] Oberhofer, W., and J. Kmenta, "A General Procedure for Obtaining Maxi-mum Likelihood Estimates in Generalized Regression Models," Econometrica,May 1974.
[52] Organization for Economic Cooperation and Development, Energy Prospectsto 1985, Paris, 1974.
[53] Pindyck, R.S., "International Comparisons of the Residential Demand forEnergy: A Preliminary Analysis," M.I.T. Energy Laboratory Working Paper76-0231JP, September, 1976.
[54] Shephard, R.W., Cost and Production Functions, Princeton University Press,Princeton, N.J., 1953.
[55] UK Department of Energy, "Report of the Working Group on Energy Elasticities,"Energy Paper No. 17, Feb. 1977.
[56] Uzawa, H., "Production Functions with Constant Elasticities of Substitution,"Review of Economics and Statistics, October, 1962.
[57] Wallace, T.D., and A. Hussain, "The Use of Error Components in Models Com-bining Cross-Section with Time Series Data," Econometrica, Vol. 36, No. 1,Jan. 1969.
(58] Gilbert, M., and I. Kravis, An International Corvoarison of National Pro-duct and the Purchasing Power of Currencies, Organization for EuropeanEconomic Cooperation, Paris, 1954.
[59] Gilbcrt, ., and Associates, Co-.-.r'tivo. atJ¢"ni:i Pr.ducts anr r. riceLevels: A Study of Western urope and the United States, Paris, 1958.
[60] Kravis, I., Z. Kenessey, A. eston, and R. Summers, A System of Inter-national Cornarirns of Gro-s roduct a.nd Prchasig Power, JohnsHopkins University Press. Baltimore. 1975.