POLICY RESEARCH WORKING PAPER wr-1297
How Relative Prices Fuel taxes wil inducefie
substitution and reductions in
Affect Fuel Use Patterns pollution. But evidence from
in Manufacturing manufacturIng firms in Chile
suggests that the response
will be very uneven - and
that the costs of asijustment
Plant-Level Evidence from Chile maybe bomemorebysome
sectors and types of
Charles C. Guo producers than others.
James R. Tybout
The World Bank
Policy Research Department
Public Economics Division
May 1994
POLICY RESEARCH WORKING PAPER 1297
Summary findings
Some economists have urged reliance on fuel taxes and sectors but across producers of different sizes. Although
other fiscal incentives to reduce air pollution in semi- Eskeland and Jimenez (1990) may be correct in arguing
industrialized countries. They argue that policies that act that fiscal incentives are easier to implement than are
on relative prices are easier to enforce than those based direct emission controls, the costs of adjustment ar,
on emission monitoring, create less misallocation of likely to be concentrated fairly narrowly for some fuels.
resources, and are relatively free of the rent-seeking and The authors found bakeries, for example, to be very
corruption that accompany regulations administered at responsive to ch. :ges in the relative prices of alternative
the plant level. fuels. By contrast, energy demand in metal products
To be effective, however, fuel-specific taxes and plants appears to be very insensitive to relative prices, no
subsidies must inspire manufacturers to significantly matter what estimates are used. Meatpackers fall
adjust their input use as relative prices charnge. somewhere between the two - with little price
Moreover, these policies must not create politically responsiveness in electricity demand, but more in the
unacceptable income redistribution. demand for energy from other sources, especially if
Guo and Tybout shed light on both issues by analyzing coherency-constrained figures are used.
detailed panel data on Chilean manufacturing plants. It seems that the effects of fuel taxes vould depend in
Overall, their estimates suggest that there is substantial significant measure on the sectoral composition of
scone for fuel taxes to encourage fuel substitution, but manufacturing, since input composition varies and some
that the response will be very uneven - not only across sectors have little flexibility.
This paper is a product of the Public Economi:s Division, Policy Research Department. The study was funded by the Bank's
Research Support Budget under the research project "Pollution and the Choice of Economic Policy Instruments in
Developing Countries" (RPO 676-48). Copies of this paper are available free from the World Bank, 1818 H Srreet NW,
Washington, DC 20433. Please contact Carlina Jones, room N .0-063, extension 37699 (29 pages). May 1994.
The Policy Research Working Paper Series disseminates the findings of ukork in progress to encourage the exchange of ideas about
development issues. An objective of the series is to get the findings out quickly, eten if the presentations re less than fully polish-d. 'I'the
papers carry the names of the authors and should be used and cited accordingly. The fintings, interpretations, and conclusions are the
authors' own and should not be attributed to the W'orld Bank, its Fxecutive Board of Directors, or any of its member countnes.
Produced by the Policy Research Dissemination Ccnter
How Relative Prices Affect Fuel Use Patterns
in Manufacturing:
Plant-Level Evidence from Chile
Charles C. Guo
and
James R. Tybout
Georgetown University
This paper was funded by .he World Bank research project "Pollution and the Choice of
Policy Instruments in Developing Countries."
Table of Contents
I. Overview .................................... 2
II. The Empirical Model ..........4
III. Estimation .................................. 7
A . Price Data .................................... 7
B. Choice of Sector and Fuel Grouping ........ ............ 8
IV. Results ........ ........... ....... ............ .. 11
A. Tests of the Coherency Constraint
B. Homotheticity ............................... 12
C. Implied Elasticities ............................. 15
V. Concluding Remarks .............................. 24
References ................................... 25
Appendix ......................................... 26
I. Overview
In the major cities cf many semi-industrialized countries, air pollution has become a serious
problem. The most cursory tour of Mexico City, Santiago, or Jakarta is sufficient to convince one that
the externalities are massive. Now, after decades of neglect, many policy-makers are turning their
attention to the issue and debating the relative merits of alternative corrective measures.
Some economists have urged reliance on carbon taxes and other fiscal incen;ives (Eskeland and
Jimenez, 1990). Policies that act on relative prices are easier to enfarce than direct controls, creatc less
misallocation of resources, and are relatively free of the rent-seeking and corruption that accompany
regulations administered at the plant level. To be effective, however, fuel-specific taxes and subsidies
must inspire manufacturers to significantly adjust their production techniques as relative prices change.
Moreover, these policies must not create politically unacceptable income redistribution. The purpose of
this paper is to generate new evidence on both issues by analyzing detailed panel data on Chilean
manufacturing plants.
There is already a large body of evidence or. fuel elasticities of derrand. However, the relevance
of this literature is limited by several factors. First, most studies are baced on sectoral time series from
OECD economies, so the product mix and technologies they describe differ to an unknown extent from
those in the semi-industrialized countries. Second, to have a reasonable number of sectoral observations,
many years of data are necessary. I But technology is unlikely to remain fixed over the twenty to thirty
year time spans that are typically studied. Third, the econometric literature almost always begins from
the assumption that production technologies are homothetic in factor inputs. This is especially unlikely
to be true in developing countries, where the population of manufacturers ranges from cottage industry
to large multinationals. Finally, this literature also presumes complete flexibility to adjust all factor
stocks every year. But adjustments in fuel use patterns often require lumpy investments in retrofitting
I Not all analyses at the sectoral level are pure time series. Some use relatively short time periods
but pool across regions or countries, e.g., Fuss (1977).
or new capital equipment, so observed fuel use patterns reflect adjustment costs and and expectations
about the future.
We can do better on all counts by using plant-level panel data from Chile. First, we can explicity
account for non-homotheticities by allowing technolog.es to vary across plants of different sizes. Second,
because transportation costs and infrastructure induce substantial spatial variation in prices, we need not
use the time dimension of our data to identify paramneters. This means we can describe the technology
at a recent point in time, rather than some ill-defined temporal average for the past thirty years. Finally,
by taking plant-specific temporal averages of all variables before fitting our model, we come closer to
a representation of long run behavior than estimators based on a simple cross section or annual time
series.2
We estimate substitution elasticities using plant-level panel data that describe expenditure and
physical consumption levels for each of 12 alternative energy sources, inter alia. The data describe
virtWally all Chilean manufacturing plants with at least ten workers for the period 1979-1986.3 We find,
first, that the degree of substitutability between fuels is sutstantial in some sectors, but very limited in
others. Second, the variation in elasticities across the plant size spectrum is at least as large as it is across
industries. For both raasons, the incidence of carbon taxes is likely to be concentrated in certain types
of plants.
Several troubiesome econometric issues complicate the analysis. First, although an industry
consumes many fuels in the aggregate, each individual plant is unlikely to consume no more than several.
2 In principle, of course, we could do better by specifying an explicitly dynamic model (e.g., Rust,
1987). Hovwever, the returns to this strategy are limited by the fact that we don't observe details of the
capital stock. Moreover, dynamic panel data models suffer from the "init.al conditions" and "incidental
parameters" problems, which would necessitate going to considerably more complicated estimation
techniques (Heckman, 1981).
3 These data were originally obtained from the Chilean government by the World Bank for the
research project "Industrial Competition, Productive Efficiency, and their Relation to Trade Regimes,"
RPO 674-46.
3
This suggests that at the typical plant, some fuels cost more than their marginal revenue products at zei J
consumption, and accordingly, the first-order conditions that are used to estimate fuel demads with
sectoral data cannot be justified. We adopt the technique developed by Lee and Pitt (1987) to deal with
this problem.
Ano.aer problem is that to estimate fuel demands we must observe a plant-specific price for every
fuel, whether it is actually used or not Given that we observe physical quantities and expenditures for
each fuel that is used, we surmount this problem by estimating fuel price equations that relate unit values
of the fuels to exogenous plant characteristics such as geographic region, industry and size. These
equations are fitted fuel by fuel, using the subset of plants for which unit fuel prices could be calculated.
Then fitted values from these equations are constructed for all plants and treated as the market prices that
producers face. We view this technique as not only solving the problem of unobservable prices, but
removing noise from plant-specific unit values.
II. The Empirical Model
The Likelihood Function: Our representation of producer behavior is a slight generalization of
Lee and Pitt's (1987). Suppose that output is a function of capital (K), labor (L), materials (M), and a
vector of energy inputs (X), some of which may not be used. Then the profit maximizing choice of
energy inputs can characterized be using the Lagrangian:
L = PKK + PLL + PmM + P,,X + X(Y -F(KL,M,XJ) - X
where 0 is a vector of Kuhn-Tucker multipliers that impose non-negativity constraints on the elements
of X. The relevant first-order conditions are:
4
aF
dX = Px, - Xi ' (2;
ax1 - (1)
oj 2G
So if producers were confronted with virtual prices, t, instead of actual prices, they would behave as if
they were at an interior solution. Accordingly, standard first-order conditions can be used to identify the
production technology once this substitution has beer, made.
Proceeding to do so, suppose that the production function is weakly separable in energy inputs:
Y = F[K,L,M,e(X)J
This ensures that for a given input of the energy aggregate, E, and a given vector of factor input prices,
the choice of energy inputs satisfies the cost minimization problem:
min eX subject to E = e(X)
x
The mix of energy inputs that solves this problem yields some levei of costs, Ce, which we approximate
with a standard translog function:
InC = aJ + , ailnti + ylnE + ; j Oij Intilnj+ 1+ I Ei InElnti + eInti (2)
Here the disturbance vector e = (e1,e2,e3) picks up plant-specific variation in technology. Then the
associated share equations implied by Sheppard's lemma are:
Si' = a;i + 0,5 E + Ej Oij In tj + ei, i = 1, 2, 3 (3)
Combined with the bounds on virtual prices implied by (1),
(i = Px, if Si. > o
t C< PX if s, = 0
5
and with the assumption that e is distributed N(O,E), these share equations form the basis for Lee and
Pitt's (1987) likelihood function. Details are provided ifi the appendix.
Parameter constrain.:: The cost function (2) must be homogtneous of degree 1 in prices, which
implies the following standard parameter constraints:
Ejcx, + Ee = 1,
i= 0l = 0 for all i and j,
(4)
Ei OEi =
j= j3, i j.
To nornalize disturbances, we restate the first restriction as: E, cii = 1 and E, ei = 0.
Depending upon which combination of inpuits is consumed, there are seven possible demand
regimes for any plant. Each of these may be classified as one of three basic types: all three inputs are
used, only two inputs are used, and only one kind of input is used. The likelihood fimction will be well
defined only if the seven regime probabilities sum to one for each possible realization on exogenous
variables. Lee and Pitt term this condition "coheiency," and show that it amounts to concavity of the
log cost function (2) in log prices. Coherency will hold automatically if the underlying production
technology is strictly concave in factor inputs. Unfortunately, concavity does not hold globally for
translog functions. Thus, to ensure a well-defined likelihood function we impose and test the coherency
constraints that ,B, < 0, 22 <0, 0 33 < 0, 01122 - (212 > 0, 011033 - 03 > 0, and t22v33 - 223 > 0. We
caution that even this is insufficient to gaurantee that our estimated cost function is concave in prices at
all data points in the sample.4
I In estimating the parameters of their energy cost function, Lee and Pitt (1987) only impose the
restrictions that all the own-price parameters 0j are non-positive.
6
Homotheticicry: Notice that we have departed from Lee and Pitt (1987), and most others, by
letting e(X) be non-homothetic. (That is, Ei * 0 may occur for particular i values.) As mentioned in
the introduction, we do so because we believe technologies in semi-industrialized countries are very size-
specific. Others have presumably imposed homotheticity to simplify estimation, given that E is both
unobserved and endogenous. In princi, le, the simultaneity problem can be dealt with by instrumenting
E with its exogenous determinants: Q, Px. and non-energy factor prices. But since E is not actually
observed, we simply include the instrumental variables directly in our cost function, sans non-energy
factor prices (which were not available). Since P. already appears directly as a cost determinant, this
amounts to replacing E with Q in equation (3).
One disavantage of our approach is that it does not permit one to isolate the role of energy prices
in changing E from the direct effect of factor priWes on shares. But this problem may well be negliglible
since the vast majority of the variation in E is due to Q, and in any case, a more severe bias is present
when homotheticity is vrongly imposed. At a minimum, our model constitutes a generalization of the
standard specification, and affords a framework for testing the homotheticity restriction.5
III. Estimation
A. Price Data
As mentioned in the introduction, we use predicted values of fuel prices for all plants. There are
two reasons for doing so. First, most plants report zero consumption for some fuels. For these plants
and fuels, the unit price is not available. Second, even though unit fuel prices are available for plants
with non-zero consumption, these are likely to partly reflect cross-plant differnces in fuel quality. Hence
I An alternative way to motivate our specification is to simply begin from a cost function that
takes the form: C = C(PK, PLP,,P, C(PX, Q), Q) where r is the rental rate on capital, w is the wage
rate, m is the price of materials, and P, is the price of the energy aggregate.
7
if we were to use unit values instead of predicted unit values, we would proba'oly be introducing
measurement error bias in our estimator, biasing elasticities toward zero. (Given that we treat the
predicted prices as the "true" ones, we make no correction to the standard errors in our estimated share
equations.)
The regression model used to impute price for energy j is given by
lnPij. = 8j + y'jZj, + niit,
where i indexes planit, t indexes year, and Z is the vector of exogenous variables. It includes dumnies
for year, 3-digit or 4-digit industry, region, and business type, and the logrithm of number of workers.
For each energy source j, Oj and yj are estimated for plants with positive consumption. The estimated
regression equation for each energy source is then used to impute its predicted price for all plants.
Further analysis of the sources of price variation in our data can be found in Moss and Tybout (1992).
B. Choice of Sector and Futl Grouping
The panel data at our disposal describe virtually all Chilean manufacturing establishments with
at least ten workers over the period 1979-86. For each plant and year, they includes expenditure and
volume data on 12 energy sources: electricity, coal, carbon, coke, fuel oil, diesel, benzine, parafin,
liquid gas, canned gas, fuel wood, and other fuels. There are 29 3-digit industries in total, but we iimit
our attention to two 4-digit and three 3-digit industries which are large and/or energy intensive: meat
processing (SIC 3111), bakeries (SIC 3117), textile (SIC 321), chemical products (SiC 351), and metal
products (SIC 381). Descriptive statistics for these sectors are presented in Table 1.
Because all sectors use a substantial amount of electricity, this is always defined as the first
energy source. We define the second and third energy sources as aggregations over subgroups of the
8
eleven fuel types, using different aggregations for different sectors. In forming these groups we
considered two facLors: shares in total energy expenditure, and similarity of the fuels. The second
subgroup is firewood for meatpackcrs and bakeries; it is coal, carbon and coke for textiles; it is fuel cil
and diesel for chemical products and metal prod.;cts. The third subgroup is, of course, everything else.
9
Table 1: Basic Characteristics
Meatpacking | Bakeries Textiles Chemicals Metal Prodlets
Mean S.D. Mean S.D. Mean S.D. Mean S.D. Mean S.D.
Electricity Share 0.497 0.236 0.419 0.215 0.790 0.251 0.562 0.346 0.667 0.284
2nd Input Share 0.107 0.177 0.326 0.244 0.010 0.069 0.220 0.290 0.077 0.175
3rd Input Share 0.396 0.253 0.256 0.270 0.200 0.245 0.218 0.281 0-256 0.248
Electricity Price (In) 1.460 0.138 1.622 0.105 1.485 0.130 1.404 0.151 1.537 0.130
2nd Input Price (In) 0.748 0.190 0.690 0.136 1.576 0.104 2.564 0.107 2.665 0.099
3rd Input Price (In) 2.487 0.073 2.469 0.064 2.445 0.087 2.228 C.081 2.!59 0.084
Output Value (In) 10.422 1.647 9.284 0.790 9.746 1.271 11.215 1.496 9.658 1.299
Sample Size 173 1176 631 100 671
Cases of Positve
Consumption:
Electricity 171 1176 631 98 671
2nd Input 88 936 31 58 197
3rd Input 152 992 392 71 491
The second and third inputs are aggregated from several actual fuels (11 types in total) used by firms. The groupings of the second input are
firewood for meatpacking and bakeries; coal, carbon, and coke for textiles; fuel oil and diesel for chemicals and metal products.
Once the two non-electric energy sources had been constructed we constructed price indicies for
each as weighted averages of the prices of the individual components:
A
pa = wjpi,
Here G is the set of fuels being aggregated, w is the weight of expenditure of fuel j in that group, and
Pj is its imputed price in logarithms. The groupings of fuels for each sector are shown in Table 1.
IV. Results
A. Tests of the Coherency Constraint
Before discussing parameter estimates it is necessary to test whether the coherency constraints
required by the Lee and Pitt framework are consistent with our data. In sectors where they are not, it
is difficult to proceed. On the one hand, if the constraints are not imposed the likelihood function is ill-
defined. On the other hand, if they are imposed, we have found that it usually means that ,, or 322 are
pushed to zero, implying in turn that O12 is zero, so it becomes impossible to solve for virtual prices using
equations A2 or A5 (see the Appendix). Under these circumstances the only sensible conclusion is that
the Lee and Pitt framework does not provide a reasonable representation of the process that generated
the data. This may be due to unmodelled dynamics, to heterogenous technologies, or to inappropriate
aggregation across the individual fuels when we form our three categories.
Table 2 reports values of the likelihood function, with and without the coherency constraint
imposed, for the non-homothetic version of our model. Notice that the constraint is accepted in the cases
of bakeries, metal products, and (at a values less than .05) meatpacking. On the other hand, it is
strongly rejected for chemicals, and we were unable to obtain constrained results for the textile industry.
I1
Accoringly, in what follows we will focus on the former three sectors.
Table 2: Tests of The Coherency Restrictions*
Industry No. of Unconstrained Constrained Likelihood
Observations Log Likelihood Likelihood Ratio Statistic
Function Function
Meatpacking 173 -88.86 -93.85 9.98
Bakeries 1176 -463.06 -463.06 0.00
Textiles 631 -370.18 no convergence n.a.
Chemicals 100 -61.75 -98.72 73.94
Metal Products 671 -567.52 -568.94 2.84
C ritical values for the X2(4) distributionare 7.78 at a= .01, 9.49 at a= .05, 11.14 at c = .025 and
13.28 at a=.01.
B. Homotheticity
We next turn to parameter estimates sector by sector. These are presented in table 3. Given that
coherency is a necessary condition for the likelihood function to be well-defined, there is no clear
interpretation for tests based on sectors where coherency fails. However, following Lee and Pitt, we
report them nonetheless for completeness.
The first issue we wish to address is whether energy demands are homothetic of degree one with
respect to output. This hypothesis amount to the claim that iQ, = OQ2 = OQ3 = 0. Clearly for the
sectors where inference is possible, it can be rejected.6 In fact, almost every OQ, value for which standard
errors are obtained is highly significant. (Caution must be exercized when interpreting standard errors
for chemicals, since this sector fails the coherency test.)
6 For bakeries, the likelihood ratio statistic that tests 03Q, = OQ2 = OQ3 = 0 is 98.57. The critical
X2(2) value is 9.21 when testing at the ox=.01 level.
12
Table 3A: Unconstrained Parameter Estimates by Sector
Parameter Meatpacking Bakeries Textilesb Chemicals Metal
Productsb
aI .651 (.165) .267 (.090) 3.40 1.05 (.346) .515
a2 .039 (.148) .291 (.122) -1.27 -.739 (.232) -1.26
a3 .310 (.240) .442 (.165) -1.13 .692 (.208) 1.74
OQJ .001 (.015) -.056 (.010) -.177 -.071 (.035) .015
13Q2 -.029 (.013) -.058 (.013) .062 .101 (.023) .106
OQ3 .027 (.022) .114 (.017) .115 -.030 (.019) -.121
Oil .428 (.163) -.329 (.069) .666 -.288 (.403) .182
012 -.108 (.045) -.214 (.035) -.570 .158 (.221) -.003
013 -.320 (.124) .542 (.073) -.096 1.j (.182) -.179
022 -.088 (.049) -.207 (.044) .464 -.046 (.065) -.005
O3 _ ..196 (.088) .421 (.074) .105 -.112 (.157) .008
133 .123 (.062) -.963 (.121) -.009 -.018 (.026) .171
.227 (.017) .201 (.005) .407 .343 (.038) .258
.239 (.023) .311 (.008) .491 .267 (.025) .405
12 .012 (.011) -.003 (.003) -.169 -.072 (.017) -.046
Log
Likelihood -88.864 -463.064 -370.176 -61.751 -567.518
No.
Observations 173 1176 631 100 671
aFigures in parentheses are standard deviations.
bStandard deviations were not obtained for textiles and metal products due to irregularity of the estimated
Hessian.
13
Table 3B: Constrained Parameter Estimates by Sector"
Parameter Meatpacking Bakeries Textilesb Chemicalsc Metal
Products'
.653 .267 (.090) n.a. 1.28 .556
Ci2 -.184 .291 (.122) n.a. -1.00 -1.25
0%3 .531 .442 (.165) n.a. .727 1.70
1QI -.014 -.056 (.010) n.a. -.070 -7.5e-4
OQ2 -.052 -.058 (.013) n.a. .121 .106
OQ3 .066 .114 (.017) n.a. -.051 -.105
-5.0e-6 -.329 (.069) n.a. -.062 .000
112 -3.9e-5 -.214 (.035) n.a. .062 .000
_ 131 4.4e-5 .542 (.073) n.a. -1.9e-5 .000
022 -.422 -.207 (.044) n.a. -.062 .000
023 .422 .421 (.074) n.a. 2.3e-5 .000
033 -.422 -.963 (121) n.a. -5.0e-6 .000
a ' .255 .201 (.005) n.a. .348 .260
Cr2 .269 .311 (.008) n.a. .407 .406
a,2 -.013 -.003 (.003) n.a. -.083 -.047
Log
Likelihood -93.849 -463.064 n.a. -98.721 -568.935
No.
Observations 173 1176 631 100 671
2 Figures in parentheses are standard deviations.
b Our solution algorithm failed to converge for this sector.
Standard deviation were not obtained for meatpacking, chemicals, and metal products because
the coherency constraint was binding, making the Hessian singular.
14
Larger plants appear more likely to use fuel oil, carbon, and coke; but less likely to use firewood.
For example, in metal products, a doubling of plant size leads to about a ten percentage point increase
in the share of these fuels. This finding has clear implications concerning the incidence of dirty fuel
taxes; it also implies that virtually all of the existing econometric literature on energy substitution is mis-
specified. As we will discuss shortly, the implications concerning substitution elasticities are also non-
trivial.
C. Implied Elasticities
At the Plant Level Bccause we allow for non-homothetic technologies, each plant has its own
matrix of price elasticities. To dramatize this heterogeneity, we construct plant-specific elasticities using
predicted shares in equation (6), which are evaluated at the cross-plant mean price vector, but at plant-
specific output levels. Given energy shares, partial own and cross-price elasticities of at a particular plant
can be constructed as:7
o if Si = (
(6-1)
[Sj3 + S1(S, - 1)]/S, otherwise
and
O if Si = O
Xii 1. -(6-2)
' + S1Sj)/S, otherwise.
These elasticities are partial because they account only for substitution between fuels, and do not reflect
any adjustments in overall energy usage by the plant. Allen (1938) showed that the partial price
elasticities are related to the partial elasticities of substitution (ojj) as 71ij = criS,. Hence, even though the
' See, for example, Griffin and Gregory (1976) and Pindyck (1979).
15
Allen partial cross elasticities of substitution are symmetric, plant-level partial cross-price elasticities (and
sector elasticities) will generally not be.
Figures 1 through 9 are based on the parameter estimates in Table 3A. They show how own-
and cross-price elasticities depend upon plant size in the bakery industry, which we choose because it
seems to fit the model best. Each circle corresponds to an actual plant, so most plants lie in the ranges
of solid black along the curve. Notice that the (partial) elasticity of demand for electricity ranges from
around -1 for small plants to -2 for moderately sized plants, implying that bigness leads to more flexibility
in electricity use (figure 1). On the other hand, with the exception of a handful of outliers, ther is very
little variation in own-price elasticity of demand for 'irewood (figure 2). Moreover, small plants are
much more responsive to changes in the price of other fuels than their larger counterparts (figure 3).
Given these patterns it is unsurprising that cross-price partial elasticities are also very size-
dependent. This is particularly true for elasticities that involve energy sources other than electricity and
firewood. Interestingly, not only are cross-price elasticities non-syrnmetric, but the tend to change in
opposite directions as plant size grows. This is a consequence of the structure of equation (6-2), which
has a negative partial derivative with respect to Si and a positive partial derivative with respect to Sj.
At the Sector Level: The principal issue of policy interest is the sensitivity fuel demands to
changes in relative fuel prices. We construct these as consumption-weighted averages of the plant-specific
elasticity expressions above:
Eii = E.m 7 i(ei /Xi) and E1j = Em fj( /Xi)
Here m indexes the plant, ei is its consumption of energy source i, and Xi is industry-wide consumpition
of energy source i. Also, to obtain standard errors for these expressions, we begin by approximating the
standard errors of the plant-specific elasticities with:
16
A A A
Var[U7i] = Var[, i ]/S2a.
For this expression we have treated predicted cost shares SI as non-stochastic. We then aggregate up to
standard errors for the sectoral elasticities, treating consumption levels Xi' as non-stochastic:
Var[E J = (Em Xim/S m)2Var[,3 J, and
Var[E1 ] (E m xm/Sm) Var[4, i]
A A A
where Xtm = x1m/Xi. Obviously our assumptions about exogeneity are not strictly justified, but they
should have only a minor effect on the estimated variances.
17
Table 4a: Partial Sectoral Price Elasticities, Meatpacking'
Elasticity of Demand for:
With Electricity Fuel wood Other Fuels
Respect to:
Pelectricity .513 (.384) -.335 (.324) -.257 (.243)
-.498 (n.a.) .444 (n.a.) .371 (n.a.)
.161 (.302) -.044 (.242) .044 (.193)
-.498 (n.a.) .444 (n.a.) .371 (n a.)
Pfuel wow -.103 (.106) -1.35 (.351) .577 (.173)
.131 (n.a.) -3.75 (n.a.) 1.12 (n.a.)
-.016 (.079) -1.09 (.226) .393 (.125)
.131 (n.a.) -3.03 (n.a.) .880 (n.a.)
P.d.r -.318 (.292) 1.99 (.633) -.170 (.122)
.445 (n.a.) 3.90 (n.a.) -1.24 (n.a.)
-.059 (.231) 1.35 (.456) -.233 (.101)
.445 (n.a.) 3.05 (n.a.) -1.05 (n.a.)
The top figure in each cell is based on our nonhomothetic model without coherency restrictions;
the second figure is based on the same model with coherency restrictions; the third figure is based
on our homothetic model without coherency restrictions; and the last figure is based on the same
model with coherency restrictions. Standard deviations are in parentheses when available.
18
Table 4b: Partial Sectoral Price Elasticities, Bakeries'
l___________ Elasticity of Demand for:
With Electricity Fuel wood Other Fuels
Respect to:
PelectIkity -1.36 (.181) -.401 (.125) 1.45 (.157)
-1.36 (.181) -.401 (.125) 1.45 (.157)
-.715 (.131) .890 (.157) .153 (.050)
l__________ -.715 (.131) .890 (.157) .153 (.050)
rpf6m .W -.301 (.093) -1.26 (.155) 1.29 (.157)
-.301 (.093) -1.26 (.155) 1.29 (.157)
.661 (.117) -1.80 (.316) .723 (.166)
.661 (.117) -1.80 (.316) .723 (.166)
Pl.h. 1.82 (.193) 1.88 (.261) -2.44 (.259)
1.82 (.193) 1.88 (.261) -2.44 (.259)
.180 (.061) 1.04 (.275) -.685 (.126)
.180 (.061) 1.04 (.275) -.685 (.126)
See footnote to table 4a.
19
Table 4c: Partial Sectoral Price Elasticities, Textilesa
Elasticity of Demand for:
With Electricity Coal, Other Fuels
Respect to: Carbon,
____________ Coke
| Pelecticiry 0.967 (n.a.) -3.10 (n.a.) .206 (n.a.)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
5.20 (1.04) -11.9 (2.77) -.941 (.490)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
| pcm etc. -1.13 (n.a.) 2.30 (n.a.) .321 (n.a.)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
4.33 (.956) 13.6 (3.33) -.640 (.574)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
| POttef ~~.217 (n.a.) 1.06 (n. a.) -.445 (n.a.)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
-1.02 (.511) -2.21 (1.73) 1.53 (.263)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
See footnote to table 4a.
20
Table 4d: Partial Sectoral Price Elasticities, Chemicalsa
|_________ Elasticity of Demand for:
With Electricity Fuel Oil, Other Fuels
Respect to: Diesel
PelerLricity -.884 (.823) .618 (.364) 1.33 (1.38)
-.423 (n.a.) .407 (n.a.) .337 (n.a.)
1.02 (.693) -.779 (.412) -.969 (.763)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
Pfel od etc, .593 (.452) -.273 (.107) -.445 (1.19)
.384 (n.a.) -.300 (n.a.) .459 (n.a.)
-.787 (.511) .249 (.261) 2.11 (.922)
n.a.(n.a.) n.a. (n.a.) n.a. (n.a.)
Pother .371 (.371) -.145 (.258) -.883 (.197)
.092 (n.a.) .100 (n.a.) -.748 (n.a.)
-.276 (.205) .546 (.200) -.999 (.195)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
See footnote to table 4a.
21
Table 4e: Partial Sectoral Price Elasticities, Metal Products'
Elasticity of Demand for:
With Electricity Fuel Oil, Other Fuels
Respect to: Diesel
PelecLricty -.004 (n.a.) .302 (n.a.) -.172 (n.a.)
-.401 (n.a.) .310 (n.a.) .373 (n.a.)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
fel oil etc. .254 (n.a.) -.465 (n.a.) .213 (na.)
.262 (n.a.) -.451 (n.a.) .184 (n.a.)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
P.Ox -.134 (n.a.) .169 (n.a.) .043 (n.a.)
.288 (n.a.) .146 (n.a.) -.479 (n.a.)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
n.a. (n.a.) n.a. (n.a.) n.a. (n.a.)
a See footnote to table 4a.
22
Table 4 presents our estimates of partial price elasticity of demand at the sector level along with
their standard errors. The top figure in each cell is based on our nonhomothetic model without coherency
restrictions (Table 3A); the second figure is based on the same model with coherency restrictions (Table
3B); the third figure is based on our homothetic model without coherency restrictions (unreported
parameter estimates); and the last figure is based on the same model with coherency restrict'ias
(unreported parameter estimates). As already discussed, the framework we are using does not seem to
fit the data for textiles and chemicals well, so we confine our attention to the remaining three sectors.
The most noteworthy feature of these results is that elasticities differ substantially across sectors.
It appears that bakeries are very responsive to changes in the relative prices of alternative fuels, especially
carbon-based energy sources. In contrast, energy demand appears to be very insensitive to relative prices
among metal products plants, regardless of what set of estimates are used. Finally, rneatpackers fall
somewhere in between, with little price responsiveness in electricity demand, but more for other energy
sources, especially if coherency-constrained figures are used. Therefore, it appears that the incidence of
carbon taxes would depend in significant measure on the industrial sector, with metal products plants least
able to adjust. Of course, more information on market structure and demand in these sectors would be
needed before a full analysis of incidence could be accomplished.
In their closely related work, Lee and Pitt found elasticities that tended to be larger than the ones
we report here. There are a number of possible explanations. One is that by imposing homotheticity,
they forced cross-plant variation in technologies to show up as price-induced substitution since fuel prices
vary across the plant size spectrum (MWss and Tybout, 1992). Support for this explana.ion is provided
by contrasts between oui elasticity estimates with and without homotheticity imposed. Another
possibility is that physical quantities or expenditures are measured with error, so that when physical prices
are imputed, they are contaminated by spurious negative correlation with quantities (e.g., Deaton, 1987).
Our approach should not be subject to this bias because we have instrumented noise out of prices.
23
It is difficult to compare our results with those in most other studies because we are working with
data from a semi-industrialized country, and estimating industry-specific parameters. However, several
observations are worth making. First, sectoral-level studies tend to find partial own-price elasticities of
demand that are similar in magnitude to ours, and lower than Lee and Pitt's. Second, like us, studies
based on aggregated data tend to find that the own-price elasticity of demand for electricity is lower than
elasticities for other energy sources (e.g., Fuss (1977) and Pindyck (1979)).
V. Conduding Remarks
Overall, our estimates suggest that there is substantial scope for carbon taxes to induce fuel
substitution, but that the response will be very uneven, not only across sectors, but across producers of
different sizes. Therefore, although Eskeland and Jimenez (1990) may be correct in arguing that fiscal
incentives are less susceptible to manipulation by special interest groups than direct emission controls,
the costs of adjustment are likely to be concentrated fairly narrowly for some fuels.
Unfortunately, the evidence on elasticities we report is not sufficient to assess the distribution of
adjustment burdens. It is limited to several sectors, and it must be combined with information on the
shares of energy spending in total costs, and on product market demand elasticities. However, combined
with descriptive statistics on energy use patterns in all manufacturing sectors (see Moss and Tybout,
1992), our figures should provide the basis for an assessment of all but the latter.
24
References
Allen, R. G. D. (1938), Mathematical Analysis for Economists, London: Macmillan, 503-509.
Berndt, Ernst R. and David 0. Wood, "Technology, Prices, and the Derived Demand for Energy,"
Review of Economics and Statistics 57, 259-268.
Deaton, Angus (1987), "Quality, Quantity, and Spatial Variation of Price: Estimating Price Elasticities
from Cross-Sectional Data," Journal of Econometrics 36, 7-30.
Eskeland, Gunnar and Emanuel Jimenez (1990), "Pollution and the Choice of Policy Instrument in
Developing Countries," processed.
Fuss, Melvin (1977), "The Demand for Energy in Canadian Manufacturing," Journal of Econmetrics
5, 89-116.
Griffin, James M. and Paul R. Gregory (1976), "An Intercountry Translog Model of Energy Substitution
Responses," American Economic Review 66, 845-57.
Heckman, James (1981), "The Incidental Parameters Problem and the Problem of Initial
Conditions in Estimating A Discrete Time-Discrete Data Stochastic Process," in C.
Manski and D. McFadden (eds.), The Structure Analysis of Discrete Data, Cambridge:
MIT Press.
Lee, Lee-Fung and Mark Pitt (1986), "Microeconometric Demand Systems with Binding Non-negativity
Constraints: The Dual Approach," Econometrica 54, 1237-1242.
Lee, Lee-Fung and Mark Pitt (1987), "Microeconometric Models of Rationing, Imperfect
Markets, and Non-negativity Constraints," Journal of Econometrics 36, 89-110.
Moss, Diana and James Tybout (1992), "The Scope for Fuel Substitution in Manufacturing Industries:
A Case Study of Chile and Colombia," processed, the World Bank.
Pindyck, Robert (1979a), "Interfuel Substitution and the Industrial Demand for Energy: An International
Comparison," Review of Economics and Statitics 61, 169-179.
Pindyck, Robert (1979b), The Structure of World Energv Demand, Cambridge: MIT Press.
Rust, John (1987), "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold
Zurcher," Econometrica 55, 999-1033.
Wales, T.J. and A.D. Woodland (1983), "Estimation of Consumer Demand Systems with Binding Non-
Negativity Constraints," Journal of Econometrics 21, 263-85.
Westbrook, M. Daniel and Patricia A. Buckley (1990), "Flexible Functional Forms and Regularity:
Assessing the Competitive Relationship between Truck and Rail Transportation," Review of
Economics and Stati-ics 72, 623-30.
25
Appendix
In this appendix we summarize the likelihood function that Lee and Pitt (1987) developed. For
our purposes it is sufficient to consider three types of regimes: all three fuels are used, two of the three
fuels are used, and only one of the three fuels are used. As in the text, let asterisks denote observed (as
opposed to notional) shares, so that the first type of regime occurs whe.. all elements of S = (Sl, S;,
S3 )are strictly positive. Under these conditions notional and observed shares coincide, thus in terms of
exogenous variables and disturbances, equation (3) implies that the first regime is observed when:
61 + ,B,'lnP + el > 0, (Al-1)
62 + #2lnP + E2 > 0, (A 1-2)
61 + 62 + (1 + i2)1'nP + El + e2 < 1. (A1-3)
Here Ai = (iij,2,00), InP = (InP,lnP2,1nP3)', and 6i = cx, + OQilnQ. Given that one of the three
disturbances is redundant by equation (4), the conditional likelihood function for observations from this
regime is:
f(Si - 61 - ,B,lnP, S; - 62 - 2 InP),
where f(*) is the bivariate normal density function for (e1,e2).
An example of the second type of regime occurs when S = (0, S;, S3), where S; > 0 and S; >
0. Here the logarithmic viitual price for input I at S is obtained by setting S, = 61 + 0,/1'nP + e1 =
0:
Int, = -(63 + ,32lnP2 + 0,31nP3 + e3)/,1. (A2)
26
Substituting Int1 for InP, in equation 5, the observed cost share for the second energy subgroup satisfies.
S: = 62 + 22llnP + E2 + O3,(lnt, - lnP,)
= 62 + 12 InP + E2 - (321/111)(61 + 01 InP + e). (A3)
Hence the regime conditions i P, and 0 < S; < 1 can be expressed in terms of exogenous variables
and disturbances as:
(l/,~)(6, + 131InP + e,) 2 0, (A4- 1)
1 > 62 + 02InP + e2 - (021/22)(61 + 13InP + el) > 0. (A4-2)
If 1,, < 0, the set of (el,e2) values that satisfy these conditions will not overlap with the (e1,e2) values in
conditions (Al). This "coherency" requirement ensures, from (A4-1), that
e1 < -(6w + 1 InP),
and the conditional likelihood function, given S' = (O,S:,S;), becomes
+1 + I1nP) f(el,Z2(S;,ej)) dE,,
-oo
where 2(S241) = S- - 62 - 02'lnP + (021/311)(61 + 1 InP + e,), a rearrangement of (A3).
An example of the third type of regime occurs when S = (0,0,1), that is, inputs I and 2 are not
consumed. By setting S, = 0 and S2 = 0, the virtual prices for input 1 and 2 can be expressed as
27
ln [InPi 5 /3I132 5-1 61 + 10lnP + (AS)
l t2 I 1nP2 L321 22 62 + 32lnP + E2
The regime conditions are , S PI and t2 c P2, or using (A5):
(1/(0131122 13l2))[,B22(0I + 0, InP + el) -
012(02 + 02'nP + E,)] 2 0, (A6-1)
(1011322 - 132))[-021((1 + 1I1nP + el)
01102 + 012lnP + e2)] > O (A6-2)
The (el,e2) values that satisfy conditions (A6) will not overlap with those in (Al) or (A3) only if 01,022 -
21,2 > 0. Using this coherency requirement, (A6) becomes
ti - (012/022)E2 C ((12/022)(62 + 02 InP) - (61 + (1 lnP),
-(312/31O)E1 + E2 C (121/111)(61 + 10 InP) - (62 + 12 InP),
and the conditional likelihood function, given S' = (0,0,1), can be written as
J (1312/1322(62 + 12" lnP) - (56 +13'nP) I (012I/)(6b+O,1lnP) - (62+12lnP) g(e,,eDde,de;,
where g is the bivariate normal density function of e and e2, with
C- = e, - (012/922)e2 and eL = -(012/311)e1 + e2.
The likelihood functions for the other regimes can similarly be derived. The coherency requirements 022
28
< 0, 033 < 0, 011033 1 t3 > 0, and 033 _ t23 > 0 are also needed to ensure that the seven regimes
not overlap one another, that is, that the regime probabilities sum to one.
29
Elastici-ty and Output, Industry 5117
0 l
00 OD oO0
10
C14
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(NJ Q
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Elastici-Ly and Output, Industry 3117
9000
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1 6 8 10 12 14 16
InQ
Elastici-ty and Output, Industry 31 1
0 . , ,M - ,..
t .
00
iN
0
8 10 12 14 16
Ino
Elastici-Ly and Output, Indus-try 311 7
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to
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t0 0
0
coi <
0~~~~~~~~~~~~~
o 0
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7 89 1 0 1 1 1 2 1 3 1 4 1 5
'no
Elasticity and Output, Industry 311 7
00
0
O
0
0
41 V)0 0
(NJ-~~~~~~~~~~~~I 00
7 5 9 ~~1 0 1 1 1 2 1 3 1 4 1 5
InQ
Elastic'ity and Ouztput, Industry 31 1 7
(N
U,,
N 1
0~~~~~~~~~~~~
04~~~~~~~~~~~
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N '90
@ 1-
7 o
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' '' ' '_ ~~ ~~~~~~~12 n 13 1 4 1 5
Elasticity and Output, Industry 311 7
00
0
0
Lo
0
0
00 OD0
0 I p I pIII
7 891 0 1 1 1 2 1 3 1 4 1 5
InQ
Elasticity and Output, Industry 31 1 7
0 ,
0 0 0
0000
N0
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00
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InQ
Elas-tciLyy and Output, Indus-try 311 7
(0
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'-'
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1 6 8 10 12 14 16
InQ
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