Energy demand in Portuguese manufacturing: A two-stage model

03605442/92 $5.00 + 0.00 Pergamon Press plc

Energy Vol. 17, No. l! pp.61-77, 1992 Printed in Great B&am

ENERGY DEMAND IN PORTUaUESB MANUFACTURING: A TWO-STAGE MODEL

Antonio M. Borg@ and Alfred0 M. Pereira# t Deptment tl3epaent

(Received

of Economics, New University of Lisbon, Lisbon, Portugal of E!conomics,university of C&for&% San Diego, 500 Gihnan Dr., La Jolla, CA 92093-0508

18 December 1990;

received

for publication

27

August

1991)

1. INTRODUCI’ION The estimation of energy-demand systems has attmcted considerable interest over the past two decades. The energy shocks of the seventies provided the original impetus. But even now that energy markets am perceived tohave~~somstability,thereisstillagreatdealofinterestinanaccurateestimatioaofthemost important I#rramters determining the response of the economy to changes in energy conditions. The economy-wide fluctuations caused by the oil-price increases of the seventies now seem to be a problem of the past. Energy policy, however, contimtes to be a matter of concern for many governments. The problems of thepast~haveexposedthevulnerabilityofcountriesrelyingtoomuchonasingletypeofmergyinput, p&kmlarly if it is imported. A consensus has emerged with respect to the important long-term effects of changes in the relative prices of energy inputs. Policy has therefore changed focus. Diversivication of energy has therefore changed focus. Divemi&ation of energy supply is a major goal, even when it implies higher costs. Go vernments leaning towards intervention in energy markets have concentrated their attention on longrun allocation c&c& of energy prices and on efforts to change them. Both requite accurate knowledge of the d&rmhmnts of energy demand the possibility of substituting other inputs for energy, as well as the substitutability among energy forms, am key to the definition of appropriate scenarios for long-run energy Polk?. F!ncrgydemand functions have been estimated for sonx time. But it was only with the application of duality results to demand theory that it has become possible to obtain estimates within a framework consistent with economic theory and compatible with precise econometric methods. Concern@ the demand for energy by the manufachuing sector, the appropriate setting is a model of cost mimmization. In this model, optimal input demands are derived from output levels, given the prices of all factors of production. A complete system of input-demand equations is obtained, providing estimates of own and cross-price elasticities which depend on the substitutability or complemantarty among all factors. The pioneer contribution in this area was the work of Berndt and Wood,’ who estimated a capital-labor-energy-materials (KLEM) model for U.S. manufacturing. Bemdt and Wood’ specifieda translog cost function and obtained results with important policy implications: evidence of signifxant price elasticity $ Author to whom correspondence should be oddrer#d. 61

62

Arnomo

M. BOROES and ALpReDo M. PEREIRA

of the demand for energy and of energy+z+ital com~tarity. Their separability assumption became standard for many s&sequent authors, who attempted to reproduce their 5dings in di5rent contc~ts.~~ Knowledge acquired after almost two dscades of modeling for the U.S., as well as for many other countries, confhms that price elasticities am indeed sign&ant. Enmgyxapital compkmcntarity, howeva, is a more controversial issue, since several studies have failed to support it, cqmciany when anmtrica other than the U.S. or Canada are considered. ‘Iheaeparrrbilityasmunptionsbehind~I(LEMmodelwenlrrtetusadtojuatifytheanalysisof inter-fuel sub&&ion with models that assume total energy input as given.” The main results from this approach ill~te that substitution polD&ilitil!samong alternative energy forms am substantial. Thus, as the price of one form of energy increase+ the response of dsmand can be conceptually divided into two components: the substitution of other forms of energy for t& now mom expensive form and substitution of other inputs for energy to reduce the total energy input. Additionally, an energy-price increase will reduce the energy-demand by increasing the output price. However, this effect can only be analyzed properly in the context of general equilibrium models. The next step in energy-demand m&l@ was tbs integration of the two stages described above. This approach explicitly links the KLEM model with the energy sub-model, by using the technology estimated in the latter to provide the i&x of energy price required by the former. A twestagc model estimates the energy demand snuctum in an internally cOnsistemway, while maintaining convenient separability assumptions. It is thus possible to obtain a more precise ec.ononWric model, which is never&less compatible with data availability. In~papawepnsmttheestimationofsuchatw~~~modeloftbe~dforenergybythe manufacturing industry in Portugal. Translog functions am spcci5d for energy and total output costs. Homotheticity is assumed at both kvels. The usual separability assumptions am applied to aggregate inputs into capital, labor, energy, and materials composites. In the energy submodel, only ck&icity, firel oil, and coal are considemd, given that all other fuels have negligibleshares in total energy drmand. The two models are linked by the price of energy. Estimation premeds with a Full Information Maximum Likelihood (FILL) methodandannualdata. Thcrcsultsamvuyenaxu@ng. BothmodcJsfitthedataquitcwallandthe estimates yield &&city values that do not diffbr substantially from the consensus referred to above. The motivation for the paper has two components: first, no study of this type was ever attempted in the case of Portugal, in spite of the country’s very high depardcnca on imported energy and vulnerability to oil-price increases; second, a raxnt effort by tk Portuguem governmenttodsfiianationalcncrgyplankd to the comuruction of alternative energy-demand scenarios, which am based on the most naive projections, in particular, the exclusion of price responsiveness. ‘lbcmfom, a study of this typs is long overdue and its fmdings may have substantial policy implications. For instance, the evidence supporting signifkant price ela&ity of energy demand may, on the one hand, enable Portugal to avoid the demand-forccas5g errors that now plague other countries, thus leading to more adequa& planning of long-term energy-supply expansion; on the other hand, it may m&annel ulergy~nseNltion efTorts from costly campa@Mimposing mandatory standards and subsidizing energy-saving equipment toward a more &cimt approach based on prim managanent through taxes and the elimination of subsidies. One of the main reasons a study of this type has not been attempted before is due to the unavailability and inadequacy of published data. In fact, a very substantial proportion of the work leading to this paper was devoted to the gathering and treatment of reliable data. A description of the sources of data and of the methods employed to obtain the 5al series used in the atimation is ptwmtcd in the Appendix. Two important advantages of the data utilized in this paper should be cited. First, the period covered ends in 1979 and therefore includes a number of years after the fuat oil shock. The sample consequently contains substantial variability in prices, unlikemost other &udia. Second, all energy prism in Portugal are controlkd by the govcrnnxn t and therefon do not naccs&ly rcfkct changes in local demand or world-market conditions. Thus, the energy-price variables should not be correlated with disturbanas of the demand CqWtiOllS. 'Ihe paper is organized as follows. In Won 2 we present a brief description of the model and its theoretical foundations. Section 3 is an outline of the estimation methodology and contains a discussion of the basic results. saction 4 contains an analysis of the estimates and their implications for the structum of energy demand. Finally, Section 5 wntains the wncluding remarks.

Energy demand in Portuguese manufacturing

63

2. THE MODEL The technology of the manufacmring industry is assumed to be separable into four composite inputs: capital (K), labor Q, energy Q, and materials @I). It is also assumed that constant returns to scale exist and that any technological progress will be Hick’s neutral (i.e. will leave factor proportions unaltered). Technology can therefore be represented by the minimum cost function C = G@toP,,P,PdY, where C is the total cost, Y output and Pk, Pt, Ps, and PMam the prices of K, L, E, and M, respectively. To estimate the parameters of this cost function, a translog functional form is chosen. The cost function can be written as

where symmetry constraints & = sii>are incorporated. Using standard duality results (Shephard’s Lemma), the demand for each factor of production can be obtained by differentiating the cost function with respect to the price of that factor. In the case of the translog, logarithmic di&rentiation yields the share of the factor in total cost. Denoting by Qi the share of factor i,

These four equations implicitly define a complete system of input demand functions, consistent with cost-nrinim&g behavior on the part of producers and price taking in factor markets. In order to satisfy homogeneity constraints, the pamnWem in these equations must satisfy as

+a,

+a, +a,

g~+gIu.+BgB+Bm gIu. +g,+g, +&M gm +g, +&,s +Itwr

g,+g,+g,+g,=~

=lp

=O, =O, =Q

Asimilarmodclisusedtostudythedemandforeachoftbtindividualenergyinputsasafunctionof relative energy prices, assuming that total energy input remains constant. Again, the technology of inter-fuel substitution is repmsented by a cost function which incorporates the optimi&g behavior of producers. Hem, level of spending nacessarytoachieveacertainlevelofenergyinpu~ tlletotalcostofenergyistheminimum given the prices of each form of energy. In order to divide the optimization process of producers into two stages, it is nv to assume homotheticity of the energy technology: factor proportions within the energy composite must be independent of the total amount ofenergy demanded. The energy technology is assumed tosatisfyconstantreturastoscale,whichimpliesthsttbeunitcortofenergydoesnotdepgldonthetotal quantityofenergy. Hence,thecostfiurctioncsnbewritLmintermsoftheunit~tofeaagyasP,= g(p,P~~,whereP,istbecompoaitcpriceofenergy,~~inthemmodel,andP,P,andP,~theprices of electricity, fuel oil and coal, mspectively. Again, a translog functional form is chosen. It can be written as

where symmetry constraints (4’

d$ am incorporated.

ANTONIOM. BORCCSand ALFREDOM. PEREIRA

64 Lqp&hmic

differentiation of this function yiel& the coat shams for each of the three energy inputs,

i.e.

which defii a complete system of demand equations. In turn, for the energy submodel, the homogeneity constraints am b, dd d, d,

+br + d, + dd +$

+b, +4 + d, + d,

=I, = 0, = 0, = 0.

GiventheflwribiLityofthetraaplogfunctionalfonn,thcreisno~~thattheestimateswillsatisfy the normal properties of cost functions. In fact, it is well known that a linear-in-pamme@rand parshnonious functional form for a unit cost function cannot be simultaneously globally con&tent and flexible for all theontically consistent data. We follow the strategy of impo&g co&ant returns to scale, homogeneity, and symmetry, and then testing monotonicity and concavity of the coet function. In doing so we adopt the procedummostoftenusedbyotherresearchersinthisama. ‘lhiaprocedumwasusedintheseminalworkof Bemdt and Woodland Fuss’and has been widely used ever since.s’s’sMonotonicityrequirea that the estimated share be positive at every point in the sample. Them am a mu&r of methods to check for concavity. The most obvious way is the verification of the negative semidefiniteness of the Hessianof the cost function. Since the second derivatives of the translog function am not constant, this test must be performed for all observations in the sample.

3. ECONOMETRIC ESMMATJON Separation of the optimizing behavior of producers into two stages also translates into a two-stage estimation procedure. The energy sub-model is estimated first and the paramters of the energy unit-cost function are then obtained. With these, it becomes possible to calculate an exact index for the price of energy 6.e. the predicted unit cost, given the prices of each energy input), which is required for the aggregate KLEM model. The aggregate model is then estimated in a second stap. Econometric estimation requhw the introduction of random dishrrbances in the sham equations of the model. These disturban~ are introduced additively and should be interpreted as execution errors in the implementation of an optimal decision. The estimates were obtained for both models with FTML based on the assumption of a joint normal distriiution for the distu&nces of the estimated equations. Using FIML represents an improvement with respect to previous stud& which typically use an iterative version of Zellnds Joint Generalixd Least Squares or Iterative Thme Stage Least Squares. FIML is the most efficient of all consistent estimators and by definition handles compIetely across+quation rest&ions and simultaneous equation bias. Moreover, the condition that the cost sharea add up to one implies that the disturbances of the share equations am linearly dependent, since they must add up to zero. Therefore, the variancocovariance matrix of the disturbances is singular. To make estimation possible one equation must be dropped. FIML estimation assures that the results am invariant with respect to the equation that is dropped. Although FIML is traditionally used under the assumption of normality, them ate some potential problems in the case of systems of share equations. In fact, the implicit distribution of the error term in the equation which is not directly estimated will not be normal. Furthenn~re~ the normal distribution does not rule out the cccurmnce of very large positive values, which would imply negative dish&ancea for the non*timati equation and perhaps even negative shares, Both models am estimated with annual data. The sample used for the energy submodel covers only the period 197@1979for lack of quantity data for previous years. Since two equations are used, and given the constraints imposed on the pamme@s, thereare 1Sdegreesoffrradom. Theof this function

65

Energy demand in Portuguese manufacturing

compute the price of energy for the aggmgate KLEM model. Since there is reliable data on energy prices, a serks can be constru&d for years not included in the energy sample. The KLEM model is estimated with data for the period 19591978. Thme equations am fitted, and given the constraints only nine Gmsequmtly,therearo48degrecsoffrcedom. Itshouldbe imkpendentpamtMUs amtobeestimated. notedthattheavailabledegraeooffnedomineitberthearetgyortbeKLBMmodelsnwellwithiothe normal bounds in comparabk ~tudks.‘~*~ arc then used to

Table 1. Estimates for the energy sub-model. Standard Deviation

Estimated

Value

t-statistic

0.507231

0.0241980

20.9616

0.337266

0.0243663

13.8415

0.155503

0.0141058

11.0240

0.111599

0.0455041

2.45250

-0.168078

0.0551672

-3.04670

0.056479

0.0400550

1.41003

0.199335

0.0973246

1.98668

-0.025275

0.0348370

5.72552

-0.031204

0.05807%

-0.53726

Table 2. Key statistics of the energy equations. Fuel

RZ

Durbin-Watson

Electricity

0.9876

0.210

FlklOil

0.9549

0.065

coal

0.9594

0.665

Parameter estimatcs, standard deviations, and t-statistics for the energy submodel are presented in _ _ Table 1. Some key statistics for each equation am presented in Tabk 2. Since only the ekctrkity and fuel oil equations wem estimated, the values corresponding to the coal equation were obtained indirectly. The estimates obtained am encouraging. In partMar, the low stamkrd errors for the estimated coeffikients indicateagoodkvelofprecision. Asa v, most of the t-statistics are quite acceptabk, justifying the effort to estimate a flexibk functional form (the translog specification is different f&m a Cobb-Douglas at a 10% signifii level). Similarly, the measums of gocdness of fit am also unusually high. The acceptability of the estimates obtained also depatds on the verification of the regukrity conditions required by the cost function. Monotonic&y is verifkd at every point in the sample. Concavity is verifii by chsckingtbenegativesemi_definitenessoftbeH~ofthecoetfunction. Thedetc * tsoftheHessians are zero, given the linear homogeneity assumption. The 5rst minors am all negative and the second ones are all positive. The estimated cost function is the&on concave fat every sample point.

66

ANTONIOM. BORGESand ALFREDOM. PEREIRA

Table 3. l?stimatea for the KLEM model.

clleffimt

E.stimated Value

t-statistics

Standard DCVhtiOll

a,

0.418681

0.0302516

13.83990

a,

0.2315%

0.0234378

9.88128

a,

0.056779

0.0043697

12.993%

a,

0.292945

0.0317585

9.22415

gKlc

a.177740

0.1422530

-1.24947

gKL

-0.030100

0.1053250

-0.28578

gKE

0.004001

0.0312615

0.12809

glUd

0.203838

0.0397806

5.12404

gLL

0.155757

0.1046100

1.48893

gLI3

-0.011739

0.0167312

-0.70163

gtbf

-0.113918

0.0919174

1.23935

gm

JCI.018303

0.0144296

-1.26841

gEM

0.026040

0.0300416

0.86680

BMM

-0.115960

0.1307012

0.88721

Table 4. Key statistics of the KLEM sham equations

Input

R2

Capital

0.979

Labor

0.919

Energy

0.986

Materials

0.937

Durbin-Watson

7 0.489

0.104

0.668 0.055

The aggregate KLEM model can only be consistently estimated a&r the results for the energy sub-model have been obtained. The energy unit cost function is used to obtain an energy price index which becomes an instrument in the estimation of the aggregate model. Parameter estimates, standard deviations, and t-statistics am presented in Table 3. Again, only the capital, labor, and energy equations were estimated. The parameters of the materials equation were obtained from the const.rah~ts across equations. Additional statistics relative to the equations in the KLEM model are presented in Table 4. Although not as exceptional as those of the energy submodel, the results of the estimation are also encouraging. Among the many previous studies of this type, it is rare to fmd such goodness of fit, and larger standard errors am quite common. The quality of these results may be due to the use of FIML, or to the better quality of data, which contains substantially mom price variability than what was normally the case iu most of the pm-1974 samples. Again, the translog structure is statistically ditkent from a Cobb-Douglas spccikation at the 10% significance level.

Energy demand in Portuguese manufacturing

67

The rcguhrity conditions that the C0st function must meet were veritil at every sample point. Monotonicity is assured by the positive values of predicted shams every year. Computation of the minors of the Hessian for every year shows that they altcmate iu sign starting with negative, while the Hessians themselves vanish. This is exactly what is required for concavity under the constant returns to scale. The single most important negative aspect of the estimation results is the very low value for the Durbin-Watson statistics. Thcsc values suggest the presence of serial correlation of first order in the residuals of the estimated equations. Serial correlation implies that the observed goodness of fit is ovemstimated, standard errors are underestimated so that t-statistics look better than they am, and t, and F tests am biased. Thisisacommon occurmnce in this type of static flexible demand system which has been identified in the seminal articlcs.31’Early attempts to deal with autocorrelation within an automgressive process of first order were developed by Bemdt and Savin.” They concluded that since the equation system is singular, this procedure introduces unreasonable rest&ions on the autocorrelation structum and generates identification problems. Furthermore, they argue that if the rest&ions are not imposed then estimates and tests am conditional on the equation deleted. Conventional wisdom stipulates that autocorrelation is a consequence of the static nature of the models. This line was fti developed by Anderson and Blundell”in the context of different error-correction mechanisms. Mom recently, Pyndick and Rotemberg”&imate a truly dynamic translog model. Results do not show any signs of autocorrelation. This establishes that, indeed, autocorrelation problems with the static models are due to dynamic mis-spec&ation. UnIorhmately, the data set in this paper cxumot support the extra enrichment of error oxrection me&a&us or truly dynamic specitications. However, it should bc noted that despite the autocorrelation problems, and in good part because of data constraints, the static approach has been widely used in the literature.

4. ANALYSIS OF THE RESULTS The estimates obtained for both models have sign&ant implications which will now be discussed. The adequacy of the translog specification implies that the Allen elasticities of substitution are not constant and may take any values. Own and cross-price elasticities of demand can also take any values, apart from sign restrictions. The magnitude and sign of many of these elasticities have signifllt consequences for energy policy. Since the two models were estimated separately, the Allen elasticities of substitution and the price elasticities of demand will also be presented separately. It is, however, important to compute the price elasticities of the demand for energy when total energy input is allowed to vary. This requires the use of information from both models. Using a well known result, Allen &sticities of substitution can be obtained from the cost function as s. = Ccv/cCl where siiis the e&i&y of substitution between factors i and j, Cl denotes the first derivative, E&l.+, and q the second derivative, dC&p&. In the case of the translog, the Allen elasticities of substitution become

where l&s the second-order m associatedwiththepricesofthetwofactorsofproductioniandj,and Qiisasbefomthecostshsreoffactori. oWn~dcross-priceelasticitiesofdemand~beobtaiasddirsctty from the Allen elasticities of substitution and the cost shares. The elas&ity of demand of factor i with respect tothepriceoffactorj,ej,canbecomputedased=Q~~ Thus,eventhoughtheAllenela&icitiesof substitution are symmetric, the cross-price elasticities need not be. It should be pointed out that the elasticities computed for each model assume that output remains constant. Thus, e, for example, describes the change in the demand for capital when the price of energy changes, assuming that total output and prices of inputs other than energy remain constant. Similarly,en, for example,describesthechangeintbedgnandforfiieloilwhentbepriceof~~incna#s,eananingthat thetotalamountofenetayinputand~pricesofotherfuelsremainconstant. AcumGgly,itisimportant tocomputetheelaaicitiesfortbtmagy~m~,~o~for~intotalenetgyinput. Astheprice ofoneformofenergyincreases,thecompositepriccfortbeenergyaggregatewillgoup. Giventheprice elasticity em in the RLFiM model, total energy input will fall. Therefore, the global own-price elasticity of

68

Amo~lo M. BORGESand Auwmo

M. Pmuaru

demand is larger in absolute value than the elasticity in the energy sub-model. On the other hand, cross-price elasticities, when they am positive, will be lower if total energy input is allowed to vary. Similarly, the Allen elasticities of substitution in the energy sub-model do not reflect appropriately the substitutability or complementarity among energy inputs. If total energy input is allowed to change, the demand for a certain type of fuel may fall when the price of another increases, even though they may be substitutes within the energy submodel. The relationship between the ditfercnt elasticities is given by E.. = ej + Qleaa where E.. is the total elasticity of the demand for fuel i when the price of fuel j changes and total energy input changes, edis the same price elasticity but without allowing for changes in total energy (i.e. the partial elasticity within the energy submodel), Qj is the share of fuel j in total energy cost, and em is the own-price elasticity of energy demand in the KLEM model. Thus, even though two forms of energy may be substitutes within the energy sub-model (cd > 0), if the share of j in energy Qj is large or the elasticity of demand for energy in the KLEM model E, is high (in absolute value), the final outcome may be a fall in the demand for i when the price of j increases (Err-Z 0), hence, complementarity. The elasticities of substitution and own and cross-price elasticities of demand will be presented for each model, followed by global price elasticities of demand for energy inputs.

Since the value of elasticities depends on the shares, it is clear that it will not be constant. Allen elasticities of substitution and price elasticities of demand were computed for every point in the sample. Tables 56, and 7 present values for some selected years. Table 5. Allen elasticities of substitution for the KLEM model.

%I4

%M

-0.679

2.565

-0.460

2.420

-0.273

2.483

0.228

2.062

The most striking result among the elasticities of substitution presented is the evidence of significant substitutability between energy and capital. other elasticities do not suggest any surprises. An elasticity of substitution between capital and labor of around 0.7 falls within the bounds obtained in similar studies for many other countries using flexible functional forms. Labor and energy are substitutes, although moderately, as in most other countries. Complementarity between labor and materials is not unusual. The value of the elasticity of substitution between capital and energy does not leave any doubt as to the substitutability of these two inputs. It seems, therefore, that the results obtained for the U.S.’ or for Canada’ do not apply in the case of Portugal. However, studies covering various countries,2” obtained elasticities of substitution between capital and labor that do not differ sign&antly from the values obtained here. In spite of attempts to reconcile and explaining alternative estimates for this elasticity of substitution, the controversy over its value is not moot. Two explanations for the high substitutability between energy and capital can be given for the case of Portugal, along the lines of previous research. Following Grit& and Gregory,2 who argue that capital energy complementarity is only a short-term phenomenon, that surfaces in time series studies because of the small variability of prices typical of those studies, it can be pointed out that the sample used for this paper includes substantial variation in relative prices and covers a period of very fast growth in output, and very high levels of investment in Portuguese manufacturing, all of which would induce faster adjustment than what is found in studies for the U.S. or Canada. Alternatively, the explanation provided by Field and Grebensteir? also applies in the case of this study. Capital shares include expenses with all types of capital where no distinction

69

Energy demand in Portuguese manufacturing

fixed and working capital is made. Working capital is a good substitute for energy while fixed capital is a complement, than the fact that both are lumped together may axplain why the linal result indicates substitutability. Thare is no data at this point that would permit a better analysis of this issue for the Portuguese case. E&mdt and Wood’ argue that a positive elasticity of substitution between capital and labor has been obtained only in studies that do not explicitly consider materials inputs, and that it is possible to have substitutabiity in this context and complementarity when materials are added in a nonseparable way. In the case of this study, materials am inch&xl as in the work of Bemdt and Wood,‘but with an important correction: the share of materials exchules those inputs that come from the industry itself. It is, however, difficult to tell whethar the lack of this corraztion in other studies has biased their estimates of the elasticities of substitution in any predictable manner.

between

Table 6. Own tuice elasticities of demand for the KLEM model. Ye43.I

%.K

%L

e,

1963

-1.006

-0.0%

-1.266

-1.103

1968

-1.089

-0.133

-1.248

-1.071

1973

-1.187

-0.192

-1.231

-1.130

1978

-1.874

-0.205

-1.257

-0.852

%i

The results obtained for own-price elasticities of demand are quite revealing. Labor is the only factor whose demand is somewhat &la&. Although it doubles during the sample period, the elasticity of the demand for labor remains rather low (between -0.1 and 0.2). Conversely, for the other factors of production, demand is very elastic. Tha elasticity of the demand for capital increases throughout the sample period and remains greater than 1 in absolute value. Similarly, the damand for materials is also fairly elastic, which is not implausible given that only materials originating outside of manufacturmg am considuud. The most signifiit result obtained is the high value of the own-price elasticity of demand for energy. It remains at about -1.25 for the entim sample period. This is considerably higher than the value obtained in other studies. The main explanation for this result is likely to be the same as for the substitutability between energy and capital. Given the substantial changes in relative prices obsarved and the fast rate of growth of output, the responses to price changes captured by the values of the elasticitiesam probably closer to long term responses than what has baen obtainad in other studies. The implications am very clear: any change in the relative price of energy will have a substantial impact on its demand, due to the pos&ility of substituting other factors of production for energy. Table 7. Cross-price ela&iciticsof demand for the KLEM model. Y&U

e,

e,

1963

0.16

0.07

1968

0.17

1973

e,

e,

e,

e,

St4

0.78

0.29

0.50

0.03

0.71

0.07

0.84

026

0.45

0.06

0.74

0.23

0.07

0.88

024

0.40

0.13

0.70

1974

0.26

0.07

0.91

023

0.38

0.16

0.71

1978

0.17

0.08

1.62

0.08

0.24

0.15

0.87

t

70

ANTONIO M. BORGES and ALFREDO M. PEREIRA

The values for the cross-price elasticitiesof demand follow the pattern of the elasticitiesof substitution. Itis,ho~~,clearthatgiventhesmallshareofcnergyintotal~~the~~ofanincnaseintheprice of energy on the demand for capital is rather small. In the case of the demand for labor, changes in energy prices have vhtually a negligible impact. In turn, the price of labor, and in particular, the price of capital, have more visible e.tTectson the demand for energy.

Tables 8,9, and 10 display the elasticities of substitution, the own-price elasticities, and the cross-price elasticities of demand, respectively, for the energy submodel. Again, only a few years in the sample were chosen. Table 8. Allen elasticities of substitution for the energy sub-model. Y&U

set

1970

0.018

1.716

0.518

1973

0.002

1.704

0.461

1978

0.141

2.251

0.532

SC

sfc

The positive sign of all elasticities of substitution indicates that, as expected, all forms of energy are substitutes for each other. However, it is clear that the possibilities of substituting electricity for fuel oil axe rather res&ted. Surprisingly, coal seems to be a better substitute for electricity than for fuel oil. This result may be due to the limited use of coal in Portuguese manufacturmg. The general incmase in the elasticitiesof substitution during the sample period is a consequence of the sign&ant relative price change. As oil and coal prices went up, producers moved along the isoquants toward points where the substitution possibilities increased. ‘Ihe changes in the values of these elasticities and the significant d.Berences among them arc additional evidence of the advantages of using a flexible functional form. Had a more rigid struchue been imposed, none of these results would have been detected. Table 9. Own-price elasticities of demand for the energy sub-model.

Own-price elasticitiesare all negative, as they should be, but rather small in absolute value. This is a consequence of the low values for the elasticities of substitution. As the price of one fuel goes up, if total energy input remains constant and the possibility of substituting this fuel for another is limited, the demand should not decrease by much. Nevertheless, keeping energy constant, own-price elasticities are far from zero. The effect of price increases on demand must not be neglected. Similarly, cross-price elasticities are quite small, especially between electricity and oil. A doubling of the oil price will induce an increase in the consumption of electricity of only 6 to 7%, in the final years of the sample. Since own and cross-price elasticities must add up to zero, this is again a reflection of the small absolute value of the former.

71

Energy demand in Portuguese manufacturing

Table 10. Cross-price elasticities of demand for the energy submodel.

%

e,

e,

=c4

ecf

1970

0.006

0.267

0.009

0.081

0.870

0.175

1973

0.001

0.255

0.001

0.069

0.915

0.145

1978

0.068

0.251

0.057

0.059

0.911

0.257

GfobaflL?ssticiti~ of the lkmand for Enagy

Tables 11 and 12 present own and cross-price elasticities of demand for each energy form, when total energy input is allowed to vary but total manufachuing output remains fixad. Table 11. Global own-price elasticities of the demand for energy.

%r -0.901

-0.507

-0.916

-0.456

-0.828

-0.725

These are the most important results for policy purposes. In fact, under the asstmrption that given the small share of energy in total output co& an illcrease in energy prices will not substantially affbct the level of output,theresponscofmanufacturingwithrespecttotbedgnandforeachtypeof~isgivenbythese elasticities. They incorporate, as shown above, the substitution of the now more expensive form of energy by alternative energy sources, plus, the possibly mom intensive use of other inputs to rephxc energy. The values obtained are n-y higher for own-price elastkities than those obtained in the energy sub-model. They indicate that, fuel is the least price responsive of all sources of energy, demand fix &&city is somewhat inelastic, and coal is the only fuel which responds more than proportionately to a price incmase. In any case, for all three sow of energy, global price elastkities of demand am sufkiently large to imply the @action of any method of energy analysis, demand fomcasting or policy shnulation, which does not include the impact of prices on demand. Table 12. Global cross-price elasticities of the demand for energy.

-0.412

0.074

-0.620

-0.112

0.241

-0.243

-0.386

0.071

-0.660

-0.115

0.254

-0.242

-0.540

0.111

-0.451

-0.081

0.402

-0.351

Global cross-price elastkitias of demand am negative, with the exception of those involving coal and electricity. Thisisacon#q~ofthehighvalueoftbeown-piiceelasticityofdmrandfor~inthe aggregate model, combined with the smah positive cross-price elasticities in tha energy submodel. The interpmtation is that when the price of fuel, for example, increases, the limited substitutability with ekctrkity

ANT~NIOM. BORGES and ALFREDO M. PEREIRA

72

or coal impliesthat the price of the energy composite increases considerably. This induces producers to reduce total energy input by using more intensively, capital, labor, and materials. The reduction in energy input translates into lower demand for electricity, coal, and Ikl. This scale effect is more important than the incentive to use ektricity or coal mom intensively as a substitute for fuel.

It is now possiile to attempt a systematic wmparison of the results obtained in this study with those of similar studies for other wuntries. The wmparisons am not always entirely valid: other studies refer to data from dikent years; deli&ion of the variables is not exactly the same; in most wuntrk other sources of energy are also important etc. However, with these qualifications, the wmparison can still provide interesting insights, by highlighting dilferences and simikities. Table 13. Comparison of Allen elasticities of substitution in the KLEM model. Elasticities of substitution

Portugal

U.S.

several

Canada

wuntries

%a.

0.68

1.01

0.39

4.70

GE

1.24

-3.25

1.04

-10.60

s,

3.12

0.54

%a

0.37

0.64

%M

a.08

0.59

0.40

%M

2.38

0.75

0.11

-0.97 0.83

4.27

ThefirstresultstobewmparedaretheAldenpsrtislelapticitiesof~~tionintheKLEMmodel. They am displayed in Table 13. It is clear from this table that the results obtained in this study are much closer to those of the international studykan to those obtained for the U.S.‘or Canada3alone. ‘Ihe elastkity of substitution between capital and labor falls between the values obtained in each of those international studies. Energy and capital seem to be more substitutable in Portugal than the international average.’ Labor and energy, on the other hand, display a much lower elasticity of substitution in Portugal. The results for the U.S.,’ and for Canada,‘cannot be reproduced in Portugal. The main di&rences are the wmplementarity between energy and capital which those two studies have found, plus, the signifikantly differurt values of the elasticitiesinvolving materials. This latter m may be due to the fact that in this study materials have been defined to include only those not originating in manufacturmg. A second wmparison is based on the price elastkities of the IUEM model. This wmparison, as displayed in Table 14, includes results for the U.S.,’ several wuntries~ and Canada? The most striking conclusion from this comparison is that own-price elasticities of demand are higher in Portugal than in other countries, with the remarkable exception of labor. The elasticitk of the demand for capital, energy, and materials are higher than the highest values obtained in all other studies. In the c89t of labor, however, the own-price elasticity, although not far from the value obtained for several ~untries,~is still below the Ilgure for any other wuntry. Cross-price elasticities r&ct the values of the Allen elasticities of substitution: there are no surprising values. It should be emphasized that energy prices seem to have a very small impact on the demands for capital or labor. Finally, the cross-price elasticities between capital and labor are not far from the values obtained in the other studies. A similar wmparison of elasticity estimates made for the energy sub-model is presented in Table 15. Hem it is possible to include, in addition to results from the U.S.“, Canada’ and several wuntries,( so= estimates for India9and Koreato to provide a wmparison with wuntries in a state of development similar to that of Portugal.

Energy demand in Portuguese manufacturing

Table 14. Comparison of price ehticiti

73

in the KLEM model.

several

U.S.

coulltlics -1.31

0.48

-0.35

-0.76

0.22

0.28

0.22

0.20

0.07

-0.15

0.13

-0.01

1.02

0.34

0.20

0.06

0.12

0.20

-0.19

-0.46

-0.23

-0.49

0.02

0.03

0.11

0.04

-0.02

0.37

0.34

-0.17

0.31

-0.05

0.12

0.18

0.48

0.55

-1.26

XI.47

-0.79

-0.49

0.78

0.47

_

-0.02

0.92

0.03

0.25

-0.02

0.16

0.11

0.14

0.03

0.00

-1.03

-0.22

0.57

0.25

I

I

-0.36

Table 15. Comparison of price elaaicities in the energy sub-model. Pria

Portugal

U.S.

-0.30

EGY 17:1-F

India

Korea

AI.12

-0.14

-0.85

-0.52

countrica

elasticiti~ a.66

0.06

0.30

0.06

0.09

0.18

0.27

0.25

0.09

0.12

0.10

0.68

0.09

0.06

1.27

0.17

0.12

0.11

0.77

-0.12

-2.75

-0.35

-0.09

-0.30

-1.22

0.06

0.69

0.35

0.15

0.19

0.30

0.90

0.31

0.27

0.16

0.83

0.27

0.23

0.74

0.38

0.13

0.39

0.32

-1.13

-1.46

-1.50

-0.15

-1.22

-1.41

74

ANTONIO

M. BOROESand

k.FREDO

M.

PEREIRA

The comparison shows that the estimates obtained for Portugal are not far from those usually found in other countries. Most of the vahtes for Portuguese elasticities in the energy sub-model fall in the interval of values for other countries. A closer look shows that own-price elasticities do not diverge very much, with the possible exception of oil. For this fuel, the price elasticities obtained for the U.S.16and for Canada’am signifiitly larger than what is common in other countries.* Clearly, the structum of energy demand in North America is suIIlciently diBrent to explain the Ilnding of a rather diRerent, and more elastic, response of oil demand to its price. Elect&ity demand seems to be the least elastic, while coal demand shows strong price responsiveness. Cross-price elasticities do not display signifiit dimmpa&es across countries. Nevertheless, it is worth noting that the cross-price elasticities between electricity and I% oil in Portugal are surprisingly low. Anincnaseinthepriceofeitherofthesetwotypesofenergywillleavethe~~dfortheother virtuahy constant, if total energy input in manufacturmg remains constant. This seems to indicate that electricity and f&l oil am used in di&rcnt circumstances or applications, and therefore are hardly substitutable. As mentioned above, the most interesting results, from a policy pempecuve, am the global price elasticities of demand. These global price elasticities obtained for the U.S.16, Canada’, and several countries’ are presented in Table 16. Unfortunately, it is no longer possible to compare the estimates for Portugal with those of countries in a similar level of development.

Table 16. Comparison of global price elasticities of energy demand.

Portugal

U.S.

several c-xxlntri~

Canada

Eoo

-0.86

-0.92

-0.60

-0.74

E#f

-0.49

0.23

-0.10

0.19

E,

0.09

0.04

-0.03

0.02

E,

-0.50

0.74

-0.31

0.55

Eff

-0.67

-2.82

-0.50

-1.30

Et%

-0.09

0.63

0.19

0.23

Eta

0.34

0.07

-0.21

0.05

Ed

-0.32

0.69

0.22

0.24

E,

-1.29

-1.52

-1.66

-1.48

Global price elasticities

As can be inferred from the previous analysis, this comparison does not display any particular surprises. The estimates obtained for Portugal are quite compatible with the evidence from other studies. The emerging pattern shows that the demands for electricity and fuel oil am less elastic than for coal. As indicated before, fuel oil is very price responsive in North America. In all studies surveyed, the demand for coal is very elastic. In the case of the other two sources of energy, although demand responds less than proportionately to price increases, the absolute value of the elasticities is large enough to force the rejection of any assumption that demand is not price responsive. As for cross-price elasticities, the only striking result is the negative sign of the elasticity of the demand for fuel oil (electricity) with respect to the price of electricity (fuel oil). This result was also found in the international study,’ and is a consequence of the small, but positive, cross-price elasticity in the energy sub-model, combined with a significant value for the price elasticity of the demand for energy in the KLEM model. Additionally, coal seems to respond stronger in Portugal than in other countries to changes in the price of oil. However, this is a consequence of the small share of coal in energy demand in Portugal. In fact, and referring again to Table 15, a similar strong cross-price elasticity is found in Korea, where coal also represents asmallshareofthetotal.

Energy demand in Portuguese manufacturing

75

thasbocn pepwing a national amqy plan. This ovathelastfcwycamtkPoltugwegowxnmen rcpmscnts a subetantial &Tortto unify eaergy policy, outline available options, and plan in~stments asociated withtbccxpanshofwrgysupply. Theplanirthe!lMtaoliouscfforttoaddlw8an3gyiEswcolErcntly and with a sound ted&al basis. Pmlhhry vwsioxu of the plan have been availabk ainca 1982 for public diswlion. The dominant liIK!Jlof govunnEn tpolicyindudc (i)p&nstomcctaprojaMrapidiacnsseia eaergy~~on,~toa~~yhighsrslrsrgylONPratiointhefutum;tbegronthin consumption in projaM to be kd by the demand for ewsgy in manufacturing (iii a policy of diversification ofenergy~~withamon~~~ofooPlPndtbein~onofnaturalgassndnudearenergy as new aoq (iii) a quite substantial hue of nuclear paws in the 8upply of electricity. As a conacquuw of this orientation, the plan predicts a vuy largs invwtmat effort in the supply of energy, which ia naturally baxxning capital intulsive. Although commended by many policy makua a8 the fti comprcknsivc study of energy policy, the plan has also hem attacked, due to some serious methodological flaws. In particular, projections of energy demand were based on models where priaa~play no role. The growth in the consumption of energy follows rtnrctunoftheaxmomy. But,ifawrgyprhweretodouble,~ GNPgrowth,andexpa%dchangeaintbu predict4 level8 of consumption would remain unaltered. The assumption of a negligiile price hticity of cacrgy demand should be dixardaI, at kaat as far According to the results of this study, all forms of energy wed asmanufachuingensgydemandiacuwmed. in Portugwsc manufacturing display signifiit price oh&it&, which fall within the values obtained for other countries. Only coal seems to have an inchtic demand. However, both fhl oil and ckctricity display sufficimttpriceresponsivaresstojustifythem~serious~~vingswithrespecttoArmnndforscastsbased on the asumption that priced do not matter. Po~msrgyprices,particulorlyinthempnufrrctuting~r,anu~toinaea#innal terms. A policy of subsidiziag -gy prkxa, followd over the last two dccadc~, haa bear abandonsd. Consequently, enagy in the manufachuing sector will be priced aaxxding to long-run marginal co& implying asignifiitinueaaeinrcalpricea. 1tisdifficulttobclisve,Oiventheevidenoeobtoiaedinthirstudy,thateaaay consumption will continue to grow rapidly, an if pricedwere to remain low. lIeMom, the current plan to expand supply, based onaninflatedforecastofemrgydemandgrawth,~rilrelvtocteateinPo~the~problemsand diffcultica that beset the energy industry in other countxiax overcapacity and the inability to pay beck invutmcnta which arc not warranted by demand growth.

5. CONCLUSIONS

76 change,

ANTONIOM. BORGESand given important

substitution

AJ_FREDO

M. PER~IRA

possibilitiesamong energy forms and between sllagy and 0th~~factors

ofproduction.Theroleofprice~inenergy-demandfo~aswellasin~policyingeaercll, is clearlyestablished.

REFERENCES 1.

2. 3. 4. 5. 6. I. 8. 9. 10. 11. 12. 13. 14. 15. 16.

E.R. Berndt and D. Wood, Z&eRe&w &&mcwn& Pndscg~LvII, l(1975). J.M. Griffin and P.R. Gregory, A~CI&UI &nom& Review66,845 (1976). M. Denny, J.D. May and C. Pinto, Cwa&n JoumaIof&onomkvXI, 300 (1978). E.R. Berndt and D. Wood, Amc&en E%ooonutcRetiw69,342 (1979). C. Field and C. Grehenstein, ZZe Revkw of Ekvnomks and Sb&i-tbIXll, 207 (1980). E. Hudson and D. Jorgenson, BcUJoourzalofEbonomfi~andMunap~~~1tSi5~~~~5,461 (1974). M. Fuss, Joz~3J of Libnometrks 5,89 (1977). R.S. Pindyck, llie Review of -nom& andSfgtitiksLXI, 169 (1979). N.D. Uri, Euvpean Ekvnomk Revzbw 12, 181 (1979). E. Shin, EhqpEcono~6,259 (1981). J. Alameda and A. Mann, tie Jot,x&ofDe~opcnt Studis25,329 (1989). E.R. Bemdt and Chrism, Artze&nn E&nom& Revkw64,391 (1974). E.R. Bemdt and Savin, &wnometka 43,937 (1975). Andemonand Bundell, Ebnometcka 50, 1559 (1982). R.S. Pindyck and Rotemberg, Amc&au &non& Review75,1066 (1985). and Strsthth LIX, 381 (1977). R. Halvorsen, Review of tinon&

APPENDM:

Data Sounxp for Ekvnometrk Btht~tions

KLEM expenditure shares were obtained from data published in “Eptatisticas Industria$ (Manufacturing Sector Statistics). An intertemporally~nsistent sample of the manufactwing sector is considered. It represents 85% to 95% of the global sample for which published data 8rt available over the period 1960-1978. Both total expenditure and expenditure with each individual input axs obtained by aggregating entries at a 6digit level of disaggmgation of the Standard ClasXcation of Economic Activities. Careful efforts were in order to make each of the series consistent for the period l-1978. Total expenditure is not reported and was obtained from the reported information by adding the expenditure3 in energy and materials to value added. As to expenditws in individual inputs, those of labor and energy are d&ctly reported. Capital expenditure was computed as a residual in the value added. Expenditure in materials is obtainedfrom the reported series, by netting out the intra-manufactwing flows under the input/output expenditure structwe for 1959, 1964, 1970, 1974 developed by Institute National the Estatistica (National Institute of Statistics). The price in&x of capital P& obtained according to Pt = P*(r+ d), where P, is the Divisia price index of investment goods, r is the interest rate on long-run (1 to 7 years) c&it and d ia the depxeciation rate of capital. The Divisia price index of investment goods aggregates the price series of &uctmw, machhwy and transportation equipment implicit in the gross capital formation series published in “Contas Nacionais” (National Accounts). The quantity weights art the constant price series for the three componenta of gross capital formation, also from “Contaa Nacionais.” The long-run intuwt rate is admi&&atively set. The corresponding series was obtained from “Diario do Govcrno” (Offial Govemment Bulletin) as ahnple annual average rates. The depreciation rate of capital is obtained from the “Inqueritos Indwtriais” 1958, 1964,197l

Energy demand in Portuguese manufacturing

77

(ctnsus of Manufacturi& as the implied rate for the intersurvey period, given investment and capital in the survey years. For the remainQ years, it is 8 linear extrapolation. The depreciation rate averages 7% over the period 1960-1978. The price index of labor is a Divisia index aggregating the hourly average price of production and non-production labor. These am obtained from total expenditures and the number of hours of work for each of the two types of labor. Expenditure in both types of labor and hours of work by production workers are reported in “Estatisticas Industriais.” The number of hours of work by non-production workers is obtained from the total number of non-production workers, as reported in “Estatisticas Industriais,” under the hypothesis that the average number of hours per worker is the same for production and non-production workers. The energy price index is estimated according to the unit cost function obtained for the energy submodel. It aggregates the price indices of electricity, fuel and coal. The price index of materials is a Divisia index aggregating the implicit output price deflators for agricultural goods, mining, and mrvices, as published in “Comas Nacionais.” The quantity weights were obtained from the input/output tables for 1959,1964,1970,1974. For the mmaining years, simple interpolated values were used.

The series corresponding to expenditure shams in total energy cost were constructed from data published by “Dire@0 Geral de Energia” @epartmcnt of Energy). Total energy expenditure was obtained from quantity and price series for electricity, fuel (which represents an average of 91% of the total input of petroleum products) and coal products. Energy prices am administratively set. ‘Ibe corresponding disaggregated series wem obtained from “Diario do Governo.” For electricity and fuel ordinary indices were used. The coal price index is a Divisia index aggregating prices of different types of coal. The quantity weights were obtained from “Dire&to Geral de Energia.”