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Assessing a disaggregated energy input
Energy Economics, Vol. 17, No. 2, pp. 125-132, 1995
i'~UTTE RWORTH E I N E M A N N
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Assessing a disaggregated energy input Using confidence intervals around translog elasticity estimates John J Hisnanick and Ben L Kyer
The role of energy in the production of manufacturing output has been debated extensively in the literature, particularly its relationship with capital and labor. In an attempt to provide some clarification in this debate, a two-step methodology was used. First, under the assumption of a five-factor production function specification, we distinguished between electric and non-electric energy and assessed each component's relationship with capital and labor. Second, we calculated both the Allen and price elasticities and constructed 95% confidence intervals around these values. Our approach led to the following conclusions: that the disaggregation of the energy input into electric and non-electric energy is justified; that capital and electric energy and capital and non-electric energy are substitutes, while labor and electric energy and labor and non-electric energy are complements in production; and that capital and energy are substitutes, while labor and energy are complements. Keywords: Energy; Elasticity estimates; AES
Since the mid-1970s, numerous studies have appeared in the economic literature focusing on the role of energy in the production process (Berndt and Wood [2]; Hisnanick and Kymn [7]; Hudson and Jorgenson [8]; Moghimzadeh and Kymn [11]; Nguyen and Andrews [12]; Norsworthy and Malmquist [13]; Pindyck [14]). While these studies have confirmed that energy belongs as an argument in a production or cost function, some disagreement remains regard-
ing the particular relationship between energy and the other factors of production, primarily capital and labor. For example, while the majority of the empirical evidence suggests that labor and energy are substitutes in production, questions have been raised as to whether these two inputs may be complements (Hisnanick and Kymn [7] ). The evidence on the relationship in production between energy and capital is more mixed. The earliest of the above cited studies (Berndt and Wood [2]; Hudson and Jorgenson [8]), concluded that energy and capital are complements. This conclusion was based upon the estimation of a translog cost function using time series data for the US manufacturing sector. Similarly, the complementarity between capital and energy was later supported by the work of Denny and Fuss [3] using data from Canada and by Norsworthy and Malmquist [13], who analyzed the manufacturing sectors of the USA and
John J Hisnanick is with the US Department of Veterans Affairs, NCVAS (008C12), 810 Vermont Ave NW, Washington, DC 20420, USA; Ben L Kyer is with Francis Marion University, Florence, SC 29501, USA. The views expressed in this paper are the responsibility of the authors and shouldnot be taken as the officialposition of the US Department of Veterans Affairs. Final manuscript received 6 December 1994 125
Assessing a disaggregated energy input: J J Hisnanick and B L Kyer Japan. However, Griffen and Gregory [5], Pindyck [14] and Hisnanick and Kymn [7] have concluded that energy and capital are substitutes in the production process. The findings of Griffen and Gregory [5] and Pindyck [14] were based upon the estimation of a translog cost function using pooled cross-sectional time series data, which these authors argued were more appropriate data for estimating long-run elasticities. In addition, Griffen and Gregory [5] proposed that while energy and capital naight indeed be considered complements in the short run, these inputs should be expected to be defined as substitutes in the long run because 'new equipment could be designed to achieve higher thermal efficiencies but at greater capital costs.' This long-run argument does not, however, apply to the work by Hisnanick and Kymn [7], who also found energy and capital to be substitutes by using a short-run time series for the US manufacturing sector. In their 1986 paper, Moghimzadeh and Kymn [11] suggested an alternative explanation for the conflicting evidence between energy and capital. They argued that a disaggregation of the energy input into its two main types or forms, electric and non-electric energy, might account for some of the different empirical results. Using a translog cost function specification and annual data from 1954 to 1977 for the US manufacturing sector, these authors found that the disaggregation of the energy input was statistically justified. By estimating cross-price elasticities for the disaggregated energy inputs, they concluded that capital and electric energy were complements, as were labor and non-electric energy. Alternatively, they concluded that capital and nonelectric energy as well as labor and electric energy to be substitutes in production. A common characteristic of all the studies cited above is their reliance on the sign of the Allen partial elasticity of substitution or the cross-price elasticity of demand to define any two inputs as substitutes or complements in production. Anderson and Thursby [1] have demonstrated that confidence intervals for the traditional point elasticity estimates provide more information on the structure of production or factor demand. More specifically, these authors consider the point elasticity estimates to be non-informative when the confidence intervals about these point elasticities contain both positive and negative values. Anderson and Thursby [1] developed confidence intervals based on the ratio of normals and the normal distribution for the Allen and demand elasticity estimators in the translog production model. Applications of these confidence intervals to the 126
elasticity estimates of Griffen and Gregory [5] exhibited both positive and negative values. This led Anderson and Thursby [1] to conclude that the Griffen and Gregory [5] definition of capital and energy as substitutes was based on weak evidence. Similarly, the construction of confidence intervals did not support the conclusion by Berndt and Wood [2] that capital and energy were complements. These findings suggest that uncertainty remains with respect to the production relationship between capital and energy. The primary purpose of this paper, therefore, is to analyze the production process in the US manufacturing sector by combining the suggested approaches of Moghimzadeh and Kymn [11] and Anderson and Thursby [1] in order to more completely examine the existing uncertainty regarding the relationships between energy and capital and labor. In particular, we estimate a translog cost function which includes a disaggregated energy input and construct confidence intervals for the calculated Allen and demand elasticities. The data set used contained an end-point in 1985 and appropriate tests of separability were also conducted and evaluated. The paper proceeds as follows. The following section specifies the model and briefly discusses the data employed for its estimation. The next section develops the hypotheses to be examined and the appropriate statistical tests. Then we present our empirical results and lastly, a summary and conclusion.
The model specification and data In modeling the productive behavior of the US manufacturing sector, it was assumed that output could be characterized by an aggregate production function of the following general form
Q = f ( K , L, M, EL, NEL)
(1)
where Q = manufacturing output, K = capital, L = labor, M = materials, EL = electric energy, and NEL = non-electric energy. In addition, we assume that (1) is twice differentiable, quasiconcave, monotonic and experiences linear homogeneity. Associated with this production function there exists a dual cost function which reflects the production technology and the general form of the cost function is as follows:
C = C(Q, Px, PL, PM, PeL, PNeL)
(2)
where C is total cost and PK, PL, I'M, PEL and PNeL are the input prices of the respective factor inputs. By representing (2) through a Taylor series expan-
EnergyEconomics1995 Volume17 Number2
Assessing a disaggregated energy input: J J Hisnanick and B L Kyer sion and dropping terms of order two and higher, we arrive at the flexible translog specification. Therefore, the translog approximation to the (natural) logarithm of the total cost function results in (2) being written as: lnC = A o + AQ lnQ + 1/2AQQ(InQ) 2
+ ~,iZi lnPi +l//2Ei~jAij
lnP/ l n ~
+ EiAoilnQlnPi for i, j = K, L, M, EL, NEL and where symmetry, theorem. Keeping in tions associated with parameter restrictions
(3)
A~ = Aj~, is due to Young's mind the regularity assump(1), results in the following on (3):
~,iAi = O,EiAij = EjAij
=
0
duces to the seemingly unrelated estimation technique (Intriligator [9]). Finally, all reported coefficient values where estimated with software which does not employ a maximum likelihood estimation procedure, but rather an objective function minimization procedure (SAS/ETS [16]). The objective function minimization procedure yielded a test statistic, T ° , which is an analog of the log-likelihood ratio test and is distributed asymptotically as a chi-square distribution with (r - s) degrees of freedom (Gallant and Jorgenson [4]). This test statistic was used in evaluating the issue of separability between electric and non-electric energy and factor inputs of capital and labor. Under the translog cost specification the Allen partical elasticities of substitution can be defined as follows (Berndt and Wood [2] ):
(for all j), O'ii = ( A i i + Si;z - S i ) / / S i 2
E,jAij = 0
for i = K, L, M, EL, NEL
and
(6)
crzj = (Aij + S~Sj)/S~Sj
EiAe~ = 0 Under duality theory, every cost function implies a set of derived demand equations. These demand equations will be linear in the parameters and at the same time represent very general production structures. Therefore, the modified first order conditions with respect to the production at minimum cost, assuming perfect competition in the factor market, results in the following equality as a result of Shepard's [17] lemma: S~ = (8 In C,/8 In P~) = ( S C / S P ~ ) ( P J C ) = piXi//~_,i p i X i
(4)
This implies directly that the factor share equations (Si), resulting from (3) can be written as: S~ = A~ + Ae~ lnQ + ~,jA~j lnPi for i = K, L, M, EL, NEL
(5)
Given the complete system of equations (3) and (5), under the assumption of homogeneity and symmetry across the model's parameters, the estimation of the full model would result in the disturbance covariance matrix to be singular. To avoid this problem one of the derived factor share equations can be dropped from the system without a loss of generality. Therefore, the stochastic model for estimation will consist of the system of equations composed of (3) and ( n - 1) of the share equations from (5). To estimate the parameters of the system, an iterative non-linear three stage least square procedure was used, which under this specification reEnergy Economics 1995 Volume 17 Number 2
for i, j = K, L, M, EL, NEL, i = j
(7)
with the own- and cross-price elasticities of demand being defined as
Eij = Sio-ij
(8)
Because cost shares vary over time, in general Eij Eji, even though ~rij = o3i, by definition. For this paper, the prices and quantities of the inputs capital, labor, materials, electric energy and non-electric energy for the US manufacturing sector were measured by the respective Divisia indices. The data cover the years 1958-85, and were collected from two sources. The capital, labor and materials Divisia indices were obtained from the US Department of Labor, Bureau of Labor Statistics, Office of Productivity and Technology. The energy data were taken from the US Department of Commerce, National Energy Account (NEA) [18]. This NEA file allowed us to disaggregate the energy component for the US manufacturing sector into the two components of electric energy and a non-electric energy. The price and quantity indices for these two types of energy were created using the Divisia aggregation process. A more complete description of the data used in the construction of the energy indices is available upon request from the authors. Despite the fact that recent years of data are not covered, use of this data was desirable for two reasons. First, the data series are well constructed and have been checked and used extensively by other researchers. Second we chose to use aggregate 127
Assessing a disaggregated energy input." J J Hisnanick and B L Kyer
manufacturing data in order to maintain comparability with prior published studies that focused on the relationship of energy in the manufacturing production process.
Hypotheses development and associated tests To address our concerns regarding the relationship of capital and labor relative to the disaggregated energy input, we investigated both the strong (or linear) and approximate (or weak) separability of these factor inputs. In looking at linear separability, interest centered around whether the factor inputs within the stated functional form are linearly related. In testing this type of hypothesis, the parameter restrictions imposed on the estimated model are that the cross-product terms with respect to the factor input in question are assumed equal to zero. In looking at the issue of weak separability of the input factors, a necessary and sufficient condition for two inputs to be weakly separable is that the marginal rates of substitution between the inputs be independent of the quantities of the other factor inputs. For a five factor production function, the testing for the weak separability of X 1 and X 2 with respect to the inputs 3(3, X 4 and X 5 can be expressed by the following constraints on the Allen partial elasticities of substitution: S13 = S23 = 1 ; S14 = $24 -h- 1 ; S15 = $25 =
1
This is equivalent to the following non-linear restrictions being placed upon the parameter estimates:
Previous authors have concluded that pairs of inputs are either substitutes or complements in production by evaluating exclusively the signs of the Allen elasticities of substitution and the price elasticities of demand. However, Anderson and Thursby [1] demonstrated that these elasticity estimators derived from the translog specification are non-linear transformations of the parameter estimates and factor cost shares. The general problems involved in non-linear estimation may underlie the inclusive nature often surrounding the issue of the relationship between inputs in production. Therefore, to more appropriately address the issue of substitution versus complementarity, confidence intervals were constructed for the calculated Allen elasticities of substitution and price elasticities of demand. These confidence intervals are based upon the means of the observed factor shares and, in all cases, refer to 95% confidence intervals about the point elasticity estimates. The use of confidence intervals highlights the shortcomings of the more commonly used sign test. That is, confidence intervals may span both positive and negative values which would simultaneously support the mutually exclusive conclusions that the ith and jth inputs are substitutes and complements. Adding to the confusion is the possibility that confidence intervals for the price elasticities may span positive and negative values while the confidence intervals for the Allen elasticities may not and vice versa. Thus, tests for substitution and complementarity based upon confidence intervals may not support the same conclusions as tests based solely upon the signs of point elasticity estimates.
AIB23 -A2B13 = 0; A1B24 -A2B14 = 0 AIB25 -A2B15 = 0; BuB22 - (B12)2 = 0 For the above parameter restrictions, Denny and Fuss [3] proposed a test at the point of approximation by dropping the last constraint. This approach was adopted for the testing of the hypothesis of weak separability of the input factors capital and labor relative to the disaggregated energy input. Lastly, one of our major concerns focused on the mixed conclusions from previous studies regarding the relationships between energy inputs and the other factors of production, especially for the US manufacturing sector. To measure factor substitution possibilities, we calculate both the Allen partial elasticities of substitution and the price elasticities of demand for the considered factors of production using Equations (6), (7) and (8), and the parameter estimates of the translog cost function. 128
Empirical results In keeping with the objective of investigating the interaction of a disaggregate energy input under a translog cost function specification, our first concern focused on testing the hypotheses of both strong and approximate (weak) separability for the two energy inputs; a summary of findings regarding these issues can be found in Table 1. The hypothesis of strong separability could not be rejected for either electric or non-electric energy, thus implying that the conditions for the consistent aggregation of these two inputs could not be rejected. Similarly, and for all cases evaluated, the hypothesis of approximate (or weak) separability could not be rejected. From these findings associated with testing of strong and approximate (weak) separability, it Energy Economics 1995 Volume 17 Number 2
Assessing a disaggregated energy input: J J Hisnanick and B L Kyer Table 1
Summary of results in testing for the separability of electric energy and non-electric energy
Hypothesis
S* n ~
Number of parameters estimated
Unrestricted model Strong separability Electric energy Non-electric energy Weak/approximate separability Capital and electric energy Labor and electric energy Capital and non-electric energy Labor and non-electric energy
117.09
21
.
124.12 124.74
16 16
6.43 7.05
5 5
120.86
19
3.17
3
7.18
A
119.87
19
2.18
3
7.18
A
118.94
19
1.25
3
7.18
A
119.07
19
1.38
3
7.18
A
T °b
Degrees of freedom .
.
Critical chisquared c
Rule d
11.1 11.1
A A
.
"S*n equals the (number of observations in the sample) x (the value of the objective function that results from the iterative minimization grocedure for the model associated with the alternative hypothesis). T o is distributed asymptotically as a chi-squared distribution with (r - s) degrees of freedom, (ie X Z ( r - s)). Therefore, if T O > X 2 ( r - s) at some prescribed level of significance, then the null hypothesis, H0, is rejected. Conversely, if T O < X 2 ( r - s), then H 0 cannot be rejected. CThe critical chi-squared value used is that associated with a 5% level of significance at the respective degrees of freedom. dThe decision rule as related to the null hypothesis; A implies accept, R implies reject.
appears that the translog specification was consistent with the data and, with a high degree of certainty, the existence of an aggregate two-factor energy input for the study of the production process of the US manufacturing sector could be assumed. Notably, these findings support the conclusions reached in an earlier cited study (Moghimzadeh and Kymn [11] ). To provide an insight into the interaction of a disaggregated energy component within the structure of production for the US manufacturing sector, both the Allen elasticities of substitution (AES) and the price elasticities of demand were calculated from the parameters resulting from our translog cost function estimation (see Table 2). Tables 3-5 present these estimates for all factor inputs used in the estimation of our cost function specification (2), and served as the focus in the evaluation of those elasticity estimates associated with the two energy inputs, electric ( E L ) and non-electric ( N E L ) energy. From the AES estimates presented in Table 3, the sign test indicates that capital and electric energy, a s well as capital and non-electric energy, are substitutes in the production process. These conclusions are supported by the confidence intervals constructed around the respective AES estimates, because in neither case is there a sign change over the interval range. Similarly, both the sign test and the confidence intervals for the AES of materials and electric energy and materials and non-electric energy implies that these inputs are substitutes. Energy Economics 1995 Volume 17 Number 2
With respect to the AES estimates for labor and electric energy and labor and non-electric energy, the sign test indicates that these factors are compleTable 2 Parameter estimates and approximate standard errors from the translog cost function specification under the assumption of symmetry and homogeneity
Parameter
Estimated value
Approximate standard error
A0
45.91 0.46 0.20 0.33 - O.OO3 0.01 0.13 0.02 0.13 0.004 0.003 - 0.01 -0.12 - 0.003 - 0.0001 - 0.12 - 0.001 - 0.003 0.0003 0.0006 - 0.0005 - 13.69 2.38 - 0.025 - 0.028 0.0013 - 0.0015
7.55 0.06 0.02 0.02 0.001 0.003 0.01 0.007 0.002 0.0001 0.0002 0.004 0.004 0.0003 0,0006 0.004 0,0004 0,0007 0,0002 0.0003 0.0001 2.43 0.39 0.003 0.003 0.0002 0.0005
AK AL AM AEL A NEI~ A~ ALL mum AELeL A~'ELNeL A~L AK~t AKEL
AKNEL
ALM ALEL ALNEL AM~L AMN~L AELNEL AQ
AQK AeL AQM AoEL AQNH~
129
Assessing a disaggregatedenergy input: J J Hisnanick and B L Kyer Table 3 Estimates of the Allen elasticities of substitution (AES) at the means for the cost shares and the 95% confidence intervals around the estimates
AES
°'L L
6ELEL ~NELUEL
8KL tr/¢ M
O'KEL ~rNEL trLm
O'LEL O'LNEL O'MEL O'MNEL O'ELNEL
Estimated value - 0.065 - 8.438 -0.594 -- 4 0 . 5 9 9 -- 8 3 . 8 7 6 0.582 0.140 0.311 0.954 -- 0.488 - - 5.033 - 16.814 1.342 1.811 -- 28.994
95% confidence interval
Table 4 T h e estimated own-price elasticities (OPE) of demand at the means of the cost s h a r e s OPE
Estimated value
Erx ELL
--0.051 - 0.305
EMM EELEL ENELNEL
---[0.281, 0.883] [0.084, 0.195] [0.167, 0.455] [0.843, 1.064] [ -- 1.373, 0.397] [ - 9.426, - 0.641] [ - 27.354, - 6.275] [0.804, 1.880] [0.026, 2.696] [ - 42.660, - 15.330]
ments in production. These conclusions are further supported, once again, by the constructed confidence intervals around the AES estimates, which for both cases span only negative values. Similarly, regarding the nature of the interaction between the two factor inputs electric energy and non-electric energy, both the sign test and the constructed confidence intervals suggest that these inputs are complements in the production process. In Tables 4 and 5 the estimates for the price elasticities of demand for the five factors of production are presented. As expected, the signs of the own elasticities are negative, which corresponds to the conventional downward sloping demand curve. Both the sign test applied to the price elasticities and the confidence intervals constructed around these values lead to the conclusion that capital and electric energy and capital and non-electric energy are substitutes, further supporting the finding found using the estimated AES from Table 3. However, the calculated cross-price elasticities for electric energy and capital and non-electric energy and capital do not
-- 0.105 -0.185 -- 0.322
entirely support this finding since the confidence intervals constructed around these values contain both positive and negative values. The same situation holds regarding the cross-price elasticities for electric energy and materials and non-electric energy and materials. Similarly, looking at the estimates of the crossprice elasticities and the respective confidence intervals around these values once again suggested that labor and electric energy and labor and non-electric energy are complements. However, the estimated cross-price elasticities for electric energy and labor and non-electric energy and labor do not support this conclusion because the confidence intervals contain both positive and negative values. Concerning this inconsistency observed in the cross-price elasticities, (ie EELK, E E L L , ENELK, ENeLL, EELM, ENeLM), with regard to the range of confidence interval estimates, there is a trade off involved. This trade off centers around models which provide a high information content versus those which result in tighter confidence interval estimates resulting from more aggregated data. While the translog specification has its greatest value in highly disaggregated models with a large number of factor inputs, this functional form often results in small factor shares for each input. The elasticity estimates based on the smaller factor share will then generally display wider confidence intervals. This becomes most apparent in estimates for the cross-price elasticity estimates, which based upon the factor inputs
Table 5 The estimated cross-price elasticities (CPE) of demand at the means of the cost shares and 95% confidence intervals around the estimates
CPE
Estimated value
95% CI
CPE
EKL Eru EKe L EKNeL ELM ELEL ELNEL EMeL EM~¢gL EEL NEL
0.454 0.109 0.242 0.743 --0.018 -- 0.182 -- 0.607 0.318 0.247 -- 0.132
[0.426, 0.482] [0.096, 0.122] [0.236, 0.248] [0.731, 0.756] [--0.174, 0.1391 [ -- 0.242, -- 0.122] [-- 0.663, -- 0.552] [0.296, 0.340] [0.229, 0.265] [ -- 0.183, -- 0.081]
ELK E~r EELr ENELK EUL EeL L ENELL EELM E~EL~t
130
EreEL EL
Estimated value 0.021
0.025 0.001
0.004 --0.086 -- 0.023 -- 0.065 0.007 -- 0.023 -- 0.111
95% CI [ - 0 . 2 1 7 , 0.259] [ - 0.031, 0.081] [ - 0.012, 0.0122] [ - 0.084, 0.091] [-0.117, -0.054] [ - 0 . 1 8 1 , 0.135] [ - 0.442, 0.312] [ - 0 . 1 4 5 , 0.159] [-0.146,0.157] [-0.172, -0.051]
Energy Economics 1995 Volume 17 Number 2
Assessing a disaggregated energy input: J J Hisnanick and B L Kyer tend to have the smaller factor shares. However, this computational inconsistency should not overshadow the insights gained from the respective sign of the AES, in conjunction with the range of the confidence intervals.
Summary and conclusions A primary objective of this paper was to address the uncertainty surrounding the relationships in production between capital and energy and labor and energy which has been presented in previous studies in the literature. This uncertainty exists because earlier investigations used an aggregate energy input and focused their attention exclusively on the estimated signs of either the AES or the price elasticities of demand. We have investigated this controversy with a twostep approach. First, by disaggregating the energy input into an electric energy component and a nonelectric energy component (Moghimzadeh and Kymn [11] ), and estimating a translog cost function specification. Then, we calculated both the Allen elasticities of substitution and the price elasticities of demand, and constructed 95% confidence intervals for these values (Anderson and Thursby [1] ). By performing separability tests derived from a five factor translog cost function, the conclusion was reached that the disaggregation of the energy input into the two components of electric and non-electric energy was justified. Given this finding, it was further concluded that capital and electric energy and capital and non-electric energy are substitutes in the production process of the US manufacturing sector. We also found that labor and electric energy and labor and non-electric energy are complements in production. While our findings with respect to the relationships between capital and non-electric energy and
Table 6
labor and non-electric energy parallel those of an earlier cited study (Moghimzadeh and Kymn [11]), these two studies reach different conclusions regarding the relationship between capital and electric energy and labor and electric energy. Moghimzadeh and Kymn find capital and electric energy to be complements, while conversely, we have concluded that these two inputs are substitutes. Similarly, we found that labor and electric energy are complements whereas the prior study (Moghimzadeh and Kymn [11]) concluded that these two inputs were substitutes. These differences could have resulted from an expanded and enhanced database, as well as differences in model specification and estimation. The findings presented in this paper lead to the conclusion (by deduction) that capital and energy are substitutes in US manufacturing while labor and energy are complements. Table 6 summarizes our findings and those of previous studies which have investigated the relationships between capital, labor, and energy. This conclusion-by-deduction that capital and energy are substitutes supports the results from at least three prior cited studies (Hisnanick and Kymn [7]; Pindyck [14]; Griffen and Gregory [5] ). However, the conclusion that labor and energy are complements is contrary to all other studies that examined the interaction of these two inputs, with one exception [Hisnanick and Kymn [7] ). The strength of our conclusion rest, upon the construction and analysis of confidence intervals for the calculated Allen and price elasticities. Earlier works did not contain the additional information provided by these confidence intervals. However, what has been presented reflects but only one way by which to arrive at resolving the debate centering around the relationship of energy within the production process. Pindyck and Rotemberg [15] used a non-linear model of dynamic factor demand consistent with the assumption of rational expectations.
Summary of results regarding the relationship of capital, labor and energy in the production process of the US manufacturing
sector a Study
K&E
L &E
Hudson and Jorgenson [8] Berndt and Wood [2] Griffen and Gregory [5] Pindyck [14] Norsworthy and Malmquist [13] Moghimzadeh and Kymn [11] Hisnanick and Kymn [7] Present study
C C S S C
S S S S S
S S
C C
K & EL
K & NEL
L & EL
L & NEL
C
S
S
C
S
S
C
C
aK refers to the capital input; L refers to the labor input; E refers to the energy input; E L refers to the electric energy input; N E L refers to the non-electric energy input; C implies that the two inputs were found to be complements in the production process; S implies that the two inputs were found to be substitutes in the production process.
Energy Economics 1995 Volume 17 Number 2
131
Assessing a disaggregated energy input: J J Hisnanick and B L Kyer
Their suggested approach would be the most logical point for additional study to (possibly) clear up the debate surrounding the relationship of energy input in the production process.
8 9
References 1 Anderson, R G and Thursby, J G 'Confidence intervals for elasticity estimators in translog models' The Review of Economics and Statistics 1987 67 647-656 2 Berndt, E R and Wood, D O 'Technology, prices and the derived demand for energy' The Review of Economics and Statistics 1975 57 259-268 3 Denny, M and Fuss, M 'The use of approximate analysis to test for separability and the existence of consistent aggregates' American Economic Review 1977 67 404-418 4 Gallant, A R and Jorgenson, D W 'Statistical inference for a system of simultaneous, non-linear, implicit equations in the context of instrumental variable estimation' Journal of Econometrics 1979 11 275 -302 5 Griffen, J M and Gregory, P R 'An intercountry translog model of energy substitution response' American Economic Review 1976 66 845-857 6 Gollop, F M and Jorgenson, D W 'US productivity growth by industry, 1947-1973' in Kendricks J W and Vaccara B N (eds) New Developments in Productivity Measurement and Analysis, National Bureau of Economic Research, Chicago, IL (1980) 7 Hisnanick, J J and Kymn, K O 'The evaluation of the US manufacturing sector using multifactor inputs of capital, labor, energy and real cash balances' Interna-
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14 15 16 17 18
tional Review of Economics and Business 1990 37 149-162 Hudson, E A and Jorgenson, D W 'US energy policy and economic growth 1975-2000' Bell Journal of Economics and Management Science 1974 5 461-514 Intriligator, M D Econometric Models, Techniques and Applications Prentice-Hall, Englewood Cliffs, NJ (1978) Jorgenson, D W 'The role of energy in productivity growth' The Energy Journal, 1984 5 (3) 11-26 Moghimzadeh, M and Kymn, K O 'Cost shares, own and cross-price elasticities in US manufacturing with disaggregated energy inputs' The Energy Journal 1986 7 65-80 Nguyen, S V and Andrews, S H On Measuring Energy Input, Quality and Elasticities Discussion Paper in Economics, Center for Economic Studies, US Bureau of the Census (1986) Norsworthy, J R and Malmquist, D H 'Input measurement and productivity growth in Japanese and US manufacturing' American Economic Review 1983 73 947-967 Pindyck, R S 'Interfuel substitution and industrial demand for energy: an international comparison' Review of Economics and Statistics 1979 61 169-179 Pindyck, R S and Rotemberg, J J 'Dynamic factor demands and the effects of energy price shocks' American Economic Review 1983 75 1066-1079 SAS/ETS User's Guide Version 6, First Edition, SAS Institute Inc, Cary, NC (1988) Shepard, R W Cost and Production Functions Princeton University Press, Princeton, NJ (1953) US Department of Commerce, Office of Business Analysis National Energy Accounts April (1989)
Energy Economics 1995 Volume 17 Number 2
i'~UTTE RWORTH E I N E M A N N
Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0140-9883/95 $10.00 + 0.00
0140-9883(95)00008-9
Assessing a disaggregated energy input Using confidence intervals around translog elasticity estimates John J Hisnanick and Ben L Kyer
The role of energy in the production of manufacturing output has been debated extensively in the literature, particularly its relationship with capital and labor. In an attempt to provide some clarification in this debate, a two-step methodology was used. First, under the assumption of a five-factor production function specification, we distinguished between electric and non-electric energy and assessed each component's relationship with capital and labor. Second, we calculated both the Allen and price elasticities and constructed 95% confidence intervals around these values. Our approach led to the following conclusions: that the disaggregation of the energy input into electric and non-electric energy is justified; that capital and electric energy and capital and non-electric energy are substitutes, while labor and electric energy and labor and non-electric energy are complements in production; and that capital and energy are substitutes, while labor and energy are complements. Keywords: Energy; Elasticity estimates; AES
Since the mid-1970s, numerous studies have appeared in the economic literature focusing on the role of energy in the production process (Berndt and Wood [2]; Hisnanick and Kymn [7]; Hudson and Jorgenson [8]; Moghimzadeh and Kymn [11]; Nguyen and Andrews [12]; Norsworthy and Malmquist [13]; Pindyck [14]). While these studies have confirmed that energy belongs as an argument in a production or cost function, some disagreement remains regard-
ing the particular relationship between energy and the other factors of production, primarily capital and labor. For example, while the majority of the empirical evidence suggests that labor and energy are substitutes in production, questions have been raised as to whether these two inputs may be complements (Hisnanick and Kymn [7] ). The evidence on the relationship in production between energy and capital is more mixed. The earliest of the above cited studies (Berndt and Wood [2]; Hudson and Jorgenson [8]), concluded that energy and capital are complements. This conclusion was based upon the estimation of a translog cost function using time series data for the US manufacturing sector. Similarly, the complementarity between capital and energy was later supported by the work of Denny and Fuss [3] using data from Canada and by Norsworthy and Malmquist [13], who analyzed the manufacturing sectors of the USA and
John J Hisnanick is with the US Department of Veterans Affairs, NCVAS (008C12), 810 Vermont Ave NW, Washington, DC 20420, USA; Ben L Kyer is with Francis Marion University, Florence, SC 29501, USA. The views expressed in this paper are the responsibility of the authors and shouldnot be taken as the officialposition of the US Department of Veterans Affairs. Final manuscript received 6 December 1994 125
Assessing a disaggregated energy input: J J Hisnanick and B L Kyer Japan. However, Griffen and Gregory [5], Pindyck [14] and Hisnanick and Kymn [7] have concluded that energy and capital are substitutes in the production process. The findings of Griffen and Gregory [5] and Pindyck [14] were based upon the estimation of a translog cost function using pooled cross-sectional time series data, which these authors argued were more appropriate data for estimating long-run elasticities. In addition, Griffen and Gregory [5] proposed that while energy and capital naight indeed be considered complements in the short run, these inputs should be expected to be defined as substitutes in the long run because 'new equipment could be designed to achieve higher thermal efficiencies but at greater capital costs.' This long-run argument does not, however, apply to the work by Hisnanick and Kymn [7], who also found energy and capital to be substitutes by using a short-run time series for the US manufacturing sector. In their 1986 paper, Moghimzadeh and Kymn [11] suggested an alternative explanation for the conflicting evidence between energy and capital. They argued that a disaggregation of the energy input into its two main types or forms, electric and non-electric energy, might account for some of the different empirical results. Using a translog cost function specification and annual data from 1954 to 1977 for the US manufacturing sector, these authors found that the disaggregation of the energy input was statistically justified. By estimating cross-price elasticities for the disaggregated energy inputs, they concluded that capital and electric energy were complements, as were labor and non-electric energy. Alternatively, they concluded that capital and nonelectric energy as well as labor and electric energy to be substitutes in production. A common characteristic of all the studies cited above is their reliance on the sign of the Allen partial elasticity of substitution or the cross-price elasticity of demand to define any two inputs as substitutes or complements in production. Anderson and Thursby [1] have demonstrated that confidence intervals for the traditional point elasticity estimates provide more information on the structure of production or factor demand. More specifically, these authors consider the point elasticity estimates to be non-informative when the confidence intervals about these point elasticities contain both positive and negative values. Anderson and Thursby [1] developed confidence intervals based on the ratio of normals and the normal distribution for the Allen and demand elasticity estimators in the translog production model. Applications of these confidence intervals to the 126
elasticity estimates of Griffen and Gregory [5] exhibited both positive and negative values. This led Anderson and Thursby [1] to conclude that the Griffen and Gregory [5] definition of capital and energy as substitutes was based on weak evidence. Similarly, the construction of confidence intervals did not support the conclusion by Berndt and Wood [2] that capital and energy were complements. These findings suggest that uncertainty remains with respect to the production relationship between capital and energy. The primary purpose of this paper, therefore, is to analyze the production process in the US manufacturing sector by combining the suggested approaches of Moghimzadeh and Kymn [11] and Anderson and Thursby [1] in order to more completely examine the existing uncertainty regarding the relationships between energy and capital and labor. In particular, we estimate a translog cost function which includes a disaggregated energy input and construct confidence intervals for the calculated Allen and demand elasticities. The data set used contained an end-point in 1985 and appropriate tests of separability were also conducted and evaluated. The paper proceeds as follows. The following section specifies the model and briefly discusses the data employed for its estimation. The next section develops the hypotheses to be examined and the appropriate statistical tests. Then we present our empirical results and lastly, a summary and conclusion.
The model specification and data In modeling the productive behavior of the US manufacturing sector, it was assumed that output could be characterized by an aggregate production function of the following general form
Q = f ( K , L, M, EL, NEL)
(1)
where Q = manufacturing output, K = capital, L = labor, M = materials, EL = electric energy, and NEL = non-electric energy. In addition, we assume that (1) is twice differentiable, quasiconcave, monotonic and experiences linear homogeneity. Associated with this production function there exists a dual cost function which reflects the production technology and the general form of the cost function is as follows:
C = C(Q, Px, PL, PM, PeL, PNeL)
(2)
where C is total cost and PK, PL, I'M, PEL and PNeL are the input prices of the respective factor inputs. By representing (2) through a Taylor series expan-
EnergyEconomics1995 Volume17 Number2
Assessing a disaggregated energy input: J J Hisnanick and B L Kyer sion and dropping terms of order two and higher, we arrive at the flexible translog specification. Therefore, the translog approximation to the (natural) logarithm of the total cost function results in (2) being written as: lnC = A o + AQ lnQ + 1/2AQQ(InQ) 2
+ ~,iZi lnPi +l//2Ei~jAij
lnP/ l n ~
+ EiAoilnQlnPi for i, j = K, L, M, EL, NEL and where symmetry, theorem. Keeping in tions associated with parameter restrictions
(3)
A~ = Aj~, is due to Young's mind the regularity assump(1), results in the following on (3):
~,iAi = O,EiAij = EjAij
=
0
duces to the seemingly unrelated estimation technique (Intriligator [9]). Finally, all reported coefficient values where estimated with software which does not employ a maximum likelihood estimation procedure, but rather an objective function minimization procedure (SAS/ETS [16]). The objective function minimization procedure yielded a test statistic, T ° , which is an analog of the log-likelihood ratio test and is distributed asymptotically as a chi-square distribution with (r - s) degrees of freedom (Gallant and Jorgenson [4]). This test statistic was used in evaluating the issue of separability between electric and non-electric energy and factor inputs of capital and labor. Under the translog cost specification the Allen partical elasticities of substitution can be defined as follows (Berndt and Wood [2] ):
(for all j), O'ii = ( A i i + Si;z - S i ) / / S i 2
E,jAij = 0
for i = K, L, M, EL, NEL
and
(6)
crzj = (Aij + S~Sj)/S~Sj
EiAe~ = 0 Under duality theory, every cost function implies a set of derived demand equations. These demand equations will be linear in the parameters and at the same time represent very general production structures. Therefore, the modified first order conditions with respect to the production at minimum cost, assuming perfect competition in the factor market, results in the following equality as a result of Shepard's [17] lemma: S~ = (8 In C,/8 In P~) = ( S C / S P ~ ) ( P J C ) = piXi//~_,i p i X i
(4)
This implies directly that the factor share equations (Si), resulting from (3) can be written as: S~ = A~ + Ae~ lnQ + ~,jA~j lnPi for i = K, L, M, EL, NEL
(5)
Given the complete system of equations (3) and (5), under the assumption of homogeneity and symmetry across the model's parameters, the estimation of the full model would result in the disturbance covariance matrix to be singular. To avoid this problem one of the derived factor share equations can be dropped from the system without a loss of generality. Therefore, the stochastic model for estimation will consist of the system of equations composed of (3) and ( n - 1) of the share equations from (5). To estimate the parameters of the system, an iterative non-linear three stage least square procedure was used, which under this specification reEnergy Economics 1995 Volume 17 Number 2
for i, j = K, L, M, EL, NEL, i = j
(7)
with the own- and cross-price elasticities of demand being defined as
Eij = Sio-ij
(8)
Because cost shares vary over time, in general Eij Eji, even though ~rij = o3i, by definition. For this paper, the prices and quantities of the inputs capital, labor, materials, electric energy and non-electric energy for the US manufacturing sector were measured by the respective Divisia indices. The data cover the years 1958-85, and were collected from two sources. The capital, labor and materials Divisia indices were obtained from the US Department of Labor, Bureau of Labor Statistics, Office of Productivity and Technology. The energy data were taken from the US Department of Commerce, National Energy Account (NEA) [18]. This NEA file allowed us to disaggregate the energy component for the US manufacturing sector into the two components of electric energy and a non-electric energy. The price and quantity indices for these two types of energy were created using the Divisia aggregation process. A more complete description of the data used in the construction of the energy indices is available upon request from the authors. Despite the fact that recent years of data are not covered, use of this data was desirable for two reasons. First, the data series are well constructed and have been checked and used extensively by other researchers. Second we chose to use aggregate 127
Assessing a disaggregated energy input." J J Hisnanick and B L Kyer
manufacturing data in order to maintain comparability with prior published studies that focused on the relationship of energy in the manufacturing production process.
Hypotheses development and associated tests To address our concerns regarding the relationship of capital and labor relative to the disaggregated energy input, we investigated both the strong (or linear) and approximate (or weak) separability of these factor inputs. In looking at linear separability, interest centered around whether the factor inputs within the stated functional form are linearly related. In testing this type of hypothesis, the parameter restrictions imposed on the estimated model are that the cross-product terms with respect to the factor input in question are assumed equal to zero. In looking at the issue of weak separability of the input factors, a necessary and sufficient condition for two inputs to be weakly separable is that the marginal rates of substitution between the inputs be independent of the quantities of the other factor inputs. For a five factor production function, the testing for the weak separability of X 1 and X 2 with respect to the inputs 3(3, X 4 and X 5 can be expressed by the following constraints on the Allen partial elasticities of substitution: S13 = S23 = 1 ; S14 = $24 -h- 1 ; S15 = $25 =
1
This is equivalent to the following non-linear restrictions being placed upon the parameter estimates:
Previous authors have concluded that pairs of inputs are either substitutes or complements in production by evaluating exclusively the signs of the Allen elasticities of substitution and the price elasticities of demand. However, Anderson and Thursby [1] demonstrated that these elasticity estimators derived from the translog specification are non-linear transformations of the parameter estimates and factor cost shares. The general problems involved in non-linear estimation may underlie the inclusive nature often surrounding the issue of the relationship between inputs in production. Therefore, to more appropriately address the issue of substitution versus complementarity, confidence intervals were constructed for the calculated Allen elasticities of substitution and price elasticities of demand. These confidence intervals are based upon the means of the observed factor shares and, in all cases, refer to 95% confidence intervals about the point elasticity estimates. The use of confidence intervals highlights the shortcomings of the more commonly used sign test. That is, confidence intervals may span both positive and negative values which would simultaneously support the mutually exclusive conclusions that the ith and jth inputs are substitutes and complements. Adding to the confusion is the possibility that confidence intervals for the price elasticities may span positive and negative values while the confidence intervals for the Allen elasticities may not and vice versa. Thus, tests for substitution and complementarity based upon confidence intervals may not support the same conclusions as tests based solely upon the signs of point elasticity estimates.
AIB23 -A2B13 = 0; A1B24 -A2B14 = 0 AIB25 -A2B15 = 0; BuB22 - (B12)2 = 0 For the above parameter restrictions, Denny and Fuss [3] proposed a test at the point of approximation by dropping the last constraint. This approach was adopted for the testing of the hypothesis of weak separability of the input factors capital and labor relative to the disaggregated energy input. Lastly, one of our major concerns focused on the mixed conclusions from previous studies regarding the relationships between energy inputs and the other factors of production, especially for the US manufacturing sector. To measure factor substitution possibilities, we calculate both the Allen partial elasticities of substitution and the price elasticities of demand for the considered factors of production using Equations (6), (7) and (8), and the parameter estimates of the translog cost function. 128
Empirical results In keeping with the objective of investigating the interaction of a disaggregate energy input under a translog cost function specification, our first concern focused on testing the hypotheses of both strong and approximate (weak) separability for the two energy inputs; a summary of findings regarding these issues can be found in Table 1. The hypothesis of strong separability could not be rejected for either electric or non-electric energy, thus implying that the conditions for the consistent aggregation of these two inputs could not be rejected. Similarly, and for all cases evaluated, the hypothesis of approximate (or weak) separability could not be rejected. From these findings associated with testing of strong and approximate (weak) separability, it Energy Economics 1995 Volume 17 Number 2
Assessing a disaggregated energy input: J J Hisnanick and B L Kyer Table 1
Summary of results in testing for the separability of electric energy and non-electric energy
Hypothesis
S* n ~
Number of parameters estimated
Unrestricted model Strong separability Electric energy Non-electric energy Weak/approximate separability Capital and electric energy Labor and electric energy Capital and non-electric energy Labor and non-electric energy
117.09
21
.
124.12 124.74
16 16
6.43 7.05
5 5
120.86
19
3.17
3
7.18
A
119.87
19
2.18
3
7.18
A
118.94
19
1.25
3
7.18
A
119.07
19
1.38
3
7.18
A
T °b
Degrees of freedom .
.
Critical chisquared c
Rule d
11.1 11.1
A A
.
"S*n equals the (number of observations in the sample) x (the value of the objective function that results from the iterative minimization grocedure for the model associated with the alternative hypothesis). T o is distributed asymptotically as a chi-squared distribution with (r - s) degrees of freedom, (ie X Z ( r - s)). Therefore, if T O > X 2 ( r - s) at some prescribed level of significance, then the null hypothesis, H0, is rejected. Conversely, if T O < X 2 ( r - s), then H 0 cannot be rejected. CThe critical chi-squared value used is that associated with a 5% level of significance at the respective degrees of freedom. dThe decision rule as related to the null hypothesis; A implies accept, R implies reject.
appears that the translog specification was consistent with the data and, with a high degree of certainty, the existence of an aggregate two-factor energy input for the study of the production process of the US manufacturing sector could be assumed. Notably, these findings support the conclusions reached in an earlier cited study (Moghimzadeh and Kymn [11] ). To provide an insight into the interaction of a disaggregated energy component within the structure of production for the US manufacturing sector, both the Allen elasticities of substitution (AES) and the price elasticities of demand were calculated from the parameters resulting from our translog cost function estimation (see Table 2). Tables 3-5 present these estimates for all factor inputs used in the estimation of our cost function specification (2), and served as the focus in the evaluation of those elasticity estimates associated with the two energy inputs, electric ( E L ) and non-electric ( N E L ) energy. From the AES estimates presented in Table 3, the sign test indicates that capital and electric energy, a s well as capital and non-electric energy, are substitutes in the production process. These conclusions are supported by the confidence intervals constructed around the respective AES estimates, because in neither case is there a sign change over the interval range. Similarly, both the sign test and the confidence intervals for the AES of materials and electric energy and materials and non-electric energy implies that these inputs are substitutes. Energy Economics 1995 Volume 17 Number 2
With respect to the AES estimates for labor and electric energy and labor and non-electric energy, the sign test indicates that these factors are compleTable 2 Parameter estimates and approximate standard errors from the translog cost function specification under the assumption of symmetry and homogeneity
Parameter
Estimated value
Approximate standard error
A0
45.91 0.46 0.20 0.33 - O.OO3 0.01 0.13 0.02 0.13 0.004 0.003 - 0.01 -0.12 - 0.003 - 0.0001 - 0.12 - 0.001 - 0.003 0.0003 0.0006 - 0.0005 - 13.69 2.38 - 0.025 - 0.028 0.0013 - 0.0015
7.55 0.06 0.02 0.02 0.001 0.003 0.01 0.007 0.002 0.0001 0.0002 0.004 0.004 0.0003 0,0006 0.004 0,0004 0,0007 0,0002 0.0003 0.0001 2.43 0.39 0.003 0.003 0.0002 0.0005
AK AL AM AEL A NEI~ A~ ALL mum AELeL A~'ELNeL A~L AK~t AKEL
AKNEL
ALM ALEL ALNEL AM~L AMN~L AELNEL AQ
AQK AeL AQM AoEL AQNH~
129
Assessing a disaggregatedenergy input: J J Hisnanick and B L Kyer Table 3 Estimates of the Allen elasticities of substitution (AES) at the means for the cost shares and the 95% confidence intervals around the estimates
AES
°'L L
6ELEL ~NELUEL
8KL tr/¢ M
O'KEL ~rNEL trLm
O'LEL O'LNEL O'MEL O'MNEL O'ELNEL
Estimated value - 0.065 - 8.438 -0.594 -- 4 0 . 5 9 9 -- 8 3 . 8 7 6 0.582 0.140 0.311 0.954 -- 0.488 - - 5.033 - 16.814 1.342 1.811 -- 28.994
95% confidence interval
Table 4 T h e estimated own-price elasticities (OPE) of demand at the means of the cost s h a r e s OPE
Estimated value
Erx ELL
--0.051 - 0.305
EMM EELEL ENELNEL
---[0.281, 0.883] [0.084, 0.195] [0.167, 0.455] [0.843, 1.064] [ -- 1.373, 0.397] [ - 9.426, - 0.641] [ - 27.354, - 6.275] [0.804, 1.880] [0.026, 2.696] [ - 42.660, - 15.330]
ments in production. These conclusions are further supported, once again, by the constructed confidence intervals around the AES estimates, which for both cases span only negative values. Similarly, regarding the nature of the interaction between the two factor inputs electric energy and non-electric energy, both the sign test and the constructed confidence intervals suggest that these inputs are complements in the production process. In Tables 4 and 5 the estimates for the price elasticities of demand for the five factors of production are presented. As expected, the signs of the own elasticities are negative, which corresponds to the conventional downward sloping demand curve. Both the sign test applied to the price elasticities and the confidence intervals constructed around these values lead to the conclusion that capital and electric energy and capital and non-electric energy are substitutes, further supporting the finding found using the estimated AES from Table 3. However, the calculated cross-price elasticities for electric energy and capital and non-electric energy and capital do not
-- 0.105 -0.185 -- 0.322
entirely support this finding since the confidence intervals constructed around these values contain both positive and negative values. The same situation holds regarding the cross-price elasticities for electric energy and materials and non-electric energy and materials. Similarly, looking at the estimates of the crossprice elasticities and the respective confidence intervals around these values once again suggested that labor and electric energy and labor and non-electric energy are complements. However, the estimated cross-price elasticities for electric energy and labor and non-electric energy and labor do not support this conclusion because the confidence intervals contain both positive and negative values. Concerning this inconsistency observed in the cross-price elasticities, (ie EELK, E E L L , ENELK, ENeLL, EELM, ENeLM), with regard to the range of confidence interval estimates, there is a trade off involved. This trade off centers around models which provide a high information content versus those which result in tighter confidence interval estimates resulting from more aggregated data. While the translog specification has its greatest value in highly disaggregated models with a large number of factor inputs, this functional form often results in small factor shares for each input. The elasticity estimates based on the smaller factor share will then generally display wider confidence intervals. This becomes most apparent in estimates for the cross-price elasticity estimates, which based upon the factor inputs
Table 5 The estimated cross-price elasticities (CPE) of demand at the means of the cost shares and 95% confidence intervals around the estimates
CPE
Estimated value
95% CI
CPE
EKL Eru EKe L EKNeL ELM ELEL ELNEL EMeL EM~¢gL EEL NEL
0.454 0.109 0.242 0.743 --0.018 -- 0.182 -- 0.607 0.318 0.247 -- 0.132
[0.426, 0.482] [0.096, 0.122] [0.236, 0.248] [0.731, 0.756] [--0.174, 0.1391 [ -- 0.242, -- 0.122] [-- 0.663, -- 0.552] [0.296, 0.340] [0.229, 0.265] [ -- 0.183, -- 0.081]
ELK E~r EELr ENELK EUL EeL L ENELL EELM E~EL~t
130
EreEL EL
Estimated value 0.021
0.025 0.001
0.004 --0.086 -- 0.023 -- 0.065 0.007 -- 0.023 -- 0.111
95% CI [ - 0 . 2 1 7 , 0.259] [ - 0.031, 0.081] [ - 0.012, 0.0122] [ - 0.084, 0.091] [-0.117, -0.054] [ - 0 . 1 8 1 , 0.135] [ - 0.442, 0.312] [ - 0 . 1 4 5 , 0.159] [-0.146,0.157] [-0.172, -0.051]
Energy Economics 1995 Volume 17 Number 2
Assessing a disaggregated energy input: J J Hisnanick and B L Kyer tend to have the smaller factor shares. However, this computational inconsistency should not overshadow the insights gained from the respective sign of the AES, in conjunction with the range of the confidence intervals.
Summary and conclusions A primary objective of this paper was to address the uncertainty surrounding the relationships in production between capital and energy and labor and energy which has been presented in previous studies in the literature. This uncertainty exists because earlier investigations used an aggregate energy input and focused their attention exclusively on the estimated signs of either the AES or the price elasticities of demand. We have investigated this controversy with a twostep approach. First, by disaggregating the energy input into an electric energy component and a nonelectric energy component (Moghimzadeh and Kymn [11] ), and estimating a translog cost function specification. Then, we calculated both the Allen elasticities of substitution and the price elasticities of demand, and constructed 95% confidence intervals for these values (Anderson and Thursby [1] ). By performing separability tests derived from a five factor translog cost function, the conclusion was reached that the disaggregation of the energy input into the two components of electric and non-electric energy was justified. Given this finding, it was further concluded that capital and electric energy and capital and non-electric energy are substitutes in the production process of the US manufacturing sector. We also found that labor and electric energy and labor and non-electric energy are complements in production. While our findings with respect to the relationships between capital and non-electric energy and
Table 6
labor and non-electric energy parallel those of an earlier cited study (Moghimzadeh and Kymn [11]), these two studies reach different conclusions regarding the relationship between capital and electric energy and labor and electric energy. Moghimzadeh and Kymn find capital and electric energy to be complements, while conversely, we have concluded that these two inputs are substitutes. Similarly, we found that labor and electric energy are complements whereas the prior study (Moghimzadeh and Kymn [11]) concluded that these two inputs were substitutes. These differences could have resulted from an expanded and enhanced database, as well as differences in model specification and estimation. The findings presented in this paper lead to the conclusion (by deduction) that capital and energy are substitutes in US manufacturing while labor and energy are complements. Table 6 summarizes our findings and those of previous studies which have investigated the relationships between capital, labor, and energy. This conclusion-by-deduction that capital and energy are substitutes supports the results from at least three prior cited studies (Hisnanick and Kymn [7]; Pindyck [14]; Griffen and Gregory [5] ). However, the conclusion that labor and energy are complements is contrary to all other studies that examined the interaction of these two inputs, with one exception [Hisnanick and Kymn [7] ). The strength of our conclusion rest, upon the construction and analysis of confidence intervals for the calculated Allen and price elasticities. Earlier works did not contain the additional information provided by these confidence intervals. However, what has been presented reflects but only one way by which to arrive at resolving the debate centering around the relationship of energy within the production process. Pindyck and Rotemberg [15] used a non-linear model of dynamic factor demand consistent with the assumption of rational expectations.
Summary of results regarding the relationship of capital, labor and energy in the production process of the US manufacturing
sector a Study
K&E
L &E
Hudson and Jorgenson [8] Berndt and Wood [2] Griffen and Gregory [5] Pindyck [14] Norsworthy and Malmquist [13] Moghimzadeh and Kymn [11] Hisnanick and Kymn [7] Present study
C C S S C
S S S S S
S S
C C
K & EL
K & NEL
L & EL
L & NEL
C
S
S
C
S
S
C
C
aK refers to the capital input; L refers to the labor input; E refers to the energy input; E L refers to the electric energy input; N E L refers to the non-electric energy input; C implies that the two inputs were found to be complements in the production process; S implies that the two inputs were found to be substitutes in the production process.
Energy Economics 1995 Volume 17 Number 2
131
Assessing a disaggregated energy input: J J Hisnanick and B L Kyer
Their suggested approach would be the most logical point for additional study to (possibly) clear up the debate surrounding the relationship of energy input in the production process.
8 9
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