Energy Economics 22 2000 569]586
The demand for energy in Greek
manufacturing
Dimitris K. Christopoulos
UDepartment of Economics and Regional De¨elopment, Panteion Uni¨ersity, Syngrou A¨e.
136, 17671 Athens, Greece
Abstract
This paper considers an econometric approach to measuring substitutability of three types of energy, i.e. crude oil, electricity and diesel with capital and labour in the manufacturing sector of Greek industry during the period 1970]1990. A general dynamic framework is developed under the assumption that the structure of the production process is weakly separable in capital, labour and energy aggregates. The translog total cost function is used to represent the production technology. The main advantages of the proposed dynamic structure are that it is both disaggregated in energy components and consistent with the neo-classical theory of production.Q2000 Elsevier Science B.V. All rights reserved.
JEL classifications:C51; D24; Q41
Keywords:Energy; Separability; Dynamic structure
1. Introduction
Greek industry has undergone considerable restructuring during the last two decades, bringing great changes in the inputs used, especially of energy. On the one hand, the cost share of capital dropped in every two-digit industry under
Ž .
consideration Palaskas et al., 1999 . On the other hand, the problem of labour
Ž .
scarcity that emerged in the late 1960s and early 1970s see Lianos, 1975 has been
U
Fax:q30-1-9229-315.
Ž .
E-mail address:Christod@panteion.gr D.K. Christopoulos .
0140-9883r99r$ - see front matterQ2000 Elsevier Science B.V. All rights reserved.
Ž .
Ž .
eliminated see Christopoulos, 1995 . The rate of unemployment in 1972 was 1.8% and the emigration rate was still quite high. At the same time, energy emerged as an important input in the production process of Greek manufacturing. The share of the three main sources of energy, crude oil, diesel and electricity, increased significantly during the last two decades, as a percentage of the total cost in the
Ž .
sector Palaskas et al., 1999 .
Given these changes in the Greek industrial sector in recent years a number of
Ž
authors Samouilidis and Mitropoulos, 1982; Vlachou and Samoulidis, 1986; Do-natos and Mergos, 1989; Kintis and Panas, 1989; Caloghirou et al., 1997; Palaskas
.
et al., 1999 have focused attention on the degree of substitution among energy
Ž .
sources and primary inputs of production capital and labour . The question of the degree of energy substitutability is of great importance in predicting economic disruptions arising from energy shortages and it has important implications for public policy. For example, higher energy prices induce cost-minimising firms to substitute toward capital and labour, and higher electricity prices induce firms to substitute towards some combination of capital, labour and alternative energy types. This will have important industrial effects and it will affect capital utilisation, employment, etc. In addition, energy substitutability can assist in addressing important issues, including the feasibility of various energy demand profiles, the evaluation of alternative environmental policies, and the impact of carbon or energy-use taxes.
All previous empirical studies of energy substitution in Greek manufacturing suggest that energy and labour, and energy and capital are substitutes, with the
Ž .
exception of Kintis and Panas 1989 who found that energy and capital are complements. However, these studies have some shortcomings. All approaches are static and hold only in equilibrium. More specifically, none of the previous studies takes into account the static misspecification errors that arise when an instanta-neous adjustment process is not appropriate. The static versions of the models neglect the dynamics of adjustment, which results in inadequate knowledge of the adjustment path and the long-run structure. Knowledge of the adjustment process is important in addressing policy issues arising from alternative tax structures or exogenous energy price shocks. Therefore, under the static specification the estimators will not provide reliable computed elasticity for policy design and policy making. Thus, by assuming a static production model the applied researcher may be led to misguided conclusions.
Given the drawbacks of the static models in terms of estimation, hypothesis
Ž .
testing and analysis, a different approach is adopted here. Following Fuss 1977
Ž .
To incorporate dynamic adjustments, a general dynamic demand framework is constructed using the translog cost-function. Thus, a dynamic structure of the demand for energy in Greek manufacturing is obtained, which is both disaggre-gated in energy components, consistent with the neo-classical theory of production, and flexible enough to accommodate a rich pattern of dynamic behaviour.
The paper is organised as follows. In Section 2 the theoretical model is pre-sented. The dynamic formulation of the adopted model is contained and analysed in Section 3. In Section 4 the statistical estimation is presented and the empirical results are analysed. Also, in Section 4 we examine whether or not the estimated relationships are structural or spurious. Section 5 concludes the paper.
2. The theoretical model
The specification of the model starts with the assumption that the technology applied in the production process can be described by a twice differentiable production function which relates the flow of output to various inputs of produc-tion. In algebraic terms it can be expressed as
Ž . Ž .
It is also assumed that monotonicity is valid for F Xj,T and that the production
Ž . Ž .
function is strictly convex, see for example, Diewert 1971 and Hall 1973 .
Ž .
Next it is assumed that the production function 1 is weakly separable with
4
respect to partition N1, . . . .Ns. This means that the marginal rate of
substitu-Ž . 4
tion MRS between any two inputs i and j from any subset Nss 1, . . . .m is independent of the quantities of inputs outside Ns, see Berndt and Christensen
Ž1973a . In other words,.
ensures that the aggregates exist and permits us to write the production function
Ž .
Furthermore, we assume that aggregated functions in 3 are homothetic in their components. This assumption provides a necessary and sufficient condition for an
Ž .
underlying two stage optimisation procedure see Denny and Fuss, 1977 : optimise the mix of components within each aggregate and then optimise the level of each aggregate. The existence of homothetic aggregation functions does not imply that
Ž .
the overall production process is homothetic Apostolakis, 1988 .
Ž .
Given the production function 1 and the associated assumptions, the cost
Ž .
function can be derived. According to duality principles, Samuelson 1947 , Uzawa
Ž1964 and Shephard 1970 , there is a cost function equivalent to the production. Ž .
function that can represent the technology of production and vice versa.
To start with, it is assumed that the cost function that corresponds to the production function can be written as
Ž . Ž .
C Pj,Y,T sminP)XsTC 4
where C stands for total cost, Pj is the vector of input prices, and TC is the total
Ž . Ž .
cost. The cost function 2 is considered, similarly to 1 , to be twice differentiable in Pj and T, finite for every Pj, YG0 and T, continuous in Y and Pj, linear homogeneous in Pj and YG0, non-decreasing inY and Pj, and concave in Pj.
Ž .
Also the dual cost function 4 will be weakly separable if the aggregation in
Ž . Ž .
production function 1 exists and the aggregate functions in 3 are homothetic in
Ž .
their components see Berndt and Christensen, 1973b .
Ž .
Finally it is assumed that the specifiable factors of production are capital K ,
Ž . Ž . Ž . Ž . Ž .
labour L , electricity EL , diesel D and crude oil M . So the cost function 4 can be written as follows:
w Ž . x Ž .
Csg PE PM, PEL, PD , PK, PL, Y, T 5
where PK is the price of capital, PL is the price of labour, PM is the price of crude oil, PEL is the price of electricity, PD is the price of diesel and PE is an aggregate price index of energy, i.e. a function that aggregates the energy prices of three components types. As assumed previously, this aggregator function is homothetic in the mix of energy types.1
Ž .
Eq. 5 can be estimated in two stages: First a sub energy homothetic model with constant returns to scale will be considered to construct an instrumental variable for the price of energy. Second an aggregate non-homothetic cost function associ-ated with Hicks non-neutral technological progress. So, the firms first minimise the energy cost and then the total cost of production.
Ž . Ž .
Under the hypothesis of minimisation of total cost TC the cost function 5 may
Ž
take various forms. The translog form is one, it can be expressed as Christensen et
.
al., 1973
1
2
Under conditions of perfect competition the logarithmic differentiation of Eq.
Ž .6 with respect to input prices PK, PL, PE yields expressions for the demanded
Ž .
quantity of the corresponding inputs in terms of cost shares Shephard’s Lemma , i.e.
TC Ž . Ž .
Mi slnTCrlnPis P Xi i rTCsaiq
Ý
yi jln Pjqdi YlnYqmT iT 7j
where Xi is the quantity demanded of the production input i and Mi is the cost share of the input i demanded.
Ž . TC
For the cost function 6 to satisfy the adding-up criterion
Ý
Mi s1,isK,L,Ei
and the properties of the neo-classical production theory, the following linear restrictions must be satisfied,
The restrictions 8 are necessary and sufficient conditions ensuring TC is linearly homogeneous in input prices.
Ž .
However, the price of energy PE is considered also to be an aggregate
2 w Ž .x
function see function 5 . This aggregate function can be represented by a homothetic translog cost function with constant returns to scale
1 Ž .
lnPEsaoq
Ý
bilnPiq2Ý Ý
yi jlnPilnPj 9i i j
The following energy cost share equations are implied by Shephard’s Lemma:
E Ž .
Mi sbiq
Ý
yi jlnPj 10j
where i,jsEL,D,M.
Again the adding-up criterion and the properties of neo-classical production theory require the parameter restrictions
2P
it is not a consistent aggregate price index if it is a simple weighted average of the P,
E i
isEL,D,M unless the energy components are perfectly substitutable or complements in the production
Ž .
Ž .
b s1, y sy , y s0 11
Ý
i i j jiÝ
i ji i
to be satisfied by the aggregate function.
Let us now review the steps involved in estimating the proposed model: first the
Ž . Ž .
sub-energy model 10 is estimated subject to the constraints 11 . The estimated
Ž . Ž .
parameters in 10 are substituted into 9 to obtain an aggregate price index for
Ž . Ž .
energy. Next the factor share Eq. 7 is estimated subject to the restrictions 8 using the estimated energy price index as an instrumental variable.
3. Modelling the dynamic structure of production using the translog cost function
Ž . Ž .
The factor demand system 7 derived from the translog total cost function 6 is static and holds only in equilibrium. This happens because the existence of convex adjustment costs and the imperfections involved in obtaining information imply that there is some delay in adjusting instantaneously actual capital, labour and energy to their desired level following exogenous price and demand shifts.
Analyti-Ž .
cally, the cost share Eq. 7 describes long-run structure. According to Anderson
Ž . TC
and Blundell 1982 changes in the share in total cost Mi of inputiare responses to anticipated and unanticipated changes in capital, energy and labour prices in an
Ž .
attempt to maintain a long-run relationship of the form 6 in the sense that, should capital, energy and labour prices stabilise to some constant value over time,
Ž TC.
then so would the expected share of capital, energy and labour in total cost Mi . Furthermore, in the short-run there is uncertainty about the future course of capital, energy and labour prices and output. Therefore, following an exogenous shock the firms do not adjust instantaneously the three inputs, capital, energy and
Ž .
labour to the desired level Nissim, 1984 . Thus, ignoring the dynamic element would lead to inadequate knowledge of the adjustment process and of the long-run structure.
Ž .3
To model the dynamic form of total cost share Eq. 7 the transformation
Ž . Ž .
proposed by Wickens and Breusch 1988 and Kesavan et al. 1993 is used. This transformation identifies the long-run structure together with the short-run dy-namics in demand for capital, labour and energy which it merges the long-run steady-state theory with short-run time series properties of data and produces elasticities that are robust for policy implication. In addition one more general dynamic framework is obtained which achieves the desirable aspects of flexibility, simplicity and identification of long-run parameters which can be considered as
Ž
long side alternative transformations see Anderson and Blundell, 1982; Nissim,
.
1984; Banerjee et al., 1990 .
A way to incorporate the dynamic structure of production in the total cost share
Ž .
Eq. 7 is to write the system in the following form:
3
The short-run total cost function remains unspecified in our model because the total cost share Eq.
L L L L
TC
Mi s
Ý
Fi kMi,tykqaiqÝ
gi jlnPj,tykqÝ
di jlnYtykqÝ
mT iTtyki,ks1 j,ks0 j,ks0 j,ks0
Ž12.
where in our application only the lag structure, ks1 will be used.
L
Ž .
The equations in the system 12 can be transformed by subtracting
Ý
FkMtks1
Ž . Ž .
from both sides of 12 Wickens and Breusch, 1988; Kesavan et al., 1993 . By algebrical manipulation we obtain
where D refers to annual differences and isK,L,E.
Ž .
In a similar way we transform the share Eq. 10 derived from the aggregator energy function, obtaining
4.1. The estimation of the sub-energy model
Ž .
Empirical implementation requires that the energy share Eq. 14 should be statistically specified. Consequently, an error term is added to each equation because of lags of cost in response to the changes in exogenous variables. Since the
Ž . Ž
shares of the three energy inputs EL,D,M always sum to unity adding-up
E .
criterion
Ý
Mi s1, isEL,D,M the sum of the disturbances across the threei
share energy equations is zero at each observation. This implies a singular disturbance covariance matrix. Therefore, in order to avoid singularity, one share
Ž .
equation must be dropped the equation of crude oil is deleted . Following
Ž .
Anderson and Blundell 1982 for the invariance of results due to arbitrary deletion of one equation the restriction that the adjustment coefficients must be equal across equations together with the one for long-run symmetry is considered
Ž .
for the general dynamic form 14 .
Ž .
Non-linear iterative Zellner estimation see Zellner, 1962, 1963 is used to
Ž .
estimate the parameters of the dynamic model 14 . This procedure, which is
Ž .
Table 1
Tests of dynamic structure for the energy-sub model
2 2 2 2
x Number of x0.95 x0.90 x0.75
restrtion
Partial adjustment 13.890 4 9.488 7.779 5.385
Static 12.428 5 11.070 9.236 6.625
that the estimates will be invariant to which the equation is deleted only under the
Ž
acceptance of null hypothesis of error correlations across equations see Berndt
.
and Savin, 1975; Christopoulos, 1995 .
For the reasons presented above, the IZEF method is adopted for estimating the
Ž .
two dynamic equations in 14 , using annual data from the Greek manufacturing sector for the period 1970]1990.4 Also, its partial adjustment and the static
Ž .
specifications of the general dynamic form 14 are estimated and compared
Ž .5
against the general specification 14 .
Starting with the statistical comparison between the general dynamic, the partial
Ž .
adjustment and the static specification of the dynamic share energy system 14 , the likelihood ratio test of its dynamic structure is computed. The results are presented in Table 1.
Thex2 results in the second column of Table 1 reveal that the general dynamic
Ž .
specification of the model 14 is superior to its corresponding partial adjustment. Also, the general dynamic specification nests that of static at the 5% level of significance. Therefore, the dynamic specification is adopted to estimate and analyse the own and cross price elasticities of demand for energy components. Parameter estimates for this model are presented in Table 2.
Next the own and cross price elasticities are estimated to measure the price
Ž .
responsiveness. It can be shown, that for the translog energy cost function 9
Ž .
under the dynamic specification of share Eq. 14 , these estimates can be calcu-lated as follow:
For the nature and the structure of the variables see Appendix A.
5
Table 2
Parameter estimates of translog-energy sub model for Greek manufacturing with homogeneity and
a
symmetry imposed in the long-run: 1970]1990
Ž . Ž .
Equation I electricity Equation II diesel
Parameters Coefficients Parameters Coefficients
The numbers in parentheses are the standard errors.U
,UUU
Indicate statistical significance at 1% and 10%, respectively.Qdenotes the Box]Pierce Qstatistic for serial correlation in the residuals. The figures in parentheses are the degrees of freedom for x2 statistics. The 5% critical values are 11.070 and 18.307, respectively, for 5 and 10 d.f.s.
Ž . Ž . 6
The estimates of own Ei i and cross price Ei j elasticities evaluated at the mean values in the period 1970]1990 are presented in Table 3.
It can be seen from Table 3 that all long-run own price elasticites are negative except for crude oil. However, the only result that appears to be statistically different from zero is that for diesel. For this energy component the estimated
Table 3
a
Estimates of own and cross long-run price elasticities
Ž . Ž . Ž .
Electricity EL Diesel D Crude oil M
U
Ž . Ž . Ž . Ž .
Electricity EL y0.02 0.10 1.12 0.27 y0.07 0.15
U U
The effect of a change in the price of electricity on each of the components is contained in the first row, etc. The figures in parentheses are the standard errors.U
, denotes significance at 1%.
6
long-run own price elasticity is higher, in absolute value, than unity. This means that the demand for diesel is very responsive to a change in its own price. So, an increase in the price of diesel by 10% will decrease the amount of diesel demanded by 12.9%.
Turning to long-run cross price elasticities, the results suggest that they are positive but statistically zero, apart from cross price elasticities of diesel and electricity which also exhibit a positive sign but, are statistically different from zero at the 1% level. The size of substitution between electricity and diesel is high7with
respect to the price of electricity and low with respect to the price of diesel. This means that a 5% increase in price of electricity, given the price of other inputs, will lead to a 5.6% increase in the relative share of diesel whereas a 5% increase in price of diesel, given the price of other inputs, will lead to a 0.4% increase in the relative share of electricity.
Overall the results suggest that the demand for diesel, holding constant the total energy cost, is highly sensitive to price movement, while for electricity and crude oil the high standard errors make it impossible to draw any conclusion about their price responsiveness. Finally, there is no evidence for inter-energy substitution except for high level of substitutability of diesel for electricity.
Next the aggregate total cost is considered in order to determine the demand for total energy.
4.2. Estimation of the total cost function
Before proceeding to the estimation of the general dynamic system of share Eq.
Ž13 the aggregate price index for energy has to be generated. For this reason the. Ž .
estimated long-run parameters from 14 are used as starting values for the energy
Ž . Ž .
cost function 9 and then the energy cost function 9 is estimated using maximum
ˆ
Ž .
likelihood techniques. Thus, an aggregate price index PE is obtained which serves
Ž .
as an instrumental variable for the price of energy PE in the estimation of the
Ž .
dynamic system 13 of the shares of total cost.
Ž .
The test for dynamic structure of 13 is shown in Table 4.
The results in Table 4 suggest that the general dynamic specification nests such of partial adjustment as the static at the 25% level of significance while the static specification is also nested by the general dynamic at the 10% level of significance.
Table 4
Tests of dynamic structure for the total cost share equations
2 2 2 2
x Number of x0.95 x0.90 x0.75
restrtions
Partial adjustment 9.187 6 12.592 10.644 7.841
Static 12.173 7 14.067 12.017 9.037
7 Ž .
Table 5
Parameter estimates of translog total cost function for the Greek manufacturing with homogeneity and
a
symmetry imposed in the long-run: 1970]1990
Ž . Ž .
Equation I capital Equation II labour
Parameters Coefficients Parameters Coefficients
The numbers in parentheses are the standard errors.U
,UU
,UUU
Indicate statistical significance at 1%, 5% and 10%, respectively. Q denotes the Box]Pierce Q statistic for serial correlation in the residuals. The figures in the parentheses are the degrees of freedom forx2statistics. The critical values
at the 5% level are 11.070 and 18.307, respectively, for 5 and 10 d.f.s.
Parameter estimates using the IZEF method for the general dynamic specification are presented in Table 5.
Ž . Ž .
Using the parameter estimates from 13 and the formulas 15 the long-run own and cross price elasticities for the total cost function were computed. The results are tabulated in Table 6.
Table 6
a
Own and cross long-run price elasticity estimates
Ž . Ž . Ž .
Capital K Labour L Energy E
U U UU
Ž . Ž . Ž . Ž .
Capital K y0.15 0.03 0.17 0.04 0.14 0.07
U U
Ž . Ž . Ž . Ž .
Labour L 0.13 0.03 y0.19 0.06 0.02 0.10
Ž . Ž . Ž . Ž .
Energy E 0.03 0.02 0.005 0.03 y0.19 0.17
a
The effect of a change in the price of capital on each of the other inputs is contained in the first row, etc. The figures in parentheses are the standard errors.U
,UU
denote significance at 1% and 5%, respectively.
remains invariant to change in its price. This might be attributed to the fact that the share of energy did not gain a dominant share in the total cost of production. Regarding the cross price elasticities, our results strongly suggest that the possibilities of substitution between capital, labour and energy in Greek manufac-turing are extremely limited. This finding is also confirmed by the computed Allen-Uzawa partial elasticities of substitution. These are sKLs0.33,sKEs0.25 and sLEs0.05. It can therefore be concluded that the Greek entrepreneur is faced with difficulties in obtaining the best combination of inputs, which minimise total cost. For example an increase in the price of aggregate energy will not
Ž
decrease considerably the amount of energy the own price elasticity of energy is
.
statistically zero and as a result will not increase considerably the demand for
Ž . Ž .
labour ELEs0.005 and the demand for capital EKEs0.03 .
Finally to complete our analysis the total own and cross price elasticity are
Ž .
calculated for each energy component see Fuss, 1977 .
Y E E Y Ž .
Ei jsEi jqMj ?EEE i,jsK,L,E. 16
where Ei jY the cross price elasticity of demand for energy component i with respect
E Ž . Ž
to PEj} Y held constant; Ei j is the elasticity with energy cost E constant from
. E Y
Table 3 ; Mj is the defined share in the energy-sub model, and EEE is the own price elasticity of aggregate energy.
The results are presented in Table 7. It is noteworthy that these total own and cross price elasticities take into account that a change in the price of an energy
ˆ
Ž .component also causes a change in the aggregate price energy index PE . This results in substitution between energy and other aggregate factors which affects the
Ž .
demand for the energy component Fuss, 1977 .
Table 7
Total energy price elasticities
Ž . Ž . Ž .
Electricity EL Diesel D Crude oil M
Ž .
Electricity EL y0.11 1.01 y0.18
Ž .
Diesel D 0.07 y1.30 0.11
Ž .
Crude oil M y0.13 0.11 y0.03
4.3. Cointegration analysis
Decisions on factors of production may be confounded by growth in manufactur-ing itself. In other words, there is a ‘spurious regression’ issue in connection with estimation of energy demand systems. A cointegration issue arises and the question is, whether or not the estimated relationships are meaningful in the long-run.8
Ž .
Following the cointegration approaches of Engle and Granger 1987 and Philips
Ž .
and Ouliaris 1990 , we have performed unit root tests on the residuals from the demand equations for the various types of energy, that is electricity, diesel and crude oil, and on the residuals from the demand equations for aggregate inputs, i.e. capital, labour and energy. Following standard practice, we have used the
aug-Ž . Ž .
mented Dickey]Fuller ADF test Dickey and Fuller, 1981 . If the ADF test indicates the presence of a unit root, demand system residuals are non-stationary implying that the estimated relationships are not structural.
The results in Table 8 suggest that residuals do not contain a unit root implying
Ž .
that these series are I 0 . Therefore, there is evidence to support that the estimated relationships are indeed structural and not spurious.
4.4. Structural stability
Since there are several epochs of energy prices in the data, an issue of structural stability arises. In other words, model parameters may have changed from epoch to epoch. Full-blown Chow tests involving hypotheses about structural stability of all parameters are impossible to implement, because of the small number of observa-tions. One can, however, examine the structural stability of the constant term by
Ž
testing the significance of dummy variables one following 1973 and one following
.
1979 in the estimated relationships. These dummies turn out to be insignificant
Ž
and, therefore, we do not have evidence against the stability of the model the computedx2 for the sub-energy model is 11.63 and for the aggregate model 10.10, .
while the critical value for 4 d.f. at the 1% level of statistical significance is 13.277 An independent test of model stability is provided by examining the forecasting ability of the model. If the model were subject to structural changes its forecasting performance should deteriorate. From an inspection of Figs. 1 and 2, it turns out that the dynamic forecasting performance of the model is excellent in the entire
8
Table 8
a
Unit root test
Equation residual Augmented
Dickey]Fuller test
Sub-energy model
Electricity y3.197
Diesel y3.334
Crude oil y2.811
Aggregate model
Capital y5.033
Labour y3.752
Energy y3.275
a Ž .
The critical value of the ADF statistic with no constant and no time trend isy1.96 at the 5% level. Number of lags was selected optimally using the Schwarz criterion. The ADF regression is performed without constant term because it is known that residuals have mean zero.
sample. This provides additional evidence in favour of the model’s structural stability
5. Concluding observations
The present paper investigates the demand for different types of energy, namely, electricity, diesel and crude oil, and the elasticities of substitution among energy
Fig. 2. Dynamic forecasting performance: equation of labour.
components and the substitution among aggregate energy and aggregate
non-en-Ž .
ergy inputs capital and labour , in Greek manufacturing, for the period 1970]1990. A dynamic two-stage optimisation procedure for the derived demand for each type of energy and for aggregate energy, capital and labour is adopted. In particular, it is assumed that an aggregate energy cost function exists that is weakly separable in its components. Thus, we aggregated a sub-energy model in order to construct an aggregate energy price index. In the second stage the computed instrumental
ˆ
Ž .variable PE from this stage is substituted in the aggregate cost function in the place of PE. In both stages the translog cost function is used under a general dynamic specification. The dynamic specification is derived using a transformation suggested in the error correction literature. The partial adjustment and the static formulations are tested against the general dynamic framework. Therefore, the dynamic specification is tested rather than arbitrarily imposed. The main character-istic of the dynamic model is that it merges the long-run steady-state theory with short-run time series properties of data and produces elasticities that are robust for policy implications.
The empirical evidence can be summarised as follows:
v Inter-energy substitution is limited in the case of Greek manufacturing. An
exception is the high degree of substitution of diesel for electricity. Also, our
Ž
results provide support for inelastic demand for crude oil and electricity their
. Ž
computed values are close to zero and elastic demand for diesel EDDs
.
y1.36 .
Also, there is little evidence that capital and labour substitute each other in the
Ž
production process of Greek manufacturing the Alien-Uzava partial elasticity of
.
substitution is sKLs0.33 . This conclusion is also partly confirmed by a previous
Ž .
paper Christopoulos, 1995 where a total cost function approach was used to estimate technological progress in Greek two-digit industry. For regardless of the own price elasticities for aggregate inputs capital and labour those are inelastic with the labour responsiveness to a change in its own price to be higher than the corresponding capital responsiveness of capital. The own price elasticity for aggre-gate energy is statistically insignificant and no conclusions can be drawn. Finally, our total own and cross price elasticities estimates suggest that an increase in the price of aggregate energy does not affect substantially the demand for energy components apart from the demand for diesel. Therefore, the degree of substitu-tion among energy components and among aggregate energy is low except for substitution of electricity by diesel.
Acknowledgements
The author wishes to acknowledge the helpful comments of Professor Panayiotis Reppas, Professor Clive Richardson, Dr Efthymios Tsionas and an anonymous referee. Any remaining errors are my own.
Appendix A
The data used in this analysis consist of annual time-series data for two-digit industry of the Greek economy employing more than 10 individuals, for the years 1970]1990.
Ž .
Output Y is measured in value added terms. Value added in 1970 constant prices is obtained by value added deflators. The data on value added are published
Ž .
in the Annual Industrial Surveys AIS of the National Statistical Service of Greece
ŽNSSG.
Ž .
VAy WqS
Ž .
The price series of capital PK was calculated as PKs where NFC
VA is the value added, W and S the wages and salaries, respectively, and NFC is the net fixed capital. The data on wages and salaries are published in the Annual
Ž . Ž .
Industrial Surveys AIS of the National Statistical Service of Greece NSSG while the deflator was taken from the National Accounts of NSSG. The data on capital
Ž .
stock for the period 1970]1980 were provided by Kintis 1986 . For the period 1981]1990 his approach was followed for the calculation of these data. All figures are expressed in 1970 constant prices. Value added deflators were used to deflate
Ž .
Ž . Ž .
Following the procedure outlined by Lianos 1975 and Panas 1986 the price W?L
Ž .
series of labour PL was estimated by PLs H where W?L is the wage bill and H is the total number of hours worked by paid workers and employees. The wage bill is expressed by means of value added deflators in 1970 constant prices. The necessary data on hours and on the number of employees were taken from the AIS of NSSG and from the ‘Year Book of Labour Statistics’ of the International Labour Office, respectively.
Diesel]Crude Oil]Electricity: The prices series for the three types of energy were calculated by dividing expenditures by consumption in physical units for each type of energy input. The physical unit for each type of energy is expressed in
Ž . Ž .
equivalent tons of oil TOE see Samouilidis, 1982 . All the data are expressed in 1970 constant prices and are taken from the AIS of NSSG. The deflation was made by value added deflators.
The annual series for the total cost was constructed as follows:
CsValue AddedqTotal Value of Three Types of Energy.
The NSSG did not undertake an industrial survey in 1978]1979. The mean of the series was used to fill the gap for these 2 years
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