D.K. Christopoulos r Energy Economics 22 2000 569]586 574
Ž .
b s 1,
y s y ,
y s 11
Ý Ý
i i j
ji i j
i 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 M of input i are responses
i
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 M
.
i
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. Ž .
6 contains all the information necessary to derive estimates for the long-run demand for energy and input energy and non energy substitution.
D.K. Christopoulos r Energy Economics 22 2000 569]586 575
L L
L L
TC
M s
F M
q a q g
ln P q
d lnY
q m
T
Ý Ý
Ý Ý
i i k
i ,tyk
i i j
j ,tyk
i j tyk
T i tyk
i ,ks1
j ,ks0
j ,ks0
j ,ks0
Ž .
12 where in our application only the lag structure, k s 1 will be used.
L
Ž .
The equations in the system 12 can be transformed by subtracting F
M
Ý
k t
ks 1
Ž . Ž
. from both sides of 12
Wickens and Breusch, 1988; Kesavan et al., 1993 . By algebrical manipulation we obtain
L L
TC TC
M s
F D M
q a q g
ln P q d lnY q m T y b D
ln P
Ý Ý
Ý
i i k
k i
i i j
j i Y
T i i j
k j
i ,ks1
j j
,ks1
Ž .
y b D lnY y b D T
13
i Y k
iT k
where D refers to annual differences and i s K,L,E. Ž
. In a similar way we transform the share Eq. 10 derived from the aggregator
energy function, obtaining
L L
E E
Ž .
M s F
D M q b q
g ln P y
b D ln P
14
Ý Ý
Ý
i i
,K K
i i
i j j
i j K
j
i ,ks1
j j
,ks1
i s EL,D,M.
4. Statistical estimation
