This assumption of weak separability places restrictions on the AES; the linear valueadded separability restrictions imply that oKE=aLE=aKM =aLM = 1.0, which produces a partial CobbDouglas structure. The nonlinear valueadded separability restrictions imply that aKE=aLE¿1.0 and that aKM =aIM41.0. The former implies that the sum of SK and SL is constant, while the latter implies constancy of the ratio of SK and SL. Berndt and Wood conclude that the separability conditions for the valueadded specification (3.27) are not satisfied by their data. However, the separability of K and E from the other inputs could not be rejected so that Y=ff1(K, E), L, M]. (This is discussed at greater length below. In addition, see Berndt and Wood (1979).) Clearly, these findings are of broader significance for international studies and not solely of relevance to the data analysed by Berndt and Wood.
A further methodological issue arises from the fact that, since the level of aggregation employed is aggregate manufacturing, Berndt and Wood suggest it may be inappropriate to assume that prices are exogenous and that the regressors in the inputcostshare equations are uncorrelated with the disturbances. Few other translogbased studies have considered the endogeneity of prices. In Berndt and Wood, each of the regressors in the inputcostshare equations is regressed on a set of variables considered exogenous to US manufacturing and the fitted values from these firststage regressions replace the original regressors in the inputcostshare equations.
Positivity of the input demand functions and concavity of the cost function are both satisfied so the translog cost function is well behaved for their data set. Energy demand is found to be responsive to changes in its own price, the ownprice elasticity being around 0.47, and energy and labour are found to be slight substitutes, the AES being around 0.65 while the crossprice elasticities for nLE and nEL are about 0.03 and 0.08 respectively. Energy and capital are complements with an AES of approximately 3.2 while the crossprice elasticities nKE and nEK are about 0.15 and 0.18. Moreover, capital and labour are substitutes with an AES of 1.01, while the ownprice elasticities nKK and nLL are 0.48 and 0.45 (see Tables 3.1 and 3.2 for summary details). Although the elasticities seem stable over the period, they are calculated from timeinvariant secondorder coefficient estimates and the actual factor expenditure shares are fairly constant over their data period (see Berndt and Wood 1975).
The study by Griffin and Gregory (1976) also uses a static translog cost function to study energy substitution responses in the manufacturing sector but uses data from Belgium, Denmark, France, West Germany, Italy, the Netherlands, Norway, the United States and the United Kingdom. As is common in many similar studies, three factors—capital, energy and labour— are explicitly analysed and are assumed to be weakly separable from material inputs despite the earlier findings of Berndt and Wood (1975). This assumption is partly necessitated by an absence of reliable data on materials. However, it should be noted that separability of (K, E) from L is supported by the data used in Berndt and Wood (1979).
Griffin and Gregory note that higher energy prices might induce shortrun substitution towards the labour and material inputs and away from capital. This follows from the technological relationship between energy inputs and a given stock of capital equipment. Thus in the short run labour and materials are likely to be substitutes for energy whilst capital and energy are complementary. However, in the long run, capital and energy are more likely to be substitutes as more recent vintages of capital embody energysaving technological advances. Griffin and Gregory therefore point to the possibility of sign reversals in elasticity estimates depending on whether the short run or long run is being analysed.
Their interest in longrun elasticities leads to their consideration of only four crosssections (1955, 1960, 1965 and 1969) while post1969 information was rejected on the grounds that energy prices had started to rise. In effect, substantial timeseries relativeprice variation is explicitly excluded and elasticities identified by crosssectional variation within the data are interpreted as long run. As noted, this interpretation of crosssection studies providing longrun elasticity estimates and timeseries studies providing shortrun estimates pervades much of the literature.
In common with many studies of this type, Griffin and Gregory estimate variants on the basis of a pooled translog model including countryspecific intercepts and, to allow fully for heterogeneity between countries, they also estimate separate translog models for each country. Given their choice of sample, the latter results are based on very few degrees of freedom, as the authors admit. The system of factorshare equations estimated by iterative Zellner efficient techniques fails to reject the symmetry, positivity and concavity assumptions regardless of whether countryspecific intercepts are present in the estimated factorshare equations. Furthermore, the assumption of uniform bj coefficients cannot be rejected although this is hardly surprising given that only four observations per country are used in estimation. In effect, the data set investigated by Griffin and Gregory necessitates the use of a uniform price coefficient matrix despite the presence of idiosyncratic countryspecific effects within the data. These effects, they state, 'will also capture a variety of disequilibrium factors relating to differences in industrial structure amongst countries' (our emphasis). Given uniformity of the bj values, similarity of elasticities must follow for countries having similar cost shares but the underlying estimates are based on very few observations for each country. They find that energy and labour are substitutes with nEL~0.45 but, in contrast to Berndt and Wood, energy and capital are also substitutes since nEK~0.30, while both cKE and cLE are not statistically different from unity. Griffin and Gregory's main findings are summarized in Tables 3.1 and 3.2. The accuracy of Griffin and Gregory's data on capital and labour expenditure in the United States has been questioned by Wood and Hirsch (1981) who note incompatibilities with the sources documented in the appendix.
Griffin and Gregory conclude that their model provides a reasonable longrun alternative to the preexisting timeseries literature on energy, capital and labour substitution and price elasticities such as Berndt and Wood (1975) and Hudson and Jorgenson (1974). They admit to potential measurement error, simultaneous equation bias and specification error problems in their approach, but conclude 'that translog applications to pooled international data represent fruitful lines of inquiry into the issue of energy, capital and labour substitution'.
The demand for energy in the Canadian manufacturing sector is analysed in Fuss (1977b) who assumes that the production structure is weakly separable in the categories of labour, capital, materials and energy. According to Denny and Fuss (1977), the assumption of weak separability implies aggregates which are homothetic in their components, and this is sufficient for an underlying twostage optimization procedure to exist. First, the mix of components within each aggregate is optimized, followed by the level of each aggregate (see Pindyck (1979a) for further details). Under these assumptions, the cost function can be expressed as C = g[PE(.PEI Pen),Pp Pm 01 (3.28)
Study 
Sector 
Data 
Model 
nEQ 
nEE 
nEL 
nEK 
nEM Notes 
analysed 
period 
and estimation technique  
Berndt 
Time 
194771 
KLEM 
N/A 
0.45 to 
0.16 to 0. 
0.17 to 
0.46 to 0. 
and 
series for 
translog 
0.49 
20 
0.18 
49  
Wood 
US 
by I3SLS  
(1975) 
manufact uring  
Griffin 
Pooled 
195569 
KLE 
N/A 
0.79 (0. 
0.48(0. 
0.31(0. 
N/A 
and 
manufact 
translog 
77 to 0. 
40 to 0. 
15 to 0.  
Gregory 
uring 
by IZEF 
80) 
64) 
40)  
(1976) 
data for nine nations 
Study 
Sector 
Data 
Model 
VBQ 
VEE VEL 
nEK Vem 
Notes  
analysed 
period 
and  
estimation  
technique  
Kouris 
Pooled 
195570 
Ad hoc 
0.84 
0.77 N/A 
N/A N/A  
(1976) 
cross 
logarithm  
section 
ic model  
time  
series for  
eight  
nations  
Smil and 
Aggregat 
195060 
Ad hoc 
0.60 to 2. 
N/A N/A 
N/A N/A  
Kuz 
e time 
00  
(1976) 
series for  
twenty  
six  
nations  
Smil and 
Aggregat 
196070 
Ad hoc 
0.82 to 1. 
N/A N/A 
N/A N/A  
Kuz 
e time 
63  
(1976) 
series for  
twenty  
six  
nations  
Fuss 
Pooled 
196171 
KLEM 
N/A 
0.49 0.55 
0.05 0.02 
Figures  
(1977b) 
cross 
translog 
for  
section 
by 
Ontario  
time 
iterative  
series for 
minimum  
Canadian 
distance  
manufact 
estimatio  
uring 
n  
Nordhaus 
Cross 
195572 
KLE 
0.29 to 1. 
0.03 to N/A 
N/A N/A 
Koyck  
(1977) 
section 
dynamic 
11 (short 
0.68 
and  
time 
Cobb 
run) 0.26 
(short 
Almon  
series for 
Douglas 
to 1.42 
run) 1. 
distribute  
seven 
productio 
(long run) 94 to 1. 
d lag  
nations 
n function 
45 (long 
schemes  
run) 
used  
Berndt 
Time 
194771 
KLEM 
N/A 
0.13 N/A 
0.13 N/A 
Results  
and Wood 
series for 
translog 
(gross 
(gross 
for 1971  
(1979) 
US 
by I3SLS 
elasticity 
elasticity)  
manufact 
) 0.57 
0.33  
uring 
(net 
(net  
elasticity ) 
elasticity)  
Pindyck 
Pooled 
196373 
KLE 
N/A 
0.84 0.02 to C 
I. 0.02 to 0. N/A 
The  
(1979a) 
industrial 
translog 
(0.83 to 08 
08 
United  
time 
by IZEF 
0.87) 
States and  
series for 
Canada  
Field and Grebenste in (1980) ten nations Pooled residentia l time series for ten nations Pooled cross section for US manufact uring 196074 Translog by IZEF 1971 KLE translog pooled separately Study Sector Data Model nEQ nEE nEL qEK nEM Notes analysed period and estimation technique Study Sector Data Model nEQ nEE nEL qEK nEM Notes analysed period and estimation technique

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