YffiKLM327

This assumption of weak separability places restrictions on the AES; the linear value-added separability restrictions imply that oKE=aLE=aKM =aLM = 1.0, which produces a partial Cobb-Douglas structure. The nonlinear value-added separability restrictions imply that aKE=aLE¿1.0 and that aKM =aIM4-1.0. 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 value-added 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 input-cost-share equations are uncorrelated with the disturbances. Few other translog-based studies have considered the endogeneity of prices. In Berndt and Wood, each of the regressors in the input-cost-share equations is regressed on a set of variables considered exogenous to US manufacturing and the fitted values from these first-stage regressions replace the original regressors in the input-cost-share 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 own-price elasticity being around -0.47, and energy and labour are found to be slight substitutes, the AES being around 0.65 while the cross-price 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 cross-price 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 own-price 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 time-invariant second-order 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 short-run 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 energy-saving 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 long-run elasticities leads to their consideration of only four cross-sections (1955, 1960, 1965 and 1969) while post-1969 information was rejected on the grounds that energy prices had started to rise. In effect, substantial time-series relative-price variation is explicitly excluded and elasticities identified by cross-sectional variation within the data are interpreted as long run. As noted, this interpretation of cross-section studies providing long-run elasticity estimates and time-series studies providing short-run 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 country-specific 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 factor-share equations estimated by iterative Zellner efficient techniques fails to reject the symmetry, positivity and concavity assumptions regardless of whether country-specific intercepts are present in the estimated factor-share 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 country-specific 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 long-run alternative to the preexisting time-series 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 two-stage 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)

Table 3.1 Energy demand elasticities with respect to income and price

Study

Sector

Data

Model

nEQ

nEE

nEL

nEK

nEM Notes

analysed

period

and estimation technique

Berndt

Time

1947-71

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

1955-69

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

1955-70

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

1950-60

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

1960-70

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

1961-71

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-

1955-72

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

1947-71

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

1963-73

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

1960-74 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

Beenstoc

Aggregat

1950-

-78

KLE

1.78

-0.06

N/A

N/A

N/A

Long-run

k and

e time

dynamic

elasticiti

Willcock

series for

error

es

s(1981)

develope

correctio

reported

d market

n model

economi es

Turnovsk

Time

1946-

75

KLEM

N/A

-0.22

-0.64

0.44

0.42

y et al.

series for

translog

(1982)

Australia

by FIML

n manufact

uring

Kouris

Aggregat

1961-

81

Dynamic

1.08

-0.15

N/A

N/A

N/A

Koyck

(1983)

e time

ad hoc

(short

(short

distribute

series for

logarithm

term)

term) -0.

d lag

the

ic model

43 (long

scheme

OECD

term)

used

Pindyck

Time

1948

71

KLEM

N/A

-0.36

-1.37

0.47

0.36

Capital

and

series for

dynamic

(short

(short

(short

(short

and

Rotember

US

translog

run) -0.

run) 1.07

run) 0.46

run) 0.13

labour

g(1983)

manufact

by 3SLS

58 (inter-

(inter-

(inter-

(inter-

quasi-

uring

run) -0.

run) 1.03

run) -1.

run) 1.31

fixed

99 (long

(long

34 (long

(long

run)

run)

run)

run)

Pindyck

Time

1948

71

KLEM

N/A

-0.66

0.88

0.35

-0.22

Capital

and

series for

dynamic

(short

(short

(short

(short

quasi-

Rotember

US

translog

run) -0.

run) 0.70

run) -1.

run) 1.15

fixed

g (1983)

manufact

by 3SLS

93 (long

(long

01 (long

(long

uring

run)

run)

run)

run)

Prosser

Aggregat

1960-

82

Dynamic

1.02

-0.22

N/A

N/A

N/A

Koyck

(1985)

e time

ad hoc

(short

Sector analysed series for the

OECD

Data period

Model and estimation technique logarithm ic model nEQ

Notes d lag scheme used

Hesse and

Tarkka

Hesse and

Tarkka

Hesse and

Tarkka

Hesse and Tarkka (1986) Fiebig et al. (1987)

Apostolaki s (1987)

Siddayao et al. (1987)

Saicheua (1987)

Pooled cross-section time series of electricity for nine nations

Pooled cross-section time series of electricity for nine nations Other fuels

Other fuels

Cross-section for thirty nations

Aggregate time series for five nations

Cross-section time series for manufactur ing in the Far East

Cross-section time series for manufactur

1960-72

translog by FIML

1973-80

translog by FIML

1960-72 KLE N/A translog by FIML

1973-80 KLE N/A translog by FIML

Not stated Ad hoc 1.33(1.24

logarithmic to 1.64)

1953-84 KLE N/A

translog

1970-80 KLE N/A

translog by IZEF

1974-7 KLE N/A

translog by IZEF

ing in Thailand

Study

Sector analysed

estimation technique

nEE

vel nEK

Welsch (1989)

Welsch (1989)

Lynk (1989)

Hunt and Manning (1989)

Aggregate time series for eight nations

Aggregate time series for eight nations

Time series for the UK manufactur ing sector

Aggregate time series for the UK

Industrial time series for seven OECD nations

197O-84

197O-84

1948-81

1967-8

196O-87

Dynamic ad hoc linear and logarithmic models

Dynamic ad hoc linear and logarithmic models models KLE

translog by FIML

Dynamic error correction model

Cointegrati on analysis

Dynamic logarithmic specificatio n with multinomin al logit by

IZEF

0.24 (short term)

O.634

(long term)

Koyc distributed lag scheme used

Koyck distributed lag scheme used

Dynamic maximizin g model with costs of adjustment used

Long-run elasticities reported

Watkins

Time

1957-82 KLEM

N/A

-O.48

-O.12

N/A

O.6O

Third

(1991)

series for

dynamic

(short

(short

(short

generatio

Canadian

specificat

run) -O.

run) O.21

run) O.54

n

textiles

ions

5O (long

(long

(long

dynamic

run)

run)

run)

results

reported

Hunt and

Time

1952-88 KLE

O.46 to O.

-O.O8 to

O.O8 to O.

O.OO to O.

N/A

Lynk

series for

dynamic

48 (short

-O.13

1O (short

O3 (short

(1992)

UK

error

run) O.63

(short

run) O.13

run) O.14

industry

correctio

to O.7O

run) -O.

to O.15

to O.16

n model

(long

29 (long

(long

(long

Cointegra tion

run)

run)

run)

run)

analysis

Boone et

Time

1978-89 VAR N/A

-0.09 to N/A

N/A

N/A

Energy=f

al. (1992)

Johansen (FIML)

-0.62

ossil fuels A time trend is included in the VAR Quarterly data used

Bentzen

Time

1948-90 VAR 0.67

-0.14

N/A

N/A

N/A

Temperat

et al.

series for

system (short

(short

ure

(1993)

Denmark

with run) 1.21

run) -

0.

variable

ECM by (long

47 (long

included

Johansen run)

run)

(FIML)

Table 3.2 Partial elasticities of substitution

Study

Sector analysed

Data Model and period estimation technique

aEE

aLE

gke

°ME

°KL

Berndt and

Time

1947-71 KLEM

-10.63 to

0.61 to 0.

-3.09 to

0.74 to 0.

1.01

Wood

series for

translog by

-10.70

68

-3.53

77

(1975)

manufactu ring

I3SLS

Griffin and

Pooled

1955-69 KLE

N/A

0.72 to 0.

1.02 to 1.

N/A

0.06 to 0.

Gregory

manufactu

translog by

87

07

50

(1976)

ring data for nine nations

IZEF

Pindyck

Pooled

1963-73 KLE

-10.8

8 to

0.05 to 1.

0.36 to 1.

N/A

0.64 to 1.

(1979a)

industrial

translog by

-27.21

23

77

43

time series

IZEF

for ten

nations

Özatalay et

Pooled

1963-74 KLEM

-24.60 to

1.03 to 1.

1.15 to 1.

0.42 to 0.

1.06 to 1.

al. (1979)

aggregate

translog by

-32.25

05

22

65

14

time series

FIML

for seven

nations

Turnovsky

Time

1946-75 KLEM

-8.73

-2.66

2.26

0.79

2.00

et al.

series for

translog by

(1982)

aggregate manufactu ring

FIML

Prywes

Pooled

1971-6 KLEM

N/A

N/A

-4.53 to 0.

N/A

N/A

(1986)

cross-section time series

CES

33

Sector analysed

Data period

Model and aEE

estimation technique ole

Apostolaki s (1987)

Siddayao et al. (1987)

Saicheua (1987)

for US

manufactu ring

Aggregate time series for five nations Cross-section time series for the Far East Cross-section time series for

Thailand

1953-84

1970-80

1974-7

KLE translog

translog by IZEF

translog by IZEF

97 66

where PE forms an aggregate price index. The price of energy is represented by a translog unit cost function and familiar share equations are estimated. Fuss incorporates a total of nine inputs: capital, labour, materials and six different energy inputs. The two-stage approach allows for the analysis of both interfuel substitution and substitution among energy and non-energy factors of production.

The model is estimated on a combined time-series cross-section data set for four areas of Canada from 1961 to 1971. The six types of fuel analysed in the lower stage are coal, liquid petroleum gas, fuel oil, natural gas, electricity and petrol. The own-price elasticity estimates are negative and, apart from petrol, significant at the 1 per cent level. Considerable interfuel substitution is apparent with the exception of electricity and, possibly, petrol. The demand for liquid petroleum gas, coal, fuel oil and natural gas are all price elastic but, as found in other studies, the demand for electricity is price inelastic. See Table 3.3 for details of the elasticities of individual fuel demands.

For the higher-stage model, total cost is assumed to be a constant or a smoothly changing percentage of gross output in current dollars, whilst exponentially smooth Hicks-neutral technical change is also assumed. Although Fuss finds significantly negative own-price elasticities of demand, all factors have price-inelastic demand, for instance nEE is -0.5. In general, factors are substitutes, although slight complementarity between energy and materials and between energy and capital exists. However, the cross-price elasticities are all small, typically below 0.3 in absolute value when evaluated with output held constant. Although there is substantial interfuel substitution in the Canadian manufacturing sector, only slight substitution exists between aggregate energy and other aggregate inputs.

Fuss also considers the effects on production costs in Canadian manufacturing of increases in the price of energy relative to prices of other factors of production. A 1 per cent increase in the aggregate energy price is found to lead to a 0.03 per cent increase in average production costs. Therefore, substantial increases in the price of energy seem to be accommodated by only a moderate increase in the price index of manufacturing output. This finding is related to recent work on the implications of imposing carbon taxes on energy— recent econometric work also finds a very small impact on total production costs of tax-induced increases in energy prices. (See Ingham et al. (1991b) for a summary of recent econometric work on carbon taxes.)

The analysis of capital/energy substitution in American manufacturing is also considered by Field and Grebenstein (1980) who specify the cost function C=C(PK, PW,PL, Pe), where PK and PW refer to the prices of physical capital and working capital respectively while PL and PE represent the prices of labour and energy. Because of data deficiencies, they assume that these four inputs are separable from inputs of all non-energy intermediate materials and the standard static translog cost function is used for estimation purposes over a cross-section of ten two-digit manufacturing industries in

Table 3.3 Own- and cross-price partial fuel elasticities

Fuss(1977b)

Pindyck(1979a)

Turnovsky et al. (1982)

Lynk (1989)

Atkinson and Manning (this chapter)"

Sector analysed

Pooled cross-

Pooled industrial

Time series for

Time series for

Pooled time

section/time

time series for

Australian

the UK

series of the

series for

ten nations

manufacturing

manufacturing

industrial sector

Canadian

sector

for fifteen nations

manufacturing

Data period

1961-71

1959-73

1946-75

1948-89

1960-89

Model and

Static translog

Static translog

Static translog by

Static translog

Statics translog

estimation

by iterative

by IZEF

FIML

interfuel by

by FIML

technique

minimum

FIML

distance

estimation

Notes

Homothetic and

Homothetic and

Homothetic and

Homothetic and

Homothetic and

symmetric

symmetric

symmetric

symmetric

symmetric

figures for

Ontario

ncc

-1.41

-1.04 to -2.17

-0.75

-0.20

-0.64

nco

0.30

0.15 to 0.99

0.46

N/A

0.19

ncG

0.71

0.43 to 1.66

-0.06

N/A

0.19

ncE

-0.09

-0.48 to 0.49

0.35

N/A

0.26

noc

0.32

0.12 to 0.97

1.16

0.61

0.12

noo

-1.22

-1.10 to 0.03

-0.99

-0.29

-0.16

noG

0.17

-0.03 to -0.72

0.16

0.10

0.02

noE

0.27

-0.22 to 0.85

-0.33

0.27

0.03

nGc

0.85

0.72 to 4.98

-0.59

0.47

0.12

nGO

0.20

-0.06 to -0.83

0.68

N/A

0.26

nGG

-1.21

-0.33to -2.31

-1.45

-0.69

-0.57

nGE

0.02

-1.82 to 0.12

1.37

N/A

0.13

nEC

0.27

-0.06 to 0.25

0.31

0.35

0.06

nEo

0.77

-0.05 to 0.28

-0.12

N/A

0.01

nEG

0.04

-0.02 to -0.10

0.11

0.25

0.06

nEE

-0.52

-0.07 to -0.16

-0.31

0.10

-0.10

Notes: C, coal; O, oil; G, gas; E, electricity. aSee Section 3.3.

1971. Field and Grebenstein define physical capital as the stock of capital structures and equipment. The expenditure on physical capital is estimated as the product of user cost and the capital stock. The cost of working capital is calculated by subtracting the cost of physical capital from that of total capital, which is taken as value-added minus labour costs.

The results obtained vary over sectors but a 'very large proportion' of the second-order coefficients are insignificant. In conclusion, they find that physical capital is statistically significant as a complement to energy in four sectors, in three sectors there are weak signs of complementarity and for the remaining three sectors the estimates are insignificant. With respect to working capital and energy the results indicate that they are significant substitutes for five sectors, while insignificant results are found for the other five sectors. Virtually all other cross-price elasticities signify substitutability and all own-price elasticities are of the correct sign.

Finally, they state that for the aggregate manufacturing sector a value-added approach as used by Griffin and Gregory (1976) and Pindyck (1979a) 'would be expected to show capital/energy substitutability, while a service-price approach to capital cost would show complementarity'. Thus, according to Field and Grebenstein, the very definition of 'capital' influences empirical results. For example, the own-price elasticities of demand for physical capital are considerably higher than the equivalent estimates for working capital. Similarly, energy and physical capital are typically complements but energy is a substitute for working capital.

International time-series data for manufacturing in seven countries (the United States, Canada, West Germany, Japan, the Netherlands, Norway and Sweden) from 1963 to 1974 are analysed by Ozatalay et al. (1979). A static KLEM translog cost function is assumed to display constant returns to scale and no separability assumptions are made. As in Griffin and Gregory, country dummies are employed with a pooled sample; results are presented for Germany, Japan and the United States. Although they find that all factors are substitutes, the elasticity of substitution between energy and materials is not significantly different from zero. The elasticities of substitution vary very little between countries except for aKK and the large absolute values of aLL for Japan and aEE for the United States. Ozatalay et al. conclude that this is due to the historically low prices paid for labour in Japan and for energy in the United States. The own-price elasticities of substitution in the United States, West Germany and Japan average -2.69 for capital, -4.67 for labour, -0.91 for materials and -27.33 for energy. The cross-price elasticities of substitution average 1.09 for capital and labour, 0.87 for capital and materials, 1.18 for capital and energy, 1.00 for labour and materials, 1.04 for labour and energy and 0.55 for materials and energy. Summary details are presented in Table 3.2.

Pindyck (1979a) analyses interfuel substitution and the industrial demand for energy on an international data set using a two-stage approach similar to that of Fuss. Capital, labour and energy are assumed to be weakly separable from materials as a group because of a lack of material price data. The underlying cost function can therefore be written as

C = G lg(PK, PL, pt.(pri, PF2, PF„ PF4), fi); PM, Q) (3.29)

where PE is the aggregate price of energy derived from the homothetic sub- function of the four fuels. This static non-homothetic translog model is estimated using pooled time-series data for a cross-section of ten countries: Canada, France, Italy, Japan, the Netherlands, Norway, Sweden, the United Kingdom, the United States and West Germany. Pindyck estimates the model allowing the second-order coefficients to vary across countries but, as with Griffin and Gregory (1976), inadequate degrees of freedom exist to give satisfactory results. Country-specific intercepts are included and Pindyck specifies separate slope coefficients for the United States and Canada, but does not appear to conduct any formal covariance analysis on the data. The separation of the North American economies is justified on the basis of their historically lower fuel prices. The share equations for the energy cost sub- function are estimated from 1959 to 1973 by standard IZEF methods while the share equations for the total cost function are estimated from 1963 to 1973.

The results for the share equations of the energy cost sub-function indicate that thirteen of the sixteen second-order coefficients are statistically significant. The partial fuel price elasticities given in Table 3.3 are all substantial except for electricity—Pindyck states that electricity is a much more expensive fuel on a thermal basis and so is only used when necessary. For Europe and Japan natural gas own-price elasticities are large while those for oil are small. For the higher-stage cost function most of the second-order parameters are also found to be significant. The elasticities of substitution in Table 3.2 indicate that all other factors are substitutes for energy. Significantly, the largest values for aKE and the smallest values for aLE are found for Canada and the United States.

Elasticities of the average cost of output with respect to the price of energy and the prices of the individual fuels are also estimated. A 10 per cent increase in the price of energy is found to lead to a 0.3 per cent increase in average production costs for the United States and a 0.7 per cent increase for Italy, Japan and Sweden, which echoes the conclusion in Fuss (1977b) discussed above. Pindyck also considers scale economies (see Christensen and Greene 1976) and the elasticity of energy demand with respect to output changes. Even if energy prices remain constant relative to other prices, Pindyck finds that there will be substitution away from energy as output increases, and thus non-homotheticity could not be rejected.

The demand for energy in three separate sectors—industry, residential and transport—is analysed at some length in Pindyck (1979b), but the discussion here is primarily concerned with results for the residential sector. For this sector, data from nine countries are included: the Netherlands, Belgium, Canada, France, Italy, Norway, the United Kingdom, the United States and West Germany, and data span the period from 1960 to 1974. A static translog indirect utility function with time-dependent preferences (see Jorgenson and Lau 1975) is specified with energy being weakly separable from other inputs and the standard two-stage approach is employed. National dummy intercepts are used but the data are otherwise pooled.

Pindyck estimates the models on both the pooled time-series data and on pooled cross-sections at four-year intervals: 'if the resulting estimates are nearly the same, we can conclude that most of the explanation in the data is cross-sectional, so that we are more likely to have obtained long-run estimates of the elasticities' (Pindyck 1979b:106). Clearly, this approach follows the empirical procedure in Griffin and Gregory (1976). For the translog model of consumption expenditures, the assumptions of stationarity (in this case meaning the absence of time dependence in expenditure share equations), homogeneity, separability and additivity are all rejected. The final model is 'non-stationary', based on a non-additive indirect utility function with country-specific first-order coefficients which account for a good proportion of the explanatory power of the equations. However, twenty-five of the thirty-six second-order coefficients are significant at the 5 per cent level. None of the own-price elasticities for energy are significantly different from -1 and most of the cross-price elasticities are approximately zero, although there is a significantly positive value for food and energy and a negative value for energy and transport, which is intuitive. All income elasticities are constrained to unity since the model is homothetic. An equivalent translog approach is discussed by Jorgenson (1977).

The restrictions of regional homogeneity, (time) stationarity and additivity are all rejected in the fuel submodel which, like the higher-stage equivalent, is homothetic in energy expenditure. Pindyck argues that, as fuel prices have been lower and incomes higher in the United States and Canada, they should be treated separately from the other countries. The corresponding liquid fuel and gas elasticities for the United States and Canada are about half the size of those for the other countries. However, the opposite is true for electricity, the demand being more price elastic in North America and many own-price elasticity estimates for electricity demand in Europe being positive. This may follow from the effective omission of income in the homothetic specification.

For the transport sector a different approach is taken. Detailed data are available on the stock of energy-using durables—motor cars—so that familiar stock and utilization effects can be distinguished. Pindyck pools data from 1955 to 1974 from eleven countries which have car stock information: Belgium, Canada, France, Italy, the Netherlands, Norway, Sweden, Switzerland, West Germany, the United Kingdom and the United States. Country dummy variables account for regional heterogeneity and simple regressions explain new registrations, the depreciation rate, traffic volume per car and average fuel efficiency. However, the performance of the derived car stock is poor in subsequent petrol demand equations. The price of cars and petrol both have significant negative effects and per capita GDP has an insignificant positive effect on petrol demand. Pindyck also estimates transport demand for aviation gasoline, jet fuel, diesel fuel and petrol with simple log-linear models with a Koyck lag adjustment. For Europe, the long-run price elasticity for petrol is -1.61 and the income elasticity is 0.66. The estimated long-run price elasticity of diesel fuel is -0. 62, -0.3 for jet fuel and -0.4 for aviation gasoline, while the long-run GDP elasticities are above 2.

Turnovsky et al. (1982) analyse factor substitution using a standard static KLEM translog cost function and employ data on aggregate manufacturing in Australia from 1945 to 1975. In common with Fuss (1977b) and Pindyck (1979a, b), they also model interfuel substitution in a two-stage translog model with coal, oil, gas and electricity in the weakly separable homothetic lower-stage sub-function. As elsewhere, the aggregate energy price used in the higher stage is formulated using a Divisia price index and the usual symmetry and homogeneity restrictions are imposed. They employ two specifications of time trend variables to proxy technical change, and favour a linear function over an alternative logarithmic form in the upper stage, while the logarithmic form is preferred in the energy sub-model. Although the cost functions at the higher stage are concave in input prices and the predicted shares are non-negative at each observation, the estimates reject both symmetry and homogeneity. The AES and price elasticities estimated at six points over the time period show that capital and energy as well as materials and energy are substitutes, and that labour and energy are complements, see Table 3.2. The elasticities of substitution imply that coal and gas as well as oil and electricity are complements but all the other fuels are substitutes for each other. As found elsewhere, electricity is the least price-responsive fuel with gas and oil being the most responsive. These estimates are quite sensitive, however, to the treatment of the time trend. Furthermore, if complementarity were found between fuels, Welsch (1989) would reject the specification as theoretically inadmissible (see Section 3.4).

Hall (1986) estimates a range of static and ad hoc dynamic translog cost function models for individual fuels (liquid fuels/petroleum products, gas, solid fuels/coal and electricity) for the industrial sector in seven OECD countries (Japan, West Germany, France, Italy, Canada, the United States and the United Kingdom) from 1960 to 1979. The data are not pooled and Hall does not consider the demand for energy in aggregate. The following restrictions are initially imposed in Hall's empirical work: homotheticity, symmetry, homogeneity in prices and neutral fuel-efficiency bias. Consideration of non-homotheticity follows from inclusion of post-1973-4 observations; he argues that the absence of cyclical influence could be a source of misspecification in the estimated share equations.

The results show that all four restrictions cannot be accepted for any country in a static framework. In order to assess whether rejection is due to dynamic misspecification, Hall estimates some simple dynamic models in which the lagged expenditure share of the fuel in question is included. Although this model is consistent with both partial adjustment and adaptive expectations, Hall provides little by way of theoretical justification. The coefficients on these lagged shares are both unconstrained and given a common value in each share equation. However, the imposition of symmetry, for instance, would be rather easier with a uniform parameter on the lagged shares, as discussed below in Section 3.3.1. The treatment of these restrictions is rather unclear. Hall tests the least restricted model for both uniformity and significance in its dynamic process and, once again, rejects the imposition of all four of the above restrictions for any country. According to Hall, it seems unlikely that the absence of any dynamic modelling is responsible for the failure of the four restrictions implied by economic theory. However, the dynamic model employed by Hall is not derived theoretically and expectational terms are absent.

The preferred model varies by country: for the United States, France and Canada a static model cannot not be rejected, for Japan and the United Kingdom the unrestricted dynamic model is preferred, while for West Germany and Italy Hall suggests a uniform coefficient dynamic model. In no instance are all four own-price elasticities significant and of the expected sign. On average the results for the constrained static model indicate that the demand for coal and gas are elastic (nCC=-1.9 and nGG=-1.4) while the demand for petroleum products and electricity are inelastic (nOO=-0.8 and nEE=-0.2). The corresponding results for the non-homothetic model are coal (-0.9), gas (-0.5), petroleum products (-0.5) and electricity (-0.5). The cross-price elasticities vary from model to model and the only firm conclusion is that there is evidence that coal and gas are substitutes in the United Kingdom and France.

Hall concludes that the specification preferred, the static non-homothetic non-symmetric model allowing for the possibility of indivi

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