1
Input Substitution and Business Energy Consumption: Evidence
from ABS Energy Survey Data
Kay Cao*
Senior Research Officer, Australian Bureau of Statistics, Analytical Services Branch
Abstract
This paper applies the system of equations approach to energy consumption modelling
using the ABS 2008-09 Energy, Water and Environment Survey (EWES), Economic Activity
Survey (EAS) and Business Activity Statement Unit Record Estimates (BURE) data. A system
of equations including a translog variable cost equation and an energy cost share equation is
estimated. Estimation results show that labour and energy are substitutes. Estimates of a
range of elasticity measures, including Allen-Uzawa elasticity of substitution, own and cross
price elasticities and Morishima elasticity of substitution, are also provided.
Key words: system of equations, energy consumption modelling, elasticity of substitution
JEL codes: C51, D24
* Please do not quote results without author’s permission. The author would like to thank Ruel Abello and Anil
Kumar (ABS Analytical Services) and Sean Lawson (ABS Energy Account) for their advice. Responsibility for any errors or omissions remains solely with the authors. The views in this paper are those of the author and do not necessarily represent the views of the Australian Bureau of Statistics. The results of these studies are based, in part, on tax data supplied by the Tax Office to the ABS under the Income Tax Assessment Act 1936 which requires that such data are only used for statistical purposes. No individual information collected under the Census and Statistics Act 1905 is provided back to the Tax Office for administrative or regulatory purposes. Any discussion of data limitations or weaknesses is in the context of using the data for statistical purposes, and not related to the ability of the data to support the Tax Office's core operational requirements. Legislative requirements to ensure privacy and secrecy of this data have been followed. Only people authorised under the Australian Bureau of Statistics Act 1975 have been allowed to view data about any particular firm in conducting these analysis. In accordance with the Census and Statistics Act 1905, results have been confidentialised to ensure that they are not likely to enable identification of a particular person or organisation.
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I. Introduction
The system of equations approach is one of the well documented modelling methods used
in modelling business energy consumption (see for example, Berndt and Wood, 1975;
Griffin, 1991; and Ryan and Plourde, 2009). The Australian Bureau of Statistics (ABS) ongoing
research in energy consumption modelling (for example, Cao et. al. 2012 and 2013) has
suggested several modelling approaches that could be applied to current existing datasets,
one of which is the system of cost and cost share equations.
Compared to the single equation modelling approach, using a system of cost equations can
address the interactions between energy and other inputs such as capital, labour and non-
capital materials. Analysing substitution between energy and other inputs has important
policy implications. In the energy consumption modelling literature, a large number of
studies were devoted to answering the question of whether or not capital and energy are
complements or substitutes (for a summary of existing studies, see for example Koetse et.
al., 2007). If capital and energy are complements, an increase in energy price (for example
through taxes) may have negative impact on capital investment and thus affect output. On
the other hand, if capital and energy are substitutes, an increase in energy price may induce
more capital investment (for example, in the form of more energy efficient equipment),
thus avoid the negative impact of the policy on economic growth. The same argument
applies to the interactions between energy and other inputs.
In addition to the policy implications, taking input substitution into account helps to derive
better estimates for energy price elasticities and other substitution elasticities which are
important inputs for models simulating the impact of (energy/climate change) policies.
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This study utilises the 2008-09 Energy, Water and Environment Survey (EWES), Economic
Activity Survey (EAS) and Business Activity Statement Unit Record Estimates (BURE) datasets
to estimate the system of cost and cost share equations, through which to analyse the
interactions between energy and other inputs as well as derive estimates for energy price
elasticities and cross-price elasticities. A range of measures for input substitution (e.g. Allen-
Uzawa elasticity of substitution, own and cross price elasticities and Morishima elasticity of
substitution) will be used. In the following sections, data characteristics and model structure
will be described before the discussion of model results and conclusion.
II. Data
The 2008-09 EWES provides energy consumption data at unit level, both in expenditures
and volumes. From this dataset a measure for energy price can be derived by dividing total
fuel expenditure by total volume. It was advised that, for those industries outside divisions B
(Mining), C (Manufacturing), D (Electricity, gas, water and waste services) and I (Transport,
Postal and Warehousing), the total energy volume used may be underestimated as the
questionnaire did not specifically ask for volume consumption of the insignificant fuel types.
For this reason, energy price derived for industries apart from divisions B/C/D/I might be
somewhat overestimated and hence regression outputs for these industries need to be
interpreted with caution.
When EWES is merged (linked) to EAS and/or BURE data, financial variables including
expenditures on salary and wages, capital and non-capital inputs can also be obtained. The
merged dataset also provides information on the number of employees (labour quantity),
thus a proxy for labour price can also be derived.
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The current datasets however do not provide measures of capital and non-capital quantities
and hence no measures for capital and non-capital input prices can be obtained. Due to this
reason, in the cost model, we assume both capital and non-capital inputs are fixed, that is,
we will only focus on the variable cost including labour and energy inputs. The implication
from this assumption is that the derived of elasticities are short-run estimates, where only
changes in variable costs are considered.
Between EAS and BURE, although they are both alternative datasets to be used for financial
data, EAS unit records are rather raw survey data while BURE is an edited dataset based on
tax administrative data. EAS, on the other hand, gives some better measured variables such
as capital depreciation and employee numbers.
Summary statistics (mean) of the key variables used in modelling are provided in table
below. In this dataset, capital (K) is sourced from EAS depreciation data while other
variables except energy are sourced from the BURE dataset. Energy expenditures are from
EWES.
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Table 1. Summary statistics, all divisions
Industry division
K
($000)
L
($000)
E
($000)
M
($000)
Y
($000)
Observations
Agriculture, forestry and fishing 318
1,300
269
3,827
12,000 457
Mining
27,700
23,500
9,493
47,400
362,000 626
Manufacturing
3,562
11,900
11,600
16,300
127,000 2,721
Electricity, gas, water and waste
services
24,500
27,800
16,400
142,000
349,000 206
Construction
1,386
13,500
805
35,800
91,300 1,017
Wholesale trade
2,248
17,900
3,916
127,000
296,000 748
Retail trade
3,362
27,400
1,355
41,500
266,000 647
Accommodation and food services
1,386
9,272
644
7,170
36,600 504
Transport, postal and warehousing
8,314
19,700
8,928
24,100
102,000 832
Information media and
telecommunications
19,900
22,600
894
8,620
171,000 409
Financial and insurance services
666
23,400
218
76,400
422,000 679
Rental, hiring and real estate services
1,983
2,643
377
12,400
34,800 1,128
Professional, scientific and technical
services
1,753
18,100
305
21,700
82,400 975
Administrative and support services
772
21,000
391
13,300
70,700 728
Public administration and safety
524
9,600
209
6,051
22,400 138
Education and training
905
10,600
179
8,103
24,500 419
Health care and social assistance
1,613
14,500
471
8,380
40,200 835
Arts and recreation services
1,393
3,872
175
6,663
25,300 702
Other services
439
3,841
147
8,519
17,200 633
Total
14,404
Note: K, L, M, Y are mean depreciation, wages, non-capital inputs and turnover. E is energy expenses from EWES data.
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III. Model
This modelling approach is based on the theory of production economics. Application to
modelling energy demand was facilitated especially since the introduction of the translog
(transcendental logarithmic) function by Christensen et al. (1973). Translog production
function, for example, relaxes the range of substitution possibilities between inputs which
does not require a unitary elasticity (as in the case of Cobb–Douglas production function) or
constant elasticity of substitution (Griffin, 1991).
A common translog production (or cost) function involves inputs such as capital (K), labour
(L), energy (E) and materials (M). To derive an optimal input demand equation, an optimal
(variable) cost function is specified as:
where
VC is variable cost including wages and energy expenditures ($)
PE,PL, are prices of energy and labour respectively ($)
K is capital input ($, either depreciation or capital expenditures)
M is material input ($ non-capex excluding energy expenditures)
Y is output ($ turnover)
To derive an optimal input demand equation (in this case, energy), Shephard’s lemma is
applied (for detailed explanation and proof, see for example, Coelli et al., 2005). It states
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that the partial derivatives of optimal cost function with respect to input prices give the
corresponding conditional input demand functions, which are the economically optimal
input levels to produce a given output quantity. Therefore, we obtain an input demand
equation for energy as:
where
SE is energy share in variable cost
As we only consider the variable costs including energy and labour costs, the system of
equations to be estimated would only consist of equations (1) and (2).
Seemingly unrelated regression estimation technique is used to estimate this model.
For the cost function to be homogenous in prices and symmetric in cross price parameters,
a number of parameter restrictions need to be applied. The homogeneity conditions are
specified as below.
(3)
This modelling technique is discussed widely in the production economic literature,
especially in studies using translog cost function. For further discussion on this modelling
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approach, see Berndt and Wood (1975), Watkins (2000), Coelli et al (2005), Koetse et al
(2007), and Ryan and Plourde (2009).
Measures of elasticity of substitution
Hicks (1932) is widely cited as the first study that defined a measure for elasticity of
substitution between inputs. Hick’s elasticity of substitution measures the relative change in
input proportion (e.g. L/E) due to a relative change in the marginal rate of technical
substitution while output is held constant. Under perfect competition and profit
maximisation, relative changes in marginal rate of substitution equals relative changes in
input price ratio (Frondel, 2011). Therefore Hick or Hick-Allen (HAES) elasticity of
substitution can also be written as below (using L and E as an example):
(4)
After Hicks (1932), there have been other suggestions for measures of elasticity of
substitution. The popular measures include the Allen (also called Allen-Uzawa) partial
elasticity of substitution (Hicks and Allen, 1934a,b; Uzawa, 1962), Morishima elasticity of
substitution (Morishima, 1967; Blackorby and Russel, 1975), and own price and cross price
elasticities. Stern (2011) provided an excellent summary of the various types of elasticities
of substitution and complementary and their historical development.
The above mentioned elasticity measures are commonly used in studies analysing energy
and input substitution and will be used in this study to facilitate comparison with previous
studies. The mathematical formulas for calculations of these elasticities of substitution are:
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(5)
where
AESEE.LE are the Allen elasticities of substitution, measuring changes in input due to a change in (own or cross) input price, weighted by the input share;
ηEE, LE are the own and cross-price elasticities, measuring changes in input due to a change in own or cross input price;
MLE is the Morishima elasticity of substitution, measuring the change in input ratio due to a change in cross input price;
αEE, LE are the parameters estimated from the system of equations (1) and (2);
SE, L are the shares of energy and labour in the total variable cost measured by the mean of individual shares.
The Morishima elasticity of substitution differs from other measures as it shows changes in
the input ratio as price changed. It therefore measures the curvature of the production
isoquant or the ease of factor substitution and reveals technological substitution potentials
(Koetse et al, 2008). Other measures (AES, own and cross-price elasticities) have economic
implications in terms of actual input changes in response to price changes. Some studies (for
example Frondel, 2011) argued in favour of the use of cross-price elasticities for measuring
input substitution rather than using Morishima measures. However, as mentioned,
Morishima measures have advantages in showing the technological substitution potential
between inputs (through changes in input ratios). Among the measures, only AES is
symmetric (ie AESEL = AESLE), Morishima and cross-price elasticities are asymmetric.
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IV. Results
The system of equations (1) and (2) were estimated using seemingly unrelated regression
procedure in Stata. We tested the model with both BURE and EAS data. Since there are
several measures for capital use, we estimated the model using different measures of
capital (depreciation and capital expenditures). Estimation results for the energy cost share
equation using pooled data across industries, are presented in the Table 2 below. Results for
specific industry divisions are provided in Table A1, Appendix.
Table 2. Estimated coefficients of the energy cost share equation – All industries
Model using EAS data and
depreciation as K (1)
Model using EAS data and capex as K
(2)
Model using BURE data and
capex as K (3)
Model using BURE wages and noncapex and EAS depreciation
and employee numbers (4)
lnPE -0.0340 *** -0.0288 *** -0.0432 *** -0.0226 ***
lnPL 0.0170 *** 0.0144 *** 0.0216 *** 0.0113 ***
lnK 0.0069 *** 0.0047 ** 0.0018
0.0066 ***
lnY -0.0041 -0.0007 0.0112 *** -0.0034
lnM -0.0027 -0.0050 ** -0.0146 *** -0.0101 ***
R2 0.7300 0.6998 0.6782 0.7784
Obs. 5267 5549 4314 4388
Note: PE, PL , K, Y, M are energy price, labour price, capital, output and non-capital materials respectively
For the models shown, results using pooled data do not differ much. The coefficient signs
(which imply substitution between energy and labour and relationship between energy and
other inputs) are quite consistent across models (except for lnY in model 3). Although
results at the aggregate level do not differ much between models, it might not be the case
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at the more disaggregated industry level. Hence the choice of the dataset could affect
results at the lower industry levels.
Among the four models/datasets, model (4) is our preferred option since its dataset uses a
combination of the better measured variables from both EAS and BURE.
The coefficient of energy price is significant and having expected sign (negative) in all model
cases. The coefficient of labour input price is also significant and have positive sign in all
models. This suggests labour is a substitute for energy input, given output, capital and
materials are fixed. The measures for elasticities of substitution between labour and energy
are provided in the table below. These results are based on results from the preferred
model (model 4).
Table 3. Estimates of labour-energy elasticity of substitution (All industries)
AES Price elasticity Morishima
EE -5.62 -0.96
LL -0.24 -0.20
EL 1.08 0.89 1.09
LE 1.08 0.18 1.15
Note: EE and LL are the own price elasticities for energy and labour; EL and LE are cross-price elasticities (only being asymmetric in the case of Allen elasticity of substitution). The three measured provided are Allen elasticity of substitution (AES), Price elasticity and Morishima elasticity of substitution between energy and labour.
The own price elasticity estimate shows that 1% increase in energy price could lead to about
0.96% reduction in energy use, when other variables stay the same. The cross-price
elasticity between L-E shows that a 1% increase in energy price could lead to about 0.18%
increase in labour input, when other variables stay the same. The cross-price elasticity
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between E-L is higher (0.89%) suggesting the impact from change in labour price on energy
consumption is higher than the other way around. Overall, results suggest that labour use is
more inelastic in responding to its own and cross-price changes compared to energy use.
There is impact on labour use from a change in energy price, albeit small.
Due to the unavailability of capital and non-capital input price data, we cannot directly
estimate elasticity of substitution nor can we draw any conclusions about the substitution
(or complementarity) between energy and these inputs. . However, given the coefficient for
capital input is significant and positive (in 3 out of 4 models), an increase in capital use tends
to increase energy share in the variable cost. In the case of non-capital inputs, the
coefficients all have negative signs and 3 out of 4 cases are significant, suggesting that an
increase in non-capital material inputs tends to decrease energy cost share.
Estimates at division level for selected industries are provided in the Table A2, Appendix.
Substitution effect between energy and labour is found in majority of the industry divisions
(except for divisions D (Electricity, gas, water and waste services), E (Construction) and M
(Professional, scientific and technical services) where the labour price coefficients are not
significant).
Comparison with existing estimates
There are some existing estimates of elasticities of substitution between labour and energy
from other (international) studies. Table 4 shows the comparison between the estimates
from this study and two other studies (both using US manufacturing data). In general, the
estimates have similar signs, all showing that labour is a substitute for energy. The sizes of
estimates are within comparable range, with the US showing lower energy price elasticity
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but higher labour price elasticity. Both results from Australian and US manufacturing
indicate that cross-price elasticity estimate for EL is larger than LE.
Table 4. Comparison to other international studies, manufacturing industries
Div ABS (this study) Stern (2011) Berndt and Wood (1975)
C AES Price elasticity AES AES Price elasticity
EE -8.91 -1.15
-10.66 -0.49
LL -0.20 -0.17
-1.53 -0.45
EL 1.16 1.01 1.84 0.68 0.2
LE 1.16 0.15 1.84 0.68 0.03
Labour-energy substitution at divisional level
The degree of substitution from labour to energy, or in other words, the impact from energy
price changes on labour use, can be assessed via the estimates of the cross-price elasticities
between labour and energy and vice versa. While it is found that the cross price elasticity
between labour and energy (LE) is rather small (~0.18, in the case of pooling across
industries), estimates for some specific divisions are higher than average. Table 5 shows
estimates of labour-energy substitution elasticities for different industry divisions.
It can be seen from results in Table 5 that the size of L-E cross-price elasticity is
commensurate with the share of labour in the variable cost mix. Industries with higher
labour cost share have lower L-E cross-price elasticities. This is consistent with some earlier
studies showing that input shares have a large effect on the size of the cross-price
elasticities (e.g. Frondel and Schmidt, 2002).
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Table 5. Labour-energy substitution (cross-price elasticity L-E)
ANZSIC Division L-E L share
L Rental, Hiring and Real Estate Services 0.4596 0.5601
A Agriculture, Forestry and Fishing 0.3891 0.6401
I Transport, Postal and Warehousing 0.2991 0.7231
E Construction 0.2746 0.7261
D Electricity, Gas, Water and Waste Services 0.2586 0.7395
B Mining 0.2454 0.7748
R Arts and Recreation Services 0.2274 0.8039
O Public Administration and Safety 0.1709 0.8428
S Other Services 0.1687 0.8511
H Accommodation and Food Services 0.1544 0.8682
C Manufacturing 0.1507 0.8704
K Financial and Insurance Services 0.1368 0.8732
G Retail Trade 0.1312 0.8895
Q Health Care and Social Assistance 0.1217 0.8903
N Administrative and Support Services 0.1114 0.9050
J Information Media and Telecommunications 0.1111 0.9057
M Professional, Scientific and Technical Services 0.0970 0.9055
F Wholesale Trade 0.0928 0.9173
P Education and Training 0.0925 0.9251
Note: L share is the proportion of labour input in the total variable cost consisting of energy and labour inputs.
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V. Conclusion
This paper demonstrates the use of the system of equations approach and the ABS energy
survey data to estimate energy price elasticities and elasticities of substitution between
energy and other inputs. Results show that, on average, an increase in energy price of 1%
could lead to 0.96% decrease in total energy use in the industrial sectors, when other inputs
and output stay the same. Labour is found to be a substitute for energy at both national and
lower divisional level. This suggests that changes in energy prices could also have impacts on
labour market. On average, 1% increase in energy price could lead to 0.18% increase in
labour input, other variables staying the same. On the other hand, an increase of 1% in
labour price could lead to 0.89% increase in energy inputs. Results also suggest that energy
demand is more elastic compared to labour demand in response to its own price or cross-
price changes.
Due to data constraint, both capital and non-capital inputs are assumed fixed in this study.
For this reason, detailed estimates for the substitutability between these inputs and energy
cannot be obtained. Model estimation results, however, suggest higher (lower) energy cost
share with higher level of capital (non-capital) use.
It is argued that the size of cross-price elasticity estimates derived from cross-sectional data
could be dominated by the input cost shares. A dynamic modelling approach utilising time
series data or combination of time series and cross-sectional data may be able to reduce the
cost share effect yet also able to consider changes over time. Therefore, it would be useful
to be able to apply the modelling framework shown in this study to time series or panel
data. This might be possible through a combination of the BREE industry energy
consumption time series data (BREE, 2012) and ABS industry productivity data (ABS, 2007).
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Using such data may be able to shed more insight on capital-energy substitution possibilities
given the availability of input prices at higher aggregation level. Our next research phase in
energy consumption modelling will further investigate this possibility.
References
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Hicks, J. R. 1932, Theory of wages, Macmillan, London.
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Appendixes
Table A1. Estimated coefficients of the energy cost share equation, divisions B, C, D and I
B
C
D
I
lnPE -0.0314 *** -0.0368 *** 0.0029
-0.0321 ***
lnPL 0.0157 *** 0.0184 *** -0.0014
0.0160 ***
lnK 0.0180 *** 0.0169 *** 0.0067
0.0205
lnY 0.0024
-0.0133
0.0178
-0.0010
lnM 0.0032
-0.0145 *** -0.0199
-0.0281
R2 0.7734
0.8937
0.8554
0.8528
Obs. 130
1039
51
264
Table A2. Estimates of own and cross-price elasticities, divisions B, C, D and I
AES P elasticity Morishima
B EE -4.06 -0.91
LL -0.34 -0.27
EL 1.09 0.84 1.11
LE 1.09 0.25 1.16
C EE -8.91 -1.15
LL -0.20 -0.17
EL 1.16 1.01 1.18
LE 1.16 0.15 1.31
D EE -2.80 -0.73
LL -0.35 -0.26
EL 0.99 0.73 0.99
LE 0.99 0.26 0.99
I EE -3.03 -0.84
LL -0.44 -0.32
EL 1.08 0.78 1.10
LE 1.08 0.30 1.14
Note: EE and LL are the own price elasticities for energy and labour; EL and LE are cross-price elasticities (only being asymmetric in the case of Allen elasticity of substitution). The three measured provided are Allen elasticity of substitution (AES), Price elasticity and Morishima elasticity of substitution between energy and labour.