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* Please do not quote results without author’s permission.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

ABS, 2007, ‘Information paper: Experimental Estimates of Industry Multifactor Productivity’, available at http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/5260.0.55.0012007?OpenDocument

Berndt, E. R. and Wood, D. O. 1975, ‘Technology, prices and the derived demand for energy’, Review of Economics and Statistics, vol. 57, pp. 259–68.

Blackorby, C. and Russell, R. R. 1975, ‘The partial elasticity of substitution’, Economics Discussion Paper 75-1, University of California, San Diego.

BREE, 2012, ‘Australian Energy Statistics’, available at http://bree.gov.au/publications/aes-2012.html

Cao, K., Wong, J. and Kumar, A. (2012), ‘Modelling the National Greenhouse and Energy Reporting System (NGER) energy consumption under-coverage’, Australian Bureau of Statistics (ABS) research paper, available at http://www.abs.gov.au/ausstats/abs@.nsf/mf/1351.0.55.040

Cao, K., Wong, J. and Kumar, A. (2013), ‘Modelling the National Greenhouse and Energy Reporting System (NGER) energy consumption under-coverage’, Australian Economic Review, upcoming June 2013 issue.

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Coelli, T., Rao, D. S. P., O’Donnell, C. J. and Battese, G. E. 2005, An Introduction to Efficiency and Productivity Analysis, Springer, New York.

Frondel, M. and Schmidt, C. M. 2002, ‘The capital-energy controversy: an artefact of cost share?’, The Energy Journal, vol. 23, no. 3, pp. 53-79.

Frondel, M. 2011, ‘Modelling energy and non-energy substitution – a survey of elasticities’, Ruhr Economic papers, Ruhr-Universitat Bochum, Essen, Germany.

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Hick, J. R. and Allen, R. G. D. 1934a, ‘A reconsideration of the theory of value, part I’, Economica, vol. 1, pp. 52–76.

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Hicks, J. R. 1932, Theory of wages, Macmillan, London.

Hicks, J. R. and Allen, R. G. D. 1934b, ‘A reconsideration of the theory of value, part II’, Economica, vol. 1, pp. 196–219.

Koetse, M. J., de Groot, H. L. F. and Florax, R. J. G. M. 2008, ‘Capital-energy substitution and shifts in factor demand: a meta-analysis’, Energy Economics, vol. 30, pp. 2236-2251.

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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.