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Capital–energy substitutability in manufacturing sectors: methodological and policy implications

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Abstract

The debate on the capacity of the production system to adequate to a low-carbon economy is addressed by computing the capital–energy substitution elasticities \((\sigma_{KE} )\) for manufacturing sectors. We estimated the \(\sigma_{KE}\) at aggregate level for the whole manufacturing industry and for 10 distinguished sectors for 21 OECD countries (1990–2008); average substitution values are also computed at sector level comparing alternative econometric methods and for separate sub-periods to trace the time dynamics. Such methodology allows assessing how different sectors could respond to the introduction of new (energy saving) technologies, as in terms of factor productivity and substitutability opportunities. This corresponds to a dynamic evaluation of the speed of reaction of each sector in improving its energy efficiency and the capacity to be on track in a sustainable transition. Such assessment also helps policy makers to individuate sectors deserving transition support according to the speed of adjustment of elasticity values over time.

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Notes

  1. The former is a one-factor-one-price elasticity measuring the relative change in use of one factor given a change in the other factor’s price (Berndt and Wood 1979), while the MES is an asymmetric two-factor-one-price elasticity that represents the change in the ratio of factor quantity given a change in one factor price (Blackorby and Russel 1989). See Appendix 1 for further details.

  2. For a broad overview of contributions dealing with the computation of substitution elasticities in the production function, see Table 3 in Appendix 2.

  3. The 21 OECD countries here considered are: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Japan, Luxembourg, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, UK and USA. The choice of the time span trunked at 2008 is driven by the necessity to drop out years after the financial and economic crisis given its heterogeneous impacts on different countries and sectors that would strongly influence econometric results especially in the analysis of the long-run dynamic pattern. Furthermore, estimations including the following years could also be affected by the introduction of abatement policies as fostered by the first commitment period of the Kyoto Protocol (2008–2012). Considering the informative content of substitution elasticities for applied models as CGE and the fact that these parameters represent a source of exogenous information affecting the baseline scenarios (i.e. in absence of abatement policies), for the purpose of this paper we rather focus on the indicated time period.

  4. For the sake of simplicity, hereafter the sectors may be referred to as: Food, Textile, Wood, Paper, Chemical, Minerals, Basic Metals, Machinery eq., Transport eq., Other manufacturing.

  5. To this purpose, van der Werf (2008) compares 10 models used to analyse climate policies and only in three cases materials are included in the production structure. Moreover, among the studies reviewed in the meta-analysis by Koetse et al. (2008), 20 out of 36 cases adopt a KLE model, revealing that excluding materials does not produce a systematic effect.

  6. This database is on Growth and Productivity Accounts, where KLEMS stands for capital (K), labour (L), energy (E), materials (M) and services (S) factors.

  7. An alternative way of applying PIM to GFCF is to calculate the initial capital stock at time t as a function of the sum of the investments in previous years.

  8. In the formulation known as Kmenta approximation, Translog functions can be divided in two parts: the first represents a linearized Cobb–Douglas form while the second embodies the correction due to the divergence of the substitution elasticity value from one (Kmenta 1967).

  9. In contrast, CES functions are non-linear and require non-linear optimization techniques, which may be problematic in implementation and convergence and involve assumptions on the values of other parameters included.

  10. As highlighted in Saunders (2013), for example, the Gallant (Fourier) production function is more flexible than Translog, but it also has the limit of being particularly parameter-intensive and data requirements-intensive.

  11. First, Blackorby and Russel (1989) argued that the Morishima formulation (MES) is superior to AES, because it represents the real curvature of the isoquant and the effects of changes in price or quantity ratios on relative factor shares. More recently, Frondel (2011) has shown that cross price elasticity (CPE) is at the basis for the calculation of both AES and MES and should be favoured also over MES, given that it is more relevant in term of economic content. “The ultimate reason for this conclusion is that cross-price elasticities measure the relative change of only one factor due to price changes of another input, whereas HAES, MES, and SES measure the relative change of a factor ratio due to price changes of these two factors” (Frondel 2011, p. 4603). In the same work is argued that the relative change of a factor ratio seems less important for many applications.

  12. Although the adequacy of estimators depends on specific characteristics of the analysed data, theoretically the between estimator (BE) is particularly adequate for empirical analysis of long-run elasticities (Stern 2012). If the real process determining the observed data is characterized by a dynamic path, BE is the most consistent estimator if there is no correlation between regressors and the error term in non-stationarity cases since it is less affected by measurement errors. If omitted and explanatory variables are correlated, BE is consistent when there is correlation with respect to remainder disturbance, whereas it can be more affected than OLS, panel FE and RE, GMM when there is correlation with individual effects. Nonetheless, Huak and Wacziarg (2009) affirm that BE has minimum bias compared to FE, RE and some GMM formulation because it is consistent in non-stationarity cases (even with misspecified dynamics and heterogeneous coefficients), although explanatory variables may be correlated with individual effects.

  13. Moreover, the corresponding mean value from 5-year estimations of 0.27 is also equal to the long-run result from the aggregate manufacturing sector calculated considering the time period 1975–2008 and applying the Fully Modified OLS (FMOLS) estimator for heterogeneous cointegrated panel data. Long-run results are not reported but are available upon request from the authors.

  14. Specific \(\sigma_{KE}\)-AES values for each estimator used to compute the average values reported in Table 2 are given in Tables 6, 7, 8, 9 in Appendix 2. Full details of single regression outputs are not reported for the sake of simplicity but they are available upon request from the authors.

  15. The Paper and Pulp industry also has an increasing trend, but it is only relative to the last two periods.

  16. They consider the differences in the elasticity values between pre and post 1970s oil crisis.

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Acknowledgements

We acknowledge the financial support of: (1) the European Union D.G. Research with Grant Agreement number 283002 to the research project “Environmental Macro Indicators of Innovation” (EMInInn); (2) the Roma Tre University-INEA-ENEA Consortium; (3) the Italian Ministry of Education, University and Research (Scientific Research Program of National Relevance 2010 on “Climate change in the Mediterranean area: scenarios, economic impacts, mitigation policies and technological innovation”); the University of Roma Tre for financial support to the project EDESMART. We are grateful to the two anonymous reviewers for their suggestions on previous version of the paper. The usual disclaimer applies.

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  1. Department of Economics, Roma Tre University, Via Silvio D’Amico 77, 00145, Rome, Italy

    Valeria Costantini, Francesco Crespi & Elena Paglialunga

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  1. Valeria Costantini
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  2. Francesco Crespi
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Correspondence to Francesco Crespi.

Appendices

Appendix 1: Different formulations of the elasticity of substitution

The Cross Price Elasticity (CPE) is at the basis of the distinction between gross and net substitution introduced by Berndt and Wood (1979) and is strictly linked with the separability conditions assumed in the model. In particular, in KLEM models, taking E and K as separable from L and M, the CPE is an asymmetric one-factor-one-price elasticity that represents the net substitution between E and K and measures the relative change in use of one factor (K) given a change in the other factor’s price (E), keeping output and other input prices fixed. It is the sum of the positive gross price elasticity (which measures the change in E and K demand, holding KE composite input fixed) with the negative expansion elasticity, whose magnitude depends on the cost share of K (in this case output is fixed but the demand for the composite input KE can vary in response to changes in relative prices). Complementarity or substitutability of inputs in the production function depends on which one of the two effects is larger, and the cost share of the two factors have a crucial role, thus changes in energy or capital prices will have different consequences also due to the fact that the capital cost share is usually higher than the energy one.

The Morishima Elasticity of Substitution (MES) is an asymmetric measure of substitution between production factors and, in contrast to AES and CPE, is a two-factor-one-price elasticity that represents the change in the ratio of factor quantity given a change in one factor price. It is positive in almost all cases and the sign is therefore not very useful for distinguishing substitution from complementarity. Moreover, the cost share i will decrease relatively to j (following a rise in pj) only when MES > 1. Blackorby and Russel (1989) show that the MESij can be calculated as the difference between the CPEij and the own price elasticity for input j (CPEjj). As far as AES is concerned, if two inputs are Allen substitutes they will also be MES substitutes, but when AES is negative, it is still likely to have positive MES.

Appendix 2

See Tables 3, 4, 5, 6, 7, 8 and 9.

Table 3 Review of aggregate capital–energy elasticity of substitution estimations
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Table 4 Energy intensity by manufacturing sector
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Table 5 Capital intensity by manufacturing sector
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Table 6 \(\sigma_{KE}\)-AES by manufacturing sector (1990–1994)
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Table 7 \(\sigma_{KE}\)-AES by manufacturing sector (1995–1999)
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Table 8 \(\sigma_{KE}\)-AES by manufacturing sector (2000–2004)
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Table 9 \(\sigma_{KE}\)-AES by manufacturing sector (2005–2008)
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Costantini, V., Crespi, F. & Paglialunga, E. Capital–energy substitutability in manufacturing sectors: methodological and policy implications. Eurasian Bus Rev 9, 157–182 (2019). https://doi.org/10.1007/s40821-018-0114-z

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