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Towards a carbon-neutral economy: The dynamics of factor substitution in Germany


This paper investigates the elasticity of substitution between four inputs—capital, labor, energy, and material—with the translog cost approach for a wide range of industries in Germany by incorporating the slow adjustment process in factor substitution. To this end, we take advantage of EU KLEMS database covering a wide range of industries and consider two models. The first is the static model, in which instantaneous and complete substitution adjustments are assumed. The other model, referred to as dynamic, takes into account the slow adjustment process and applies this to the cost share equations which are estimated using Zellner’s seemingly unrelated regression. The empirical results suggest that (i) the dynamic models have greater explanatory power than the static models; (ii) the production process at the national or industry level in Germany is mainly characterized by a complementarity or weak substitutability between energy and other inputs, which limits German government’s ability to reduce energy use through factor substitution; (iii) among four factor prices, energy demand seems to be more sensitive to changes in the price of material, followed by labor. Hence, an increase in energy prices can be efficient to some extent in order to reduce energy use; (iv) there is a substantial industry heterogeneity in Germany in terms of both input substitution and its adjustment process. Therefore, strategies to mitigate CO2 emissions through input substitution channel should be designed at the industry level based on the industry-specific needs and peculiarities. It is because well-designed comprehensive policies that consider different structures of industries could help to achieve a carbon-neutral economy for Germany.

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  1. 1.

    In 2015, CO2 contributed 73% of global GHG emissions and the largest source of GHG emissions was the fossil fuel combustion (IEA 2018).

  2. 2.

    Although some of these studies slightly increase the number of industries, they mainly focus on panel data series for the EU or OECD countries including Germany and do not report country- or industry-specific results (Fiorito and van den Bergh 2016; Wurlod and Noailly 2018).

  3. 3.

    For further information on theoretical derivations of the static and dynamic models, see Urga and Walters (2003); Cho et al. (2004); Coelli et al. (2005); Lin and Li (2014); Li and Lin (2016).

  4. 4.

    Although we calculate the AES in the “Empirical analysis” section in order to obtain the OPE and CPE, we do not report it in the study.

  5. 5.

    The standard errors of OPEii and CPEij can be calculated as: \( \mathrm{SE}\left({\mathrm{OPE}}_{ii}\right)=\frac{1}{s_i}\mathrm{SE}\left({\beta}_{ii}\right) \) and \( \mathrm{SE}\left({\mathrm{CPE}}_{ij}\right)=\frac{1}{s_i}\mathrm{SE}\left({\beta}_{ij}\right) \) (Koetse et al. 2008; Wurlod and Noailly 2018).

  6. 6.

    The reason for choosing March 2008 version is that the following releases or revisions after March 2008 do not include data for energy and materials.

  7. 7.

    For further information on the methodology and sources of the EU KLEMS database which is also available at, see Timmer et al. (2007).

  8. 8.

    The EU KLEMS database has negative values for capital in some industries, such as agriculture. The main reason for this is the method of calculation for capital which equals to value added minus labor compensation (LAB). In other words, labor is largely self-employed in some industries and the wage rate of it is often unobserved. For this reason, it is assumed that the self-employed received the same hourly wages as employees in these industries. This, in turn, leads to negative values for capital. For further information, see Jager 2016.

    Following Wurlod and Noailly (2018), some aggregates and industries are dropped from the estimations due to both data availability and negative values for CAP in order to obtain more robust and theoretically meaningful estimates. The aggregates and industries removed due to missing observations, data transformation process, and Stata codes used in the estimations can be found at electronic supplementary material.

  9. 9.

    A number of studies have applied the SUR method to estimate cost share equations (Ma et al. 2009; Lin and Li 2014; Li and Lin 2016; Wang et al. 2018; Liu et al. 2018).

  10. 10.

    To save space, we do not report all regression results here, but they can be found in the Appendix. See Table 10.

  11. 11.

    Note that although aggregates G, I, JtK, and LtQ have lower values than other aggregates, these coefficients are not statistically significant. For example, the adjustment parameters of energy (λE) for TOT, D, E, and F are 0.312, 0.318, 0.647, and 0.484, respectively, and all these parameters are statistically significant at conventional levels. On the other hand, these parameters for G, I, JtK, and LtQ are 0.159, 0.132, 0.101, and 0.145, respectively. As clearly seen, all these lower values are statistically insignificant.

  12. 12.

    See Table 11 for all regression results.

  13. 13.

    Empirical rejection of concavity may indicate a misspecification problem in the underlying cost function. Therefore, concavity of the second partial derivative should be investigated as a robustness check. To this end, following Baum and Linz (2009), this paper obtains Hessian matrix of second partial derivatives. As discussed by Diewert and Wales (1987) and Ryan and Wales (2000), this condition will be satisfied if and only if the matrix is negative semi definite. Therefore, the presence of positive eigenvalues indicates that the assumption of concavity of the cost function is not satisfied by the estimates. The obtained results show that the sign of eigenvalues under the static and dynamic specifications with constraint model is negative. For example, while 14 out of 84 eigenvalues are positive for both unconstraint static and dynamic specifications, none of the eigenvalues is greater than 0.05 for constraint models. The local concavity which is imposed at a reference time point (prices are rebased in the year 1978) also confirms these findings. To save space, these results are not included in the paper. They are available from the author upon request.

  14. 14.

    The reported cross price elasticities in Berndt and Wood (1975) are about − 0.15 and − 0.18 for US manufacturing industry. The computed CPEs in Fuss (1977) are − 0.004 and − 0.050 for Canadian manufacturing industry. Westoby and McGuire (1984) and that capital and energy are complements with the value of − 0.0038 and − 0.3042 for the UK electricity industry.

  15. 15.

    Welsch and Ochsen (2005) show that energy is a complement to material for Germany. The computed parameters are as follows: CPEME= − 0.126, CPEEM= − 1.278, MESME= − 0.733, and MESEM= − 0.392.

  16. 16.

    Note that the comparison of the studies at the industry level is rather difficult. This is because industrial coverage in terms of amount and classification varies across nearly all studies as they use different data sources and cover less industries than in our study. However, unlike the other studies, Kemfert (1998) and Kemfert and Welsch (2000) use the same data source and industry classification. Therefore, even if we do not report in Table 9, we will briefly discuss their industrial findings in the main text.

  17. 17.

    While Kemfert (1998) and Kemfert and Welsch (2000) estimate the original CES production function using non-linear estimation process, we estimate cost share equations derived from TPF using the linear estimation technique.

  18. 18.

    While Falk and Koebel (1999) consider 27 manufacturing industries, Welsch and Ochsen (2005) present the results for the entire German economy.

  19. 19.

    Fiorito and van den Bergh (2016) calculate the price elasticities for manufacturing sector (D) with TPF for seven countries including Germany using the EU KLEMS database over the period 1978–2005 and therefore is the closest article to our study in terms of data source, time period, and estimation methodology


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I would like to thank the anonymous reviewers and Eckhardt Bode for their constructive comments and suggestions that helped me to improve the paper. I am solely responsible for any remaining error.

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Correspondence to Sedat Alataş.

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Alataş, S. Towards a carbon-neutral economy: The dynamics of factor substitution in Germany. Environ Sci Pollut Res 27, 26554–26569 (2020).

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  • CO2 emissions
  • Input substitution
  • Translog cost function
  • Germany