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Capital-energy substitution in manufacturing for seven OECD countries: learning about potential effects of climate policy and peak oil

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The simultaneous influence of increasing oil scarcity, greenhouse gas control and renewable energy targets will result in a future of sustained energy prices. Whether modern economies can find a smooth path away from fossil fuels is a fundamental socio-economic and political question, which according to standard economics depends to a large extent on the degree of substitution between energy and capital. We study this issue by modelling the manufacturing sector with a translog cost function in seven OECD countries using the EU-KLEMS database for the period 1970–2005. After a literature survey, different production structures accounting for input substitution, returns to scale and technical change are estimated, and substitution elasticities are derived. Our results indicate a general complementarity or weak substitution relationship between energy and capital, suggesting that an increase in energy price, e.g. due to climate policy or scarcer fossil fuels, will likely reduce capital inputs, which might lead to a lower output of manufacturing.

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  1. When s → 1 the function becomes the Cobb-Douglas. For s → ∞, we obtain the linear (perfect substitutes) function; for s → 0, we get the Leontief (perfect complements) function.

  2. Heady and Dillon (1962) explicitly considered a Taylor series expansion in logarithms using a second-degree polynomial (later called translog) and a square root transformation, which took on as a special case the generalized linear production function introduced by Diewert (1971).

  3. An additional drawback of the CES is that the elasticity of substitution is the same for all inputs.

  4. For more details, the interested reader should consult surveys by Frondel (2001), Koetse et al. (2008), Sorrell (2008) and Stern (2007).

  5. Since Berndt and Wood’s contribution, the Cobb-Douglas and CES production functions lost appeal in research, and attention shifted to the four-input translog cost specification.

  6. Value added includes the contribution to production of a heterogeneous set of capital inputs, like residential buildings and financial products; these are joined into reproducible capital inputs (instead of being attributed to rent). For a review of studies estimating capital services, see Baldwin and Gu (2007).

  7. Datasets and estimation procedures can be accessed at

  8. We use the 2008 EU-KLEMS release, as the 2009 update does not include energy and materials. We opted for employing all available information as this meant that for most countries periods with important changes in energy prices could be included. EU-KLEMS input prices and derived cost shares are reported in Annexes 1 and 2, respectively.

  9. While for many countries, nominal Supply-Use tables (SUTs) are available since 1995, and few countries have SUTs going back to 1980 or earlier. Here, input-output tables have been used to derive measures of E, M and S. Energy input is defined as all energy mining products (10−12), oil refining products (23) and electricity and gas products (40). All products from industries 50−99 are included as services; the remaining products are classified as materials.

  10. The main reason to use a cost function instead of a production function is to circumvent the general problem that input quantities are not likely to be exogenous at the aggregate level, violating the necessary conditions for unbiased parameters (Binswanger 1973). The use of prices in the estimation solves the endogeneity problem, since they are more likely to be exogenous than the quantities (Diewert 1974).

  11. In the constrained model, the series have been rebased in the year 1985 to minimize positive eigenvalues and attain function concavity .


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Correspondence to Giancarlo Fiorito.


Appendix 1

Fig. 2
figure 2

Input prices over time (EU-KLEMS). Note: starting years are for France: 1981, Spain: 1980, Germany: 1978, Japan: 1973, Italy, UK and USA: 1970

Appendix 2

Table 7 EU-KLEMS input shares

Appendix 3

Table 8 Cost function parameters obtained with the constrained model
Table 9 Cross-price and direct elasticities obtained with the constrained model

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Fiorito, G., van den Bergh, J.C.J.M. Capital-energy substitution in manufacturing for seven OECD countries: learning about potential effects of climate policy and peak oil. Energy Efficiency 9, 49–65 (2016).

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