Tuesday, April 20, 2010

Substitutability of Energy and Capital

There is a large empirical literature on the issue of whether capital and energy are substitutes or complements and on how substitutable they are (e.g. Berndt and Wood, 1979; Apostolakis, 1990; Thompson and Taylor, 1995; Frondel and Schmidt, 2002; Thompson, 1997; Stern, 2007; Koetse et al., 2008). Substitutability can be measured using the Hicks or direct elasticity of substitution, which measures how the ratio of two inputs changes in response to a change in the ratio of their prices while holding output constant. However, most of the empirical literature focuses on the concept of (price) substitutability versus (price) complementarity. Two inputs are said to be p-substitutes (p-complements) if the quantity of one increases (decreases) when the price of the other increases. Blackorby and Russell (1989) correctly state that “the elasticity of substitution concept, as originally conceived by Hicks, has nothing to do with the substitute/complement taxonomy” (885). That discrimination should be made according to the sign of the cross-price elasticity, which is necessarily the same as the sign of the Allen-Uzawa substitution elasticity.

Econometric studies have come to varying conclusions regarding whether capital and energy are complements or substitutes (Berndt and Wood, 1979; Apostolakis, 1990). Based on the differences between time series and cross-sectional results, Apostolakis (1990) concluded that capital and energy act more as substitutes in the long run and more as complements in the short run. Frondel and Schmidt (2002) revisit the studies reviewed by Apostolakis and additional data from Germany and find that evidence of complementarity only occurs in cases where the cost share of energy is small. When materials are included the cost shares of capital and energy are smaller and a finding of complementarity is more likely. More time series studies than cross-sectional studies have data on materials use. Obviously the cost of materials should be included if possible and econometric results that exclude this variable are likely to be biased. Similarly, Berndt and Wood (1979) found that econometric studies using the KLE specification (i.e. not including materials) and engineering studies indicate substitution, while cost functions with the KLEM specification indicate complementarity.

The Morishima elasticity of substitution (MES) is close to Hicks’ original idea of the elasticity of substitution. However, it is asymmetric – the elasticity takes different values, depending on whether the price of energy or capital increases. Koetse et al. (2008) conduct a meta-analysis of the MES and the cross-price elasticity (CPE) between capital and energy for an increase in the price of energy. Their base case finds that energy and capital are complements and that the MES is 0.216. The MES estimated using panel and cross-section data is greater (0.592 and 0.848, respectively) while the CPE is positive in cross-sectional data. It is likely that these larger values do reflect long-run elasticities and the lower values short-run elasticities (Stern, 2009). Koetse et al. (2008) found that exclusion of materials had no significant effect.

Kaufmann and Azary-Lee (1991) demonstrate the importance of accounting for the physical interdependency between manufactured and natural capital. They use a standard production function to account for the indirect energy used elsewhere in the economy to produce the capital substituted for fuel in the U.S. forest products sector. They found that from 1958 to 1984 the indirect energy costs of capital offset a significant fraction of the direct fuel savings. In some years, the indirect energy costs of capital are greater than the direct fuel savings. The results of Kaufmann and Azary-Lee’s analysis are consistent with the arguments made above that substitution possibilities are different at macro and micro levels.

It seems that, in conclusion, that the micro-level elasticity of substitution between capital and energy is less than unity, especially in the short-run. Capital and energy are likely p-complements in the short-run and p-substitutes in the long-run.

Apostolakis, B. E. (1990). “Energy-capital substitutability / complementarity: the dichotomy.” Energy Economics 12: 48-58.
Berndt, E. R. and D. O. Wood (1979). “Engineering and econometric interpretations of energy-capital complementarity.” American Economic Review 69: 342-354.
Blackorby, C. and R. R. Russell (1989). “Will the real elasticity of substitution please stand up? (A comparison of the Allen/Uzawa and Morishima elasticities).” American Economic Review 79: 882-888.
Frondel, M. and C. M Schmidt (2002). “The capital-energy controversy: An artifact of cost shares?” The Energy Journal 23(3): 53-79.
Kaufmann, R. K. and I. G. Azary-Lee (1991) “A biophysical analysis of substitution: Does substitution save energy in the U.S. forest products industry?” In D. P. Bradley and P. O. Nilsson (eds.) Ecological Economics: Implications for Forest Management and Practice, The Swedish University of Agricultural Sciences, Garpenberg, 111-123.
Koetse, M. J., H. L. F. de Groot, and R. J. G. M. Florax (2008) Capital-energy substitution and shifts in factor demand: A meta-analysis, Energy Economics 30: 2236–2251.
Stern D. I. (2009) Interfuel substitution: A meta-analysis, Environmental Economics Research Hub Research Report 33.
Thompson, H. (1997). “Substitution elasticities with many inputs.” Applied Mathematics Letters 10(3): 123-127.
Thompson, P. and T. G. Taylor (1995). “The capital-energy substitutability debate: A new look.” The Review of Economics and Statistics 77: 565-569.

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