Energy-capital substitution and the rebound effect

Mr Steve Sorrell, Sussex Energy Group, SPRU, University of Sussex 

A long-standing controversy within energy economics is whether energy and capital may be considered as ‘substitutes’ or ‘complements’. Despite more than a hundred empirical studies over the last 30 years, there is little sign of consensus on this topic. The issue is also relevant to another long-standing controversy in energy economics, namely the size of any ‘rebound effect’ from improved energy efficiency. Several authors have suggested that:

“the greater the ease of substitution between energy and other factors of production, the larger will be the rebound effect.”

This paper provides an overview of the literature on energy-capital (E-K) substitution and highlights the implications of this for the rebound effect. It clarifies some important theoretical and methodological issues relevant to estimating E-K substitution and highlights a number of difficulties in how these studies have been interpreted. It argues that the relationship between E-K substitution and the rebound effect is more complex than above statement suggests.

The paper first clarifies the different definitions of the ‘elasticity of substitution’ and shows how the lack of consistency in the use of these definitions and the lack of clarity in the relationship between them combine to make the empirical literature both confusing and contradictory. While the majority of empirical studies use the sign of the Allen-Uzawa elasticity of substitution (AES) to classify inputs as ‘substitutes’ or ‘complements’; this measure has a number of drawbacks and its quantitative value lacks meaning. Alternatives are available, but these have yet to gain widespread use. While most empirical studies estimate the AES between different pairs of inputs, energy-economic models require assumptions about the Hicks Elasticity of Substitution (HES) between different ‘nests’ of inputs. The two measures can be difficult to relate, owing to differences in definition, functional form, assumptions about ‘separability’, the treatment of technical change, nesting structures and sectoral aggregation. These multiple differences call into question the empirical basis of many energy-economic models.

The paper argues that the above statement on the ease of substitution and the rebound effect is misleading. A more precise statement should, first, refer to ‘energy services’ (or ‘effective energy’) rather than energy; second, clarify that the elasticity in question is the AES between energy services and a composite of other inputs; third, include the qualification that this only applies when energy services can be considered to be separable from this composite; and fourth, clarify that this conclusion derives from a particular nesting structure in a CES production function. Since the majority of empirical studies use Translog cost functions, measure energy rather than energy services, do not impose the same (or sometimes any) separability restrictions and estimate the AES between energy and individual inputs, they do not provide a direct test of the above statement. For similar reasons, such studies appear to be of little value for energy-economic models.

It is concluded that an empirical finding that energy is a weak AES substitute for another factor, or even a complement to that factor, is not necessarily inconsistent with the potential for large rebound effects, or even backfire from certain types of energy efficiency improvement.