“the second-order conditions for optimizing behavior fail, and duality theory fails. The resulting first-order conditions, demand functions, and supply functions become invalid.” In this paper we investigate interfuel (i.e., oil, natural gas, coal and electricity) substitution, using international time series data. In doing so, we investigate interfuel substitution for entire economies as well as within the industrial, residential, transportation and electricity generation sectors of these economies, since the structure of interfuel substitution is different for different sectors of use. Our objective is to improve our understanding of how economic growth, government policies, and the development and implementation of new technologies, will affect interfuel substitution and the demand for energy in the future. We use recent advances in microeconometrics, including duality theory and flexible functional forms. We minimize the potential problem of using a misspecified functional form by employing a wellknown flexible functional form and provide inference, and also a policy perspective, using parameter estimates that (for the first time) are consistent with the theoretical regularity conditions of neoclassical microeconomic theory.

So far, the literature on energy demand and interfuel substitution employed locally flexible functional forms and, in particular, the translog, introduced by Christensen et al. (1975). See, for example, Fuss (1977), Pindyck (1979), Jones (1995) and Urga and Walters (2003). These forms provide the capability to approximate systems resulting from a broad class of generating functions and also to attain arbitrary elasticities of substitutions, although at only one point (that is, locally). However, although locally flexible functional forms provide arbitrary elasticity estimates at the point of approximation, there is evidence that these models fail to meet the regularity conditions of neoclassical microeconomic theory in large regions.

In this paper, we also use a locally flexible functional form to investigate interfuel substitution and to provide a comparison of our results with most of the existing empirical literature. In doing so, however, we use recent, state-of-the-art advances in microeconomet– rics to produce inference consistent with theoretical regularity see, for example, Barnett and Serletis (2008) and Feng and Serletis (2008). In particular, motivated by the widespread practice of ignoring theoretical regularity, we use the normalized quadratic (NQ) cost function, introduced by Diewert and Wales (1987), estimate the corresponding input-output equations subject to the theoretical regularity conditions using methods developed by Diewert and Wales (1987), and produce inference consistent with neoclassical microeconomic theory.

Because the existing major contributions in this area are quite outdated, since their data incorporate few (if any) observations subsequent to the oil price shocks in the 1970s, we use the most recent data (since 1980), published by the International Energy Agency (IEA), for a number of OECD countries as well as for some non-OECD countries for which reliable data are available. In particular, we provide evidence for six high-income countries (Canada, France, Japan, Italy, the United Kingdom and the United States), for five upper-middle to high-income economies (Poland, Hungary, Mexico, Turkey and Venezuela), and for four 3