A Combined Structural and Flexible Functional Approach for Modeling Energy Substitution

Abstract In theory, a flexible functional form can approximate an arbitrary elasticity of substitution; however, when faced with an actual finite data set, a parsimonious parametric functional form that imposes more structural restrictions may yield a more accurate approximation about underlying substitution. Therefore, for uncovering the underlying degree of input substitution a data-exploration strategy is suggested that combines the parametric family of a system of quadratic log-ratio demand equations and conventional flexible functional forms. This allows testing for more restrictive hypotheses about substitution. These issues are examined in the context of interfuel substitution at the two-digit SIC level for manufacturing industries in Ontario and Quebec, Canada. A basic tenet of the approach of this article is that although letting data speak for itself is preferred, economic theory should be used wherever possible, and a simple model is preferable to complicated models unless the evidence suggests otherwise. Given the variations of technologies, managerial behavior, and speed of adjustment across manufacturing sectors, the existence of a single optimal model is questioned. In fact, out of 39 industries examined, suitable models are found for 30 industries. Out of the 30, 18 can be modeled by the relatively more restricted quadratic log-ratio specifications and 12 by the more general flexible functional forms. By using a combined structural and flexible functional approach, this article obtains more precise estimates of the elasticities of substitution and models more likely to satisfy monotonicity and concavity conditions than those obtained by considering the conventional search procedures within a flexible functional approach. It is also interesting to note that, unlike previous studies of interfuel substitution, some industries display biased technological changes, and some appear to possess a dynamic adjustment process consistent with an error-correction mechanism composed of both derivative and proportional control mechanisms.