Parametric Efficiency Tests, Economies of Scale, and Input Demand in U.S. Electric Power Generation

Duality theory has been applied increasingly in recent years to study the structure of production. A major advantage of using duality theory is that systems of input demand equations can be derived by simple differentiation, facilitating the use of flexible functional forms. Also, use of duality theory makes it possible to choose a representation of the technology which has desirable properties for estimation, such as exogeneity of the regressors. However, the use of a dual representation of production structure is appropriate only if the corresponding maintained hypothesis concerning economic behavior (e.g., cost minimization or profit maximization) is valid. The perceived advantages of the dual approach to studying production structure have led to some applications in which the maintained hypothesis concerning economic behavior is unlikely to be appropriate. For example, neoclassical cost functions have been used to study the characteristics of production in regulated industries,' despite an extensive theoretical literature indicating that a profit maximizing regulated firm would not minimize costs subject to market prices.2 In this paper we propose a generalized cost function that retains the principal advantages of the neoclassical cost function but does not require that cost minimization subject to market prices be imposed as a maintained hypothesis. In our model, firms are assumed to base their production decisions on unobservable shadow prices which reflect the effects of regulation on the effective prices of inputs. Parametric tests for cost minimization are obtained by expressing shadow prices as functions of market prices. The generalized cost function is estimated with data for regulated electric utilities. The parametric restrictions corresponding to cost minimizing behavior subject to market prices are rejected, implying that the use of a neoclassical cost function is not appropriate in this application.3