Imposing monotonicity and concavity restrictions into stochastic cost frontiers: A Bayesian approac

Stochastic frontier models are designed to measure a firm's efficiency using a composed error term. The stochastic cost frontier divides any deviation from the frontier into a normal random error reflecting statistical noise beyond the firm's control and a non-negative one-sided stochastic error reflecting firm-specific technical inefficiency.;Measures of firm efficiency appear quite sensitive to the choice of the functional form used to approximate an unknown cost frontier. A misspecification error due to fitting a functional form lacking flexibility is likely to overstate the firm's inefficiency measure. This fact indicates the need to choose very flexible forms to approximate the unknown cost function. At the other extreme, most flexible functional forms frequently violate monotonicity and concavity conditions implied by economic theory. The inability of the flexible cost function form to comply with economic theory might also lead to inaccurate measures of firm inefficiency. This study incorporates monotonicity and concavity conditions using the approach proposed by Terrell (1996) into the Bayesian Stochastic cost frontier of Koop, Osiewalski, and Steel (1994). The empirical exercise is based on a cross-sectional data set of 123 utility companies in the United States.;The study examines two points related to stochastic frontier models. First, an application using several functional forms ranging from restrictive (e.g., Cobb-Douglas) to a very flexible form (e.g., Fourier) compares the inefficiency outcomes of different frontiers. Second, it examines the robustness of these inefficiency measures statistically. For more flexible forms, this study also imposes monotonicity and concavity restrictions suggested by the economic theory using Bayesian statistical approach. The Bayesian approach also allows for the calculation of standard errors required for statistical inference which are not readily available in frequentist stochastic frontier models. Gibbs sampler is used to analyze the posterior densities of parameters of interest, and an accept-reject algorithm was utilized to impose monotonicity and concavity restrictions during the sampling process.;Results indicate that efficiency measures rise when moving from Cobb-Douglas to translog, or translog to Fourier specification. However, the study also finds the measures of firm efficiency are imprecise, both for individual firms and in comparisons across firms. Our results suggest that much can be learned from the stochastic frontier models although no conclusive statement about individual firms was found. These results appear consistent with some earlier studies of stochastic frontiers using classical econometric techniques.