A Bayesian Approach to Nonparametric Frontier Model Selection: Application to U.S. Banks Cost Functions

Abstract

This contribution proposes a novel Bayesian approach to nonparametric frontier model selection based on the probabilistic framework of Laplace-type estimators. Our empirical analysis of U.S. banks provides strong evidence in favor of the nonconvexity of cost functions for any given returns to scale assumption. Furthermore, while convex and nonconvex methods agree that the large majority of observations experiences increasing economies of scale, we find conflicting evidence with regard to the economies of scale of the cost function with respect to the convexity assumption for about 20% of the sample. These results have potentially far reaching consequences. For the economic theory, the rejection of the convexity assumption casts an empirical doubt on the validity of fundamental microeconomic results. For the banking practice, the incorrect classification of the economy of scale might lead to false policy recommendation (such as mergers and acquisition).

Keywords: Bayesian analysis, Nonparametric frontier models, Nonconvex cost functions

JEL Classification: C11, D24, G21