Estimating a mixture of stochastic frontier regression models via the em algorithm: A multiproduct cost function application

Abstract.

Researchers have become increasingly interested in estimating mixtures of stochastic frontiers. Mester (1993), Caudill (1993), and Polachek and Yoon (1987), for example, estimate stochastic frontier models for different regimes, assuming sample separation information is given. Building on earlier work by Lee and Porter (1984), Douglas, Conway, and Ferrier (1995) estimate a stochastic frontier switching regression model in the presence of noisy sample separation information. The purpose of this paper is to extend earlier work by estimating a mixture of stochastic frontiers assuming no sample separation information. This case is more likely to occur in practice than even noisy sample separation information. In order to estimate a mixture of stochastic frontiers with no sample separation information, an EM algorithm to obtain maximum likelihood estimates is developed. The algorithm is used to estimate a mixture of stochastic (cost) frontiers using data on U.S. savings and loans for the years 1986, 1987, and 1988. Statistical evidence is found supporting the existence of a mixture of stochastic frontiers.