Stochastic frontier models for discrete output variables

This chapter revises the literature on discrete output stochastic frontier models. We suggest an encompassing framework within which to develop new models of production frontier when the output variable is discrete-valued. We discuss specific applications of the framework. In particular, the identification of inefficiency in binary, count and ordered output models is discussed. We provide an illustration of how existing models can be extended to allow for heterogeneous inefficiency across units. This provides the critical stepping stone towards developing panel data extensions and models allowing for endogenous regressors. Finally, semiparametric estimation via local likelihood is discussed.