This chapter reviews recent contributions to the area of stochastic frontiers models (SFM) for the analysis of discrete outcomes. More specifically, we discuss models for binary indicators (probit-SFM), ordered categorical data (ordered logit SMF) and discrete outcomes (Poisson SFM).
All these models are mixtures of a standard distribution with an asymmetric distribution. This allows us to frame the discussion within a general framework from which most SFM can be derived. Because many of these models might lack a closed form likelihood function, we suggest the use of Maximum Simulated Likelihoods to estimate the parameters of each model. The latter method is easy to implement in a modern computer and the unknown likelihood can be approximated with arbitrary accuracy using low discrepancy sequences such as Halton sequences.