Bayesian clustering of distributions in stochastic frontier analysis

In stochastic frontier analysis, firm‐specific efficiencies and their distribution are often main variables of interest. If firms fall into several groups, it is natural to allow each group to have its own distribution. This paper considers a method for nonparametrically modelling these distributions using Dirichlet processes. A common problem when applying nonparametric methods to grouped data is small sample sizes for some groups which can lead to poor inference. Methods that allow dependence between each group’s distribution are one set of solutions. The proposed model clusters the groups and assumes that the unknown distribution for each group in a cluster are the same. These clusters are inferred from the data. Markov chain Monte Carlo methods are necessary for model‐fitting and efficient methods are described. The model is illustrated on a cost frontier application to US hospitals.