Asymptotic Distribution of the Maximum Likelihood Estimator for a Stochastic Frontier Function Model with a Singular Information Matrix

Abstract

This article has investigated the asymptotic distribution of the maximum likelihood estimator in a stochastic frontier function when the firms are all technically efficient. For such a situation, the true parameter vector is on the boundary of the parameter space, and the scores are linearly dependent. The maximum likelihood estimator is shown to be a mixture of certain truncated distributions. The maximum likelihood estimates for different parameters may have different rates of convergence. The model can be reparameterized into one with a regular likelihood function. The likelihood ratio test statistic has the usual mixture of chi-square distributions as in the regular case.