On the Consistency of Maximum Likelihood Estimation of Monotone and Concave Production Frontiers

Banker and Maindiratta (1992) provides a method for the estimation of a stochastic production frontier from the class of all monotone and concave functions. A key aspect of their procedure is that the arguments in the log-likelihood function are the fitted frontier outputs themselves rather than the parameters of some assumed parametric functional form. Estimation from the desired class of functions is ensured by constraining the fitted points to lie on some monotone and concave surface via a set of inequality restrictions. In this paper, we establish that this procedure yields consistent estimates of the fitted outputs and the composed error density function parameters.