A Monte Carlo study of estimators of stochastic frontier production functions

1. Introduction In recent papers which appeared almost simultaneously, Aigner, Love11 and Schmidt (ALS) (1977) and Meeusen and van den Broeck (1977) proposed a new error specification for frontier production function models. The specification is that the error term is the sum of two components ~ one normal with zero mean, and the other non-positive. ALS refer to a model with this error specification as a ‘stochastic frontier’, since the non-positive component of the disturbance represents the shortfall of actual output from the frontier, while the frontier contains the normal component of the disturbance, and is therefore stochastic. This specification avoids the serious statistical difficulties [discussed by Schmidt (1976) and Greene (1980)] which are encountered in the estimation of full frontiers - that is, in the presence of a purely non-positive error term. Any number of one-sided distributions exist which could plausibly be assumed to represent the distribution of the shortfall of output from the frontier. ALS consider (negative) half-normal and exponential distributions, while Meeusen and van den Broeck consider exponential only. Other possibilities include Gamma [Richmond (1974)] and lognormal [Greene (1980)]. ALS find very little difference in the fit of half-normal and exponential, in two empirical applications. In this paper we will restrict our attention to the half-normal case, which is the case considered in most detail by ALS.