Moment Diagnostics and Quasi-Maximum Likelihood Estimation for the Stochastic Frontier Model

The distributional specifications for the composite regression error term most often used in Stochastic Frontier Analysis (SFA) are inherently bounded as regards their skewness and excess kurtosis coefficients. These bounds provide simple diagnostic tools and model selection/rejection criteria for empirical studies which appear to have been overlooked by practitioners. We derive general expressions for the skewness and excess kurtosis of the composed error term in the stochastic frontier model based on the ratio of standard deviations of the two separate error components as well as theoretical ranges for the most popular empirical specifications. Simulation results are presented to detail the small-sample effects as well as to speak towards the practical relevance of these diagnostic tools and the consequences of misspecification. These insights lead us to examine quasi-maximum likelihood estimation (QMLE) of the ubiquitous Normal-Half Normal stochastic frontier model and the properties of the Skew-Normal QMLE, more generally.