Normal-beta exponential stochastic frontier model: Maximum simulated likelihood approach

Abstract

This paper considers the beta exponential distribution as a distribution function of inefficacy score in a stochastic frontier model. The beta exponential distribution is a three-parameter distribution, and it is more flexible than commonly used probability density functions in a stochastic frontier model (SFM). This new model, a “Normal-Beta Exponential SFM”, nests another five SFMs. This paper presents a simulated log-likelihood function and simulated inefficiency estimator of a normal-beta exponential SFM, a closed form log-likelihood function and closed form inefficiency estimator of a normal-weighted exponential SFM, and an empirical study using a normal-beta exponential SFM. In our empirical study, we have used a likelihood ratio test to compare the performance of SFMs and a normal-beta exponential SFM fits the data better than other nested special case SFMs. Furthermore, the empirical result shows that parameters of a normal-beta exponential SFM can be estimated with less standard error or high certainty than a normal-gamma SFM.