Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency

This paper considers the estimation of Kum- bhakar et al. (J Prod Anal. doi:10.1007/s11123-012-0303- 1, 2012) (KLH) four random components stochastic fron- tier (SF) model using MLE techniques. We derive the log- likelihood function of the model using results from the closed-skew normal distribution. Our Monte Carlo analysis shows that MLE is more efficient and less biased than the multi-step KLH estimator. Moreover, we obtain closed- form expressions for the posterior expected values of the random effects, used to estimate short-run and long-run (in)efficiency as well as random-firm effects. The model is general enough to nest most of the currently used panel SF models; hence, its appropriateness can be tested. This is exemplified by analyzing empirical results from three dif- ferent applications.