Estimating Fixed Effects Stochastic Frontier Panel Models Under ‘Wrong’ Skewness with an Application to Health Care Efficiency in Germany

Abstract

Typically, the error term in stochastic frontier models is assumed to be positively skewed; however, efficiency scores are biased if this assumption is violated. This paper considers the case in which also negative skewness is allowed in the model. In contrast to other approaches, this skewness is not assumed to be a small sample issue, but is rather related to inefficiency in the market. The paper discusses estimation of a stochastic frontier panel model with unobserved fixed effects. On the one hand, the parameters can be estimated via integrating out nuisance parameters by means of marginal maximum likelihood. On the other hand, we propose an approximation based on closed skew normal distributions which turns out to be accurate enough for maximum likelihood estimation. Simulations assess finite sample performances of estimators and show that all model parameters and efficiency scores can be estimated consistently regardless of positive or negative inefficiency skewness. An empirical analysis to unravel inefficiencies in the German healthcare system demonstrates the practical relevance of the model.