Skewness Issues in Quantifying Efficiency : Insights from Stochastic Frontier Panel Models Based on Closed Skew Normal Approximations

Abstract

Typically, the inefficiency 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 negative skewness is also allowed in the model. The paper discusses estimation of a stochastic frontier panel model with unobserved fixed effects without having to identify additional parameters that determine skewness of inefficiency. 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 sufficiently accurate for maximum likelihood estimation. Simulations assess the finite sample performance 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.