Estimating efficiencies from frontier models with panel data: A comparison of parametric, non-parametric and semi-parametric methods with bootstrapping

The aim of this article is first to review how the standard econometric methods for panel data may be adapted to the problem of estimating frontier models and (in)efficiencies. The aim is to clarify the difference between the fixed and random effect model and to stress the advantages of the latter. Then a semi-parametric method is proposed (using a non-parametric method as a first step), the message being that in order to estimate frontier models and (in)efficiences with panel data, it is an appealing method. Since analytic sampling distributions of efficiencies are not available, a bootstrap method is presented in this framework. This provides a tool allowing to assess the statistical significance of the obtained estimators. All the methods are illustrated in the problem of estimating the inefficiencies of 19 railway companies observed over a period of 14 years (1970-1983). © 1992 Kluwer Academic Publishers