Bootstrapping Efficiency Probabilities in Parametric Stochastic Frontier Models

Parametric stochastic frontier models yield firm-level technical efficiency measures based on estimates of parameters from truncated normal distributions. Using boot- strapped estimates of these parameters and the parametric probability statements that they imply, this study is concerned with inference techniques on maximal efficiency for the stochastic frontier model. A non-standard multivariate distribution yields proba- bilities that each firm is efficient, while a bootstrap algorithm incorporates the sampling variability of the underlying parameters. The technique provides unique maximal effi- ciency measures that are relative (as opposed to absolute), that allow efficiency state- ments on subsets of firms based on secondary firm characteristics, and that account for all sources of variability in the analysis. Applications to a cost function of U.S. banks and to a production function for Texas electric utilities are considered.