Inferences from Cross-Sectional, Stochastic Frontier Models

Conventional approaches for inference about efficiency in parametric stochastic frontier (PSF) models are based on percentiles of the estimated distribution of the one-sided error term, conditional on the composite error. When used as prediction intervals, coverage is poor when the signal-to-noise ratio is low, but improves slowly as sample size increases. We show that prediction intervals estimated by bagging yield much better coverages than the conventional approach, even with low signal-to-noise ratios. We also present a bootstrap method that gives confidence interval estimates for (conditional) expectations of efficiency, and which have good coverage properties that improve with sample size. In addition, researchers who estimate PSF models typically reject models, samples, or both when residuals have skewness in the “wrong” direction, i.e., in a direction that would seem to indicate absence of inefficiency. We show that correctly specified models can generate samples with “wrongly” skewed residuals, even when the variance of the inefficiency process is nonzero. Both our bagging and bootstrap methods provide useful information about inefficiency and model parameters irrespective of whether residuals have skewness in the desired direction. Simar: Institut de Statistique, Université Catholique de Louvain, Voie du Roman Pays 20, B 1348 Louvain-la-Neuve, Belgium; email [email protected]. Wilson: The John E. Walker Department of Economics, 222 Sirrine Hall, Clemson University, Clemson, South Carolina 29634–1309, USA; email [email protected]. Research support from the “Inter-university Attraction Pole”, Phase V (No. P5/24) and Phase VI (No. P6/03) from the Belgian Government, and from the Clemson University Research Foundation is gratefully acknowledged. We are grateful for comments on earlier versions of this work from Peter Schmidt and from seminar participants at Florida State University, University of Kansas, University of Georgia, Georgia Institute of Technology, Michigan State University, and Texas A&M University, as well as participants at the European Productivity Workshop in Brussels, July 2005, and the Econometric Society European Meetings in Vienna, August 2006. Any remaining errors are solely our responsibility.