Inference by the m out of n bootstrap in nonparametric frontier models

Inference by the m out of n bootstrap in nonparametric frontier models

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Article ID: iaor20116972
Volume: 36
Issue: 1
Start Page Number: 33
End Page Number: 53
Publication Date: Aug 2011
Journal: Journal of Productivity Analysis
Authors: ,
Keywords: estimation, Monte Carlo method, Statistics: bootstrap, free disposal hull
Abstract:

It is well‐known that the naive bootstrap yields inconsistent inference in the context of data envelopment analysis (DEA) or free disposal hull (FDH) estimators in nonparametric frontier models. For inference about efficiency of a single, fixed point, drawing bootstrap pseudo‐samples of size m < n provides consistent inference, although coverages are quite sensitive to the choice of subsample size m. We provide a probabilistic framework in which these methods are shown to valid for statistics comprised of functions of DEA or FDH estimators. We examine a simple, data‐based rule for selecting m suggested by Politis et al. (2001), and provide Monte Carlo evidence on the size and power of our tests. Our methods (i) allow for heterogeneity in the inefficiency process, and unlike previous methods, (ii) do not require multivariate kernel smoothing, and (iii) avoid the need for solutions of intermediate linear programs.

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