Inference by subsampling in nonparametric frontier models

This paper provides a simple, tractable bootstrap for use with Data Envelopment Analysis (DEA) estimators in nonparametric frontier models. It is well-known that a naive bootstrap yields inconsistent inference in this context. However, subsampling — where for a sample of size n bootstrap pseudo-samples of size m < n are drawn from the empirical distribution of pairs of observed input-output vectors — provides consistent inference, although coverages are quite sensitive to the choice of subsample size m. We show that a simple, data-based rule for selecting m gives confidence interval estimates with good coverage properties. In addition, we show that subsampling performs well for testing hypotheses about returns to scale and other features of the model when a similar data-based rule is used to select m. 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.