Abstract
Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiency of production. Practitioners use DEA estimators far more frequently than FDH estimators, implicitly assuming that production sets are convex. Moreover, use of the constant returns to scale (CRS) version of the DEA estimator requires an assumption of CRS. Although bootstrap methods have been developed for making inference about the efficiencies of individual units, until now no methods exist for making consistent inference about differences in mean efficiency across groups of producers or for testing hypotheses about model structure such as returns to scale or convexity of the production set. We use central limit theorem results from our previous work to develop additional theoretical results permitting consistent tests of model structure and provide Monte Carlo evidence on the performance of the tests in terms of size and power. In addition, the variable returns to scale version of the DEA estimator is proved to attain the faster convergence rate of the CRS-DEA estimator under CRS. Using a sample of U.S. commercial banks, we test and reject convexity of the production set, calling into question results from numerous banking studies that have imposed convexity assumptions. Supplementary materials for this article are available online.
Highlights
Nonparametric efficiency estimators are widely used to benchmark producers’ performance by estimating distance from a producer’s location in input-output space to the boundary of the set of feasible combinations of inputs and outputs—i.e., the production set—in one of several possible directions
The presentation in the remainder of this sub-section is in terms of the variable returns to scale (VRS)-data envelopment analysis (DEA) case; the results extend to the other cases with appropriate changes in assumptions and notation
In the tables that follow, we report the proportion of cases where we reject the null hypothesis of equivalent means, constant returns to scale, or convexity of Ψ in tests of nominal sizes .10, .05, and
Summary
Nonparametric efficiency estimators are widely used to benchmark producers’ performance by estimating distance from a producer’s location in input-output space to the boundary of the set of feasible combinations of inputs and outputs—i.e., the production set—in one of several possible directions. Kneip et al (2013) develop new central limit theorems for means of nonparametric efficiency estimators, permitting inference about mean efficiency and convenient summarization of results. This paper extends the results of Kneip et al (2013) to develop methods for testing differences in mean efficiency across groups of producers, as well as model features such as returns to scale or convexity of the production set. The results of Kneip et al (2013) make clear that standard central limit theorems do not apply (except when the number of inputs and outputs are implausibly small); in addition, it is well-known that nonparametric efficiency estimators are correlated, which introduces additional complication. FDH estimators, on the other hand, remain consistent regardless of whether the production set is convex, but their convergence rate is slower than that of DEA estimators for a given number of inputs and outputs. The performance of the tests in finite samples is examined in a series of Monte Carlo experiments described in Section 4, and conclusions are given in the final section
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