Testing whether two-stage estimation is meaningful in non-parametric models of production

Cinzia C. Daraio · Léopold Simar · Paul W. Wilson

53 citations0/0 files storedRePEc: Research Papers in Economics

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Efficiency Analysis Using DEA Statistical Methods and Inference Advanced Statistical Methods and Models

Abstract

Simar and Wilson (J. Econometrics, 2007) provided a statistical model that can rationalize two-stage estimation of technical efficiency in non-parametric settings. Two-stage estimation has been widely used, but requires a strong assumption: the second-stage environmental variables cannot affect the support of the input and output variables in the first stage. In this paper, we provide a fully non-parametric test of this assumption; in addition, we provide a theoretical link to results obtained by Politis et al.(Statistica Sinica, 2001), allowing us to estimate critical values for our test statistics using bootstrap sub-sampling while optimizing the choice of sub-sample size by minimizing a measure of volatility. Our simulation results indicate that our tests perform well both in terms of size and power. We present a real-world empirical example by updating the analysis performed by Aly et al. (R. E. Stat., 1990) on U.S. commercial banks; our tests easily reject the assumption required for two-stage estimation, calling into question results that appear in hundreds of papers that have been published in recent years.

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References

1957The Measurement of Productive Efficiency 2005An Introduction to Efficiency and Productivity Analysis 2015Theory of Cost and Production Functions 1998Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models 2000A general methodology for bootstrapping in non-parametric frontier models 2000Statistical Inference in Nonparametric Frontier Models: The State of the Art 2005Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach 1990Technical, Scale, and Allocative Efficiencies in U.S. Banking: An Empirical Investigation

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