2015/21 | LEM Working Paper Series | |
Testing the "separability" condition in two-stage nonparametric models of production |
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Cinzia Daraio, Leopold Simar and Paul W. Wilson |
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Keywords | ||
technical efficiency, conditional efficiency, two-stage estimation,
bootstrap, separability, data envelopment analysis (DEA),
free-disposal hull (FDH).
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JEL Classifications | ||
C12, C14, C44, C46
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Abstract | ||
Simar and Wilson (J. Econometrics, 2007) provided a statistical model
that can rationalize two-stage estimation of technical efficiency in
nonparametric 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 nonparametric test of
this assumption. The test relies on new central limit theorem (CLT)
results for unconditional efficiency estimators developed by Kneip et
al. (Econometric Theory, 2015a) and new CLTs for conditional
efficiency estimators developed in this paper. The test can be
implemented relying on either asymptotic normality of the test
statistics or using bootstrap methods to obtain critical values. 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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