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ASYMPTOTICS AND CONSISTENT BOOTSTRAPS FOR DEA ESTIMATORS IN NONPARAMETRIC FRONTIER MODELS

Published online by Cambridge University Press:  17 July 2008

Alois Kneip ,
Léopold Simar  and
Paul W. Wilson
Alois Kneip
Affiliation:
Universität Bonn
Léopold Simar
Affiliation:
Université Catholique de Louvain
Paul W. Wilson*
Affiliation:
Clemson University
*
Address correspondence to Paul W. Wilson, Department of Economics, 222 Sirrine Hall, Clemson University, Clemson, South Carolina 29634, USA; e-mail: [email protected]
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Abstract

Nonparametric data envelopment analysis (DEA) estimators based on linear programming methods have been widely applied in analyses of productive efficiency. The distributions of these estimators remain unknown except in the simple case of one input and one output, and previous bootstrap methods proposed for inference have not been proved consistent, making inference doubtful. This paper derives the asymptotic distribution of DEA estimators under variable returns to scale. This result is used to prove consistency of two different bootstrap procedures (one based on subsampling, the other based on smoothing). The smooth bootstrap requires smoothing the irregularly bounded density of inputs and outputs and smoothing the DEA frontier estimate. Both bootstrap procedures allow for dependence of the inefficiency process on output levels and the mix of inputs in the case of input-oriented measures, or on input levels and the mix of outputs in the case of output-oriented measures.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 6 , December 2008 , pp. 1663 - 1697
Copyright
Copyright © Cambridge University Press 2008

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