Statistical Inference in Nonparametric Frontier Models: The State of the Art

Efficiency scores of firms are measured by their distance to an estimated production frontier. The economic literature proposes several nonparametric frontier estimators based on the idea of enveloping the data (FDH and DEA-type estimators). Many have claimed that FDH and DEA techniques are non-stat...

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Bibliographic Details
Published in:Journal of productivity analysis 2000-01, Vol.13 (1), p.49-78
Main Authors: SIMAR, LÉOPOLD, WILSON, PAUL W.
Format: Article
Language:English
Subjects:
Bootstrap resampling
Confidence interval
Confidence intervals
Consistent estimators
Data envelopment analysis
Economic theory
Efficiency
Efficiency metrics
Estimating techniques
Estimation bias
Estimation methods
Estimators
Experimentation
Hypotheses
Nonparametric models
Point estimators
Random variables
Statistical inference
Studies
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Summary:Efficiency scores of firms are measured by their distance to an estimated production frontier. The economic literature proposes several nonparametric frontier estimators based on the idea of enveloping the data (FDH and DEA-type estimators). Many have claimed that FDH and DEA techniques are non-statistical, as opposed to econometric approaches where particular parametric expressions are posited to model the frontier. We can now define a statistical model allowing determination of the statistical properties of the nonparametric estimators in the multi-output and multi-input case. New results provide the asymptotic sampling distribution of the FDH estimator in a multivariate setting and of the DEA estimator in the bivariate case. Sampling distributions may also be approximated by bootstrap distributions in very general situations. Consequently, statistical inference based on DEA/FDH-type estimators is now possible. These techniques allow correction for the bias of the efficiency estimators and estimation of confidence intervals for the efficiency measures. This paper summarizes the results which are now available, and provides a brief guide to the existing literature. Emphasizing the role of hypotheses and inference, we show how the results can be used or adapted for practical purposes.
ISSN:0895-562X
1573-0441
DOI:10.1023/a:1007864806704