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Statistical inference for DEA estimators of directional distances. (English) Zbl 1253.90176

Summary: In productivity and efficiency analysis, the technical efficiency of a production unit is measured through its distance to the efficient frontier of the production set. The most familiar non-parametric methods use Farrell-Debreu, Shephard, or hyperbolic radial measures. These approaches require that inputs and outputs be non-negative, which can be problematic when using financial data. Recently, R. G. Chambers et al. [J. Optimization Theory Appl. 98, No. 2, 351–364 (1998; Zbl 0909.90040)] have introduced directional distance functions which can be viewed as additive (rather than multiplicative) measures efficiency. Directional distance functions are not restricted to non-negative input and output quantities; in addition, the traditional input and output-oriented measures are nested as special cases of directional distance functions. Consequently, directional distances provide greater flexibility. However, until now, only free disposal hull (FDH) estimators of directional distances (and their conditional and robust extensions) have known statistical properties. This paper develops the statistical properties of directional d estimators, which are especially useful when the production set is assumed convex. We first establish that the directional Data Envelopment Analysis (DEA) estimators share the known properties of the traditional radial DEA estimators. We then use these properties to develop consistent bootstrap procedures for statistical inference about directional distance, estimation of confidence intervals, and bias correction. The methods are illustrated in some empirical examples.

MSC:

90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
62G05 Nonparametric estimation
62G09 Nonparametric statistical resampling methods
91B38 Production theory, theory of the firm

Citations:

Zbl 0909.90040

Software:

bootstrap; LAPACK
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Full Text: DOI Link

References:

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