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Statistical Inference for DEA Estimators of Directional Distances

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  • Simar, Leopold
  • Vanhems, Anne
  • Wilson, Paul W.
Abstract
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, Chambers et al. (1998) 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 (Simar and Vanhems, 2012). 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.
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Suggested Citation

  • Simar, Leopold & Vanhems, Anne & Wilson, Paul W., 2011. "Statistical Inference for DEA Estimators of Directional Distances," LIDAM Discussion Papers ISBA 2011035, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2011035
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    References listed on IDEAS

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    1. Simar, Léopold & Vanhems, Anne, 2012. "Probabilistic characterization of directional distances and their robust versions," Journal of Econometrics, Elsevier, vol. 166(2), pages 342-354.
    2. Torben Schubert & Léopold Simar, 2011. "Innovation and export activities in the German mechanical engineering sector: an application of testing restrictions in production analysis," Journal of Productivity Analysis, Springer, vol. 36(1), pages 55-69, August.
    3. Léopold Simar & Paul Wilson, 2011. "Inference by the m out of n bootstrap in nonparametric frontier models," Journal of Productivity Analysis, Springer, vol. 36(1), pages 33-53, August.
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    5. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, vol. 44(1), pages 49-61, January.
    6. Briec, Walter & Kerstens, Kristiaan, 2009. "Multi-horizon Markowitz portfolio performance appraisals: A general approach," Omega, Elsevier, vol. 37(1), pages 50-62, February.
    7. Daraio, Cinzia & Simar, Leopold & Wilson, Paul, 2010. "Testing whether two-stage estimation is meaningful in non-parametric models of production," LIDAM Discussion Papers ISBA 2010031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Wheelock, David C. & Wilson, Paul W., 2008. "Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 209-225, July.
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    22. Léopold Simar, 2003. "Detecting Outliers in Frontier Models: A Simple Approach," Journal of Productivity Analysis, Springer, vol. 20(3), pages 391-424, November.
    23. Kneip, Alois & Park, Byeong U. & Simar, Léopold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(6), pages 783-793, December.
    24. Park, Kang H. & Weber, William L., 2006. "Profitability of Korean banks: Test of market structure versus efficient structure," Journal of Economics and Business, Elsevier, vol. 58(3), pages 222-239.
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    26. Park, B.U. & Jeong, S.-O. & Simar, L., 2010. "Asymptotic distribution of conical-hull estimators of directional edges," LIDAM Reprints ISBA 2010025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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