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Testing Hypotheses in Nonparametric Models of Production

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  • Kneip, Alois
  • Simar, Leopold
  • Wilson, Paul
Abstract
Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiency of production. Practitioners use DEA estimators far more frequently than FDH estimators, implicitly assuming that production sets are convex. Moreover, use of the constant returns to scale (CRS) version of the DEA estimator requires an assumption of CRS. Although bootstrap methods have been developed for making inference about the efficiencies of individual units, until now no methods exist for making consistent inference about differences in mean efficiency across groups of producers or for testing hypotheses about model structure such as returns to scale or convexity of the production set. We use central limit theorem results from our previous work to develop additional theoretical results permitting consistent tests of model structure and provide Monte Carlo evidence on the performance of the tests in terms of size and power. In addition, the variable returns to scale version of the DEA estimator is proved to attain the faster convergence rate of the CRS-DEA estimator under CRS. Using a sample of U.S. commercial banks, we test and reject convexity of the production set, calling into question results from numerous banking studies that have imposed convexity assumptions. Supplementary materials for this article are available online.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Kneip, Alois & Simar, Leopold & Wilson, Paul, 2016. "Testing Hypotheses in Nonparametric Models of Production," LIDAM Reprints ISBA 2016044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2016044
    Note: In : Journal of Business and Economic Statistics, vol. 34, no. 3, p. 435-456 (2016)
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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. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    3. Léopold Simar & Paul Wilson, 2000. "Statistical Inference in Nonparametric Frontier Models: The State of the Art," Journal of Productivity Analysis, Springer, vol. 13(1), pages 49-78, January.
    4. GIJBELS, Irène & MAMMEN, Enno & PARK, Byeong U. & SIMAR, Léopold, 1997. "On estimation of monotone and concave frontier functions," LIDAM Discussion Papers CORE 1997031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Simar, Léopold & Vanhems, Anne & Wilson, Paul W., 2012. "Statistical inference for DEA estimators of directional distances," European Journal of Operational Research, Elsevier, vol. 220(3), pages 853-864.
    6. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    7. Afriat, Sidney N, 1972. "Efficiency Estimation of Production Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(3), pages 568-598, October.
    8. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2008. "Asymptotics And Consistent Bootstraps For Dea Estimators In Nonparametric Frontier Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1663-1697, December.
    9. Abdelaati Daouia & Léopold Simar & Paul W. Wilson, 2017. "Measuring firm performance using nonparametric quantile-type distances," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 156-181, March.
    10. S.‐O. Jeong & B. U. Park, 2006. "Large Sample Approximation of the Distribution for Convex‐Hull Estimators of Boundaries," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 139-151, March.
    11. 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.
    12. 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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