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Stochastic FDH/DEA estimators for Frontier Analysis

  • Leopold Simar

    (Universite Catholique de Louvain and Toulouse School of Economics)

  • Valentin Zelenyuk

    (Kyiv School of Economics and Kyiv Economics Institute)

In this paper we extend the work of Simar (2007) introducing noise in nonparametric frontier models. We develop an approach that synthesizes the best features of the two main methods in the estimation of production efficiency. Specifically, our approach first allows for statistical noise, similar to Stochastic Frontier Analysis (even in a more flexible way), and second, it allows modelling multiple-inputs-multiple-outputs technologies without imposing parametric assumptions on production relationship, similar to what is done in non-parametric methods (DEA, FDH, etc. . . ). The methodology is based on the theory of local maximum likelihood estimation and extends recent works of Park, Kumbhakar, Simar and Tsionas (2007) and Park, Simar and Zelenyuk (2006). Our method is suitable for modelling and estimation of the marginal effects onto inefficiency level jointly with estimation of marginal effects of input. The approach is robust to heteroskedastic cases and to various (unknown) distributions of statistical noise and inefficiency, despite assuming simple anchorage models. The method also improves DEA/FDH estimators, by allowing them to be quite robust to statistical noise and especially to outliers, which were the main problems of the original DEA/FDH. The procedure shows great performance for various simulated cases and is also illustrated for some real data sets.

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Paper provided by Kyiv School of Economics in its series Discussion Papers with number 8.

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Date of creation: Jun 2008
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Handle: RePEc:kse:dpaper:8
Note: Under review in Journal of Business and Economic Statistics
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  1. Atkinson, Scott E. & Primont, Daniel, 2002. "Stochastic estimation of firm technology, inefficiency, and productivity growth using shadow cost and distance functions," Journal of Econometrics, Elsevier, vol. 108(2), pages 203-225, June.
  2. Ritter, C. & Simar, L., . "Pitfalls of normal-gamma stochastic frontier models," CORE Discussion Papers RP -1272, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October.
  4. 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.
  5. Léopold Simar, 2007. "How to improve the performances of DEA/FDH estimators in the presence of noise?," Journal of Productivity Analysis, Springer, vol. 28(3), pages 183-201, December.
  6. Kumbhakar, Subal C. & Park, Byeong U. & Simar, Leopold & Tsionas, Efthymios G., 2007. "Nonparametric stochastic frontiers: A local maximum likelihood approach," Journal of Econometrics, Elsevier, vol. 137(1), pages 1-27, March.
  7. Byeong U. Park & Leopold Simar & Valentin Zelenyuk, 2008. "Local Likelihood Estimation of Truncated Regression and Its Partial Derivatives: Theory and Application," Discussion Papers 7, Kyiv School of Economics.
  8. Kneip, A. & Simar, L., . "A general framework for frontier estimation with panel data," CORE Discussion Papers RP -1224, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Alois Kneip & Léopold Simar & Paul W. Wilson, 2006. "Asymptotics and Consistent Bootstraps for DEA Estimators in Non-parametric Frontier Models," Bonn Econ Discussion Papers bgse12_2006, University of Bonn, Germany.
  10. Kneip, Alois & Park, Byeong U. & Simar, L opold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(06), pages 783-793, December.
  11. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
  12. O. B. Olesen & N. C. Petersen, 1995. "Chance Constrained Efficiency Evaluation," Management Science, INFORMS, vol. 41(3), pages 442-457, March.
  13. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
  14. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
  15. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
  16. DEPRINS, Dominique & SIMAR, Léopold & TULKENS, Henry, . "Measuring labor-efficiency in post offices," CORE Discussion Papers RP -571, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 16(06), pages 855-877, December.
  18. Leopold Simar & Paul Wilson, 2010. "Inferences from Cross-Sectional, Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, vol. 29(1), pages 62-98.
  19. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
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