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Stochastic FDH/DEA estimators for frontier analysis

  • Léopold Simar
  • Valentin Zelenyuk


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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Article provided by Springer in its journal Journal of Productivity Analysis.

Volume (Year): 36 (2011)
Issue (Month): 1 (August)
Pages: 1-20

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Handle: RePEc:kap:jproda:v:36:y:2011:i:1:p:1-20
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  1. 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.
  2. repec:cor:louvrp:-571 is not listed on IDEAS
  3. Leopold Simar & Paul Wilson, 2010. "Inferences from Cross-Sectional, Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, vol. 29(1), pages 62-98.
  4. O. B. Olesen & N. C. Petersen, 1995. "Chance Constrained Efficiency Evaluation," Management Science, INFORMS, vol. 41(3), pages 442-457, March.
  5. Simar, Léopold, 2003. "How to Improve the Performances of DEA/FDH Estimators in the Presence of Noise?," SFB 373 Discussion Papers 2003,33, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. 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).
  7. 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).
  8. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
  9. Park, Byeong & Simar, Leopold & Zelenyuk, Valentin, 2006. "Local likelihood estimation of truncated regression and its partial derivatives: theory and application," MPRA Paper 34686, University Library of Munich, Germany.
  10. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Simar, L. & Wilson, P.W., 1999. "Statistical Inference in Nonparametric Frontier Models: the State of the Art," Papers 9904, Catholique de Louvain - Institut de statistique.
  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. 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.
  19. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
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