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Stochastic FDH/DEA estimators for Frontier Analysis

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  • Leopold Simar

    (Universite Catholique de Louvain and Toulouse School of Economics)

  • Valentin Zelenyuk

    (Kyiv School of Economics and Kyiv Economics Institute)

Abstract

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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Bibliographic Info

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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Keywords: Stochastic Frontier; Nonparametric Frontier; Local Maximum Likelihood;

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References

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  1. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
  2. 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.
  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. RITTER, Christian & SIMAR, Leopold, 1994. "Pitfalls of Normal-Gamma Stochastic Frontier Models," CORE Discussion Papers 1994041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. 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.
  6. 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.
  7. 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.
  8. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
  9. 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).
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. O. B. Olesen & N. C. Petersen, 1995. "Chance Constrained Efficiency Evaluation," Management Science, INFORMS, vol. 41(3), pages 442-457, March.
  18. Leopold Simar & Paul Wilson, 2010. "Inferences from Cross-Sectional, Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, vol. 29(1), pages 62-98.
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Citations

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Cited by:
  1. Andor, Mark & Hesse, Frederik, 2012. "The StoNED age: The departure into a new era of efficiency analysis? An MC study comparing StoNED and the "oldies" (SFA and DEA)," CAWM Discussion Papers 60, Center of Applied Economic Research Münster (CAWM), University of Münster.
  2. Giovanni Dosi & Marco Grazzi & Luigi Marengo & Simona Settepanella, 2013. "Production theory: accounting for firm heterogeneity and technical change," LEM Papers Series 2013/22, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  3. Dongwei Su & Xingxing He, 2012. "Ownership structure, corporate governance and productive efficiency in China," Journal of Productivity Analysis, Springer, vol. 38(3), pages 303-318, December.
  4. Andrés J. Picazo-Tadeo & Mercedes Beltrán-Esteve & José A. Gómez-Limón, 2011. "Assessing eco-efficiency with directional distance functions," Working Papers 1110, Department of Applied Economics II, Universidad de Valencia.
  5. Minegishi, Kota, 2013. "Explaining Production Heterogeneity By Contextual Environments: Two-Stage DEA Application to Technical Change Measurement," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 150289, Agricultural and Applied Economics Association.
  6. Chavas, Jean-Paul & Kim, Kwansoo, 2013. "Nonparametric Analysis of Technology and Productivity under Non-Convexity," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149684, Agricultural and Applied Economics Association.
  7. Valentin Zelenyuk & Claudia Curi & Paolo Guarda & Ana Lozano-Vivas, 2011. "Is foreign-bank efficiency in financial centers driven by home-country characteristics?," CEPA Working Papers Series WP022011, School of Economics, University of Queensland, Australia.
  8. Uwe Cantner & Jens J. Krüger & Rene Söllner, 2010. "Product Quality, Product Price, and Share Dynamics in the German Compact Car Market," Jena Economic Research Papers 2010-024, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.
  9. Mark Andor & Frederik Hesse, . "The StoNED age: The Departure Into a New Era of Efficiency Analysis? An MC study Comparing StoNED and the "Oldies" (SFA and DEA)," Working Papers 201285, Institute of Spatial and Housing Economics, Munster Universitary.
  10. Timo Kuosmanen & Mika Kortelainen, 2012. "Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints," Journal of Productivity Analysis, Springer, vol. 38(1), pages 11-28, August.
  11. Keshvari, Abolfazl & Kuosmanen, Timo, 2013. "Stochastic non-convex envelopment of data: Applying isotonic regression to frontier estimation," European Journal of Operational Research, Elsevier, vol. 231(2), pages 481-491.
  12. Valentin Zelenyuk, 2014. "Scale efficiency and homotheticity: equivalence of primal and dual measures," Journal of Productivity Analysis, Springer, vol. 42(1), pages 15-24, August.
  13. Mark Andor & Frederik Hesse, 2014. "The StoNED age: the departure into a new era of efficiency analysis? A monte carlo comparison of StoNED and the “oldies” (SFA and DEA)," Journal of Productivity Analysis, Springer, vol. 41(1), pages 85-109, February.
  14. Anne-Kathrin Last & Heike Wetzel, 2009. "Effizienzmessverfahren – eine Einführung," Working Paper Series in Economics 145, University of Lüneburg, Institute of Economics.
  15. Madau, Fabio A., 2012. "Technical and scale efficiency in the Italian Citrus Farming: A comparison between Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis(DEA) Models," MPRA Paper 41403, University Library of Munich, Germany.
  16. Girard, Stéphane & Guillou, Armelle & Stupfler, Gilles, 2013. "Frontier estimation with kernel regression on high order moments," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 172-189.
  17. Krasnopjorovs, Olegs, 2013. "Latvijas ekonomikas izaugsmi noteicošie faktori
    [Factors of Economic Growth in Latvia]
    ," MPRA Paper 47550, University Library of Munich, Germany.
  18. Bellenger, Moriah J. & Herlihy, Alan T., 2010. "Performance-based environmental index weights: Are all metrics created equal?," Ecological Economics, Elsevier, vol. 69(5), pages 1043-1050, March.

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