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Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach

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  • Cinzia Daraio

    ()

  • Léopold Simar

    ()

Abstract

The explanation of productivity differentials is very important to identify the economic conditions that create inefficiency and to improve managerial performance. In literature two main approaches have been developed: one-stage approaches and two-stage approaches. Daraio and Simar (2003) propose a full nonparametric methodology based on conditional FDH and conditional order-m frontiers without any convexity assumption on the technology. On the one hand, convexity has always been assumed in mainstream production theory and general equilibrium. On the other hand, in many empirical applications, the convexity assumption can be reasonable and sometimes natural. Leading by these considerations, in this paper we propose a unifying approach to introduce external-environmental variables in nonparametric frontier models for convex and non convex technologies. Developing further the work done in Daraio and Simar (2003) we introduce a conditional DEA estimator, i.e., an estimator of production frontier of DEA type conditioned to some external-environmental variables which are neither inputs nor outputs under the control of the producer. A robust version of this conditional estimator is also proposed. These various measures of efficiency provide also indicators of convexity. Illustrations through simulated and real data (mutual funds) examples are reported.

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Bibliographic Info

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

Volume (Year): 28 (2007)
Issue (Month): 1 (October)
Pages: 13-32

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Handle: RePEc:kap:jproda:v:28:y:2007:i:1:p:13-32

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Web page: http://www.springerlink.com/link.asp?id=100296

Related research

Keywords: Convexity; External-environmental factors; Production frontier; Nonparametric estimation; Robust estimation; C13; C14; D20;

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  1. Cinzia Daraio & Leopold Simar, 2003. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," LEM Papers Series 2003/17, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  2. 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.
  3. Daraio, Cinzia & Simar, Leopold, 2006. "A robust nonparametric approach to evaluate and explain the performance of mutual funds," European Journal of Operational Research, Elsevier, vol. 175(1), pages 516-542, November.
  4. Simar, Leopold & Wilson, Paul W., 2007. "Estimation and inference in two-stage, semi-parametric models of production processes," Journal of Econometrics, Elsevier, vol. 136(1), pages 31-64, January.
  5. M. J. Farrell, 1959. "The Convexity Assumption in the Theory of Competitive Markets," Journal of Political Economy, University of Chicago Press, vol. 67, pages 377.
  6. Podinovski, V. V., 2005. "Selective convexity in DEA models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 552-563, March.
  7. Florens, Jean-Pierre & Simar, Leopold, 2005. "Parametric approximations of nonparametric frontiers," Journal of Econometrics, Elsevier, vol. 124(1), pages 91-116, January.
  8. Simar, Leopold & Wilson, Paul W., 2002. "Non-parametric tests of returns to scale," European Journal of Operational Research, Elsevier, vol. 139(1), pages 115-132, May.
  9. Peter Bogetoft, 1996. "DEA on Relaxed Convexity Assumptions," Management Science, INFORMS, vol. 42(3), pages 457-465, March.
  10. 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.
  11. Simar, L. & Wilson, P.W., 2000. "Testing Restrictions in Nonparametric Efficiency Models," Papers 0013, Catholique de Louvain - Institut de statistique.
  12. Walter Briec & Kristiaan Kerstens & Philippe Venden Eeckaut, 2004. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Journal of Economics, Springer, vol. 81(2), pages 155-192, 02.
  13. 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.
  14. Peter Bogetoft & Joseph M. Tama & Jørgen Tind, 2000. "Convex Input and Output Projections of Nonconvex Production Possibility Sets," Management Science, INFORMS, vol. 46(6), pages 858-869, June.
  15. Walter Briec & Kristiaan Kerstens & Philippe Vanden Eeckaut, 2006. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity (Journal of Economics 81(2):155–192)," Journal of Economics, Springer, vol. 87(3), pages 307-308, 04.
  16. Léopold Simar, 2003. "Detecting Outliers in Frontier Models: A Simple Approach," Journal of Productivity Analysis, Springer, vol. 20(3), pages 391-424, November.
  17. 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.
  18. 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.
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