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Stochastic Nonparametric Envelopment of Data: Combining Virtues of SFA and DEA in a Unified Framework

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Kuosmanen, Timo

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Abstract

The literature of productive efficiency analysis is divided into two main branches: the parametric Stochastic Frontier Analysis (SFA) and nonparametric Data Envelopment Analysis (DEA). This paper attempts to combine the virtues of both approaches in a unified framework. We follow the SFA literature and introduce a stochastic component decomposed into idiosyncratic error and technical inefficiency components imposing the standard SFA assumptions. In contrast to the SFA, we do not make any prior assumptions about the functional form of the deterministic production function. In this respect, we follow the nonparametric route of DEA that only imposes free disposability, convexity, and some specification of returns to scale. From the postulated class of production functions, the proposed method identifies the production function with the best empirical fit to the data. The resulting function will always take a piece-wise linear form analogous to the DEA frontiers. We discuss the practical implementation of the method and illustrate its potential by means empirical examples.

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Paper provided by MTT Agrifood Research Finland in its series Discussion Papers with number 11864.

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Date of creation: 2006
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Handle: RePEc:ags:mttfdp:11864

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Keywords: Productivity Analysis;

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  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August. [Downloadable!] (restricted)
  4. Bauer, Paul W., 1990. "Recent developments in the econometric estimation of frontiers," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 39-56. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June. [Downloadable!] (restricted)
  7. Luis R. Murillo-Zamorano, 2004. "Economic Efficiency and Frontier Techniques," Journal of Economic Surveys, Blackwell Publishing, vol. 18(1), pages 33-77, 02. [Downloadable!] (restricted)
  8. Efthymios G. Tsionas, 2002. "Stochastic frontier models with random coefficients," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(2), pages 127-147. [Downloadable!]
  9. Kuosmanen, Timo & Cherchye, Laurens & Sipilainen, Timo, 2006. "The law of one price in data envelopment analysis: Restricting weight flexibility across firms," European Journal of Operational Research, Elsevier, vol. 170(3), pages 735-757, May. [Downloadable!] (restricted)
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  10. Seiford, Lawrence M. & Thrall, Robert M., 1990. "Recent developments in DEA : The mathematical programming approach to frontier analysis," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 7-38. [Downloadable!] (restricted)
  11. Byeong Park & Robin C. Sickles & Leopold Simar, 2000. "Semiparametric Efficient Estimation of AR(1) Panel Data Models," Econometric Society World Congress 2000 Contributed Papers 1510, Econometric Society. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Illge, L. & Hahn, T. & Figge, F., 2008. "Applying and Extending the Sustainable Value Method related to Agriculture – an Overview," 2008 International Congress, August 26-29, 2008, Ghent, Belgium 44441, European Association of Agricultural Economists. [Downloadable!]
  2. Sipilainen, T. & Kuosmanen, T. & Kumbhakar, S.C., 2008. "Measuring productivity differentials – An application to milk production in Nordic countries," 2008 International Congress, August 26-29, 2008, Ghent, Belgium 44277, European Association of Agricultural Economists. [Downloadable!]
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