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


  • Kuosmanen, Timo


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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  • Kuosmanen, Timo, 2006. "Stochastic Nonparametric Envelopment of Data: Combining Virtues of SFA and DEA in a Unified Framework," Discussion Papers 11864, MTT Agrifood Research Finland.
  • Handle: RePEc:ags:mttfdp:11864

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    References listed on IDEAS

    1. Park, Byeong U. & Sickles, Robin C. & Simar, Leopold, 2003. "Semiparametric-efficient estimation of AR(1) panel data models," Journal of Econometrics, Elsevier, vol. 117(2), pages 279-309, December.
    2. Ondrich, Jan & Ruggiero, John, 2001. "Efficiency measurement in the stochastic frontier model," European Journal of Operational Research, Elsevier, vol. 129(2), pages 434-442, March.
    3. Timo Kuosmanen, 2003. "Duality Theory of Non-convex Technologies," Journal of Productivity Analysis, Springer, vol. 20(3), pages 273-304, November.
    4. 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.
    5. 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.
    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. Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, vol. 21(02), pages 358-389, April.
    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.
    9. Hung-jen Wang & Peter Schmidt, 2002. "One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels," Journal of Productivity Analysis, Springer, vol. 18(2), pages 129-144, September.
    10. Mette Asmild & Joseph Paradi & Vanita Aggarwall & Claire Schaffnit, 2004. "Combining DEA Window Analysis with the Malmquist Index Approach in a Study of the Canadian Banking Industry," Journal of Productivity Analysis, Springer, vol. 21(1), pages 67-89, January.
    11. 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.
    12. 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.
    13. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    14. Bauer, Paul W., 1990. "Recent developments in the econometric estimation of frontiers," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 39-56.
    15. 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.
    16. Luis R. Murillo-Zamorano, 2004. "Economic Efficiency and Frontier Techniques," Journal of Economic Surveys, Wiley Blackwell, vol. 18(1), pages 33-77, February.
    17. 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.
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    Cited by:

    1. Kenneth Rødseth & Eirik Romstad, 2014. "Environmental Regulations, Producer Responses, and Secondary Benefits: Carbon Dioxide Reductions Under the Acid Rain Program," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 59(1), pages 111-135, September.
    2. Timo Kuosmanen & Mogens Fosgerau, 2009. "Neoclassical versus Frontier Production Models? Testing for the Skewness of Regression Residuals," Scandinavian Journal of Economics, Wiley Blackwell, vol. 111(2), pages 351-367, June.
    3. Kuosmanen, Timo, 2012. "Stochastic semi-nonparametric frontier estimation of electricity distribution networks: Application of the StoNED method in the Finnish regulatory model," Energy Economics, Elsevier, vol. 34(6), pages 2189-2199.
    4. Illge, L. & Hahn, Tobias & 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.
    5. Johnson, Andrew L. & Kuosmanen, Timo, 2012. "One-stage and two-stage DEA estimation of the effects of contextual variables," European Journal of Operational Research, Elsevier, vol. 220(2), pages 559-570.
    6. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
    7. Andrew Johnson & Timo Kuosmanen, 2011. "One-stage estimation of the effects of operational conditions and practices on productive performance: asymptotically normal and efficient, root-n consistent StoNEZD method," Journal of Productivity Analysis, Springer, vol. 36(2), pages 219-230, October.
    8. repec:eee:ecolet:v:160:y:2017:i:c:p:1-3 is not listed on IDEAS
    9. Sipilainen, Timo & Kuosmanen, Timo & Kumbhakar, Subal 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.
    10. repec:eee:eneeco:v:64:y:2017:i:c:p:373-383 is not listed on IDEAS
    11. repec:eee:ejores:v:262:y:2017:i:2:p:792-801 is not listed on IDEAS
    12. Zhou, P. & Zhou, X. & Fan, L.W., 2014. "On estimating shadow prices of undesirable outputs with efficiency models: A literature review," Applied Energy, Elsevier, vol. 130(C), pages 799-806.
    13. Kuosmanen, Timo & Kuosmanen, Natalia, 2009. "How not to measure sustainable value (and how one might)," Ecological Economics, Elsevier, vol. 69(2), pages 235-243, December.
    14. Mekaroonreung, Maethee & Johnson, Andrew L., 2012. "Estimating the shadow prices of SO2 and NOx for U.S. coal power plants: A convex nonparametric least squares approach," Energy Economics, Elsevier, vol. 34(3), pages 723-732.
    15. 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.

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