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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

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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  • 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
    DOI: 10.22004/ag.econ.11864
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    1. 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.
    2. Timo Kuosmanen, 2003. "Duality Theory of Non-convex Technologies," Journal of Productivity Analysis, Springer, vol. 20(3), pages 273-304, November.
    3. John Ruggiero, 2004. "Data envelopment analysis with stochastic data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(9), pages 1008-1012, September.
    4. 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.
    5. Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, vol. 21(2), pages 358-389, April.
    6. 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.
    7. 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.
    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. Luis R. Murillo‐Zamorano, 2004. "Economic Efficiency and Frontier Techniques," Journal of Economic Surveys, Wiley Blackwell, vol. 18(1), pages 33-77, February.
    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.
    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. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    17. Bauer, Paul W., 1990. "Recent developments in the econometric estimation of frontiers," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 39-56.
    18. 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.
    19. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
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    Cited by:

    1. 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.
    2. 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.
    3. Nguyen, Trang T.T. & Prior, Diego & Van Hemmen, Stefan, 2020. "Stochastic semi-nonparametric frontier approach for tax administration efficiency measure: Evidence from a cross-country study," Economic Analysis and Policy, Elsevier, vol. 66(C), pages 137-153.
    4. Elvira Silva & Pedro Macedo & Isabel Soares, 2019. "Maximum entropy: a stochastic frontier approach for electricity distribution regulation," Journal of Regulatory Economics, Springer, vol. 55(3), pages 237-257, June.
    5. Jose M. Cordero & Cristina Polo & Daniel Santín, 2020. "Assessment of new methods for incorporating contextual variables into efficiency measures: a Monte Carlo simulation," Operational Research, Springer, vol. 20(4), pages 2245-2265, December.
    6. 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.
    7. Dai, Sheng & Zhou, Xun & Kuosmanen, Timo, 2020. "Forward-looking assessment of the GHG abatement cost: Application to China," Energy Economics, Elsevier, vol. 88(C).
    8. Kuosmanen, Timo & Johnson, Andrew, 2017. "Modeling joint production of multiple outputs in StoNED: Directional distance function approach," European Journal of Operational Research, Elsevier, vol. 262(2), pages 792-801.
    9. Xian, Yujiao & Yu, Dan & Wang, Ke & Yu, Jian & Huang, Zhimin, 2022. "Capturing the least costly measure of CO2 emission abatement: Evidence from the iron and steel industry in China," Energy Economics, Elsevier, vol. 106(C).
    10. 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.
    11. 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.
    12. Afsharian, Mohsen, 2017. "Metafrontier efficiency analysis with convex and non-convex metatechnologies by stochastic nonparametric envelopment of data," Economics Letters, Elsevier, vol. 160(C), pages 1-3.
    13. Gil, Guilherme Dôco Roberti & Costa, Marcelo Azevedo & Lopes, Ana Lúcia Miranda & Mayrink, Vinícius Diniz, 2017. "Spatial statistical methods applied to the 2015 Brazilian energy distribution benchmarking model: Accounting for unobserved determinants of inefficiencies," Energy Economics, Elsevier, vol. 64(C), pages 373-383.
    14. Chen, Ya & Tsionas, Mike G. & Zelenyuk, Valentin, 2021. "LASSO+DEA for small and big wide data," Omega, Elsevier, vol. 102(C).
    15. Timo Kuosmanen & Andrew L. Johnson, 2010. "Data Envelopment Analysis as Nonparametric Least-Squares Regression," Operations Research, INFORMS, vol. 58(1), pages 149-160, February.
    16. 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.
    17. 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.
    18. Sekitani, Kazuyuki & Zhao, Yu, 2021. "Performance benchmarking of achievements in the Olympics: An application of Data Envelopment Analysis with restricted multipliers," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1202-1212.
    19. Shirong Zhao & Guangshun Qiao, 2022. "The shadow prices of CO2, SO2 and NOx for U.S. coal power industry 2010–2017: a convex quantile regression method," Journal of Productivity Analysis, Springer, vol. 57(3), pages 243-253, June.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. Ya Chen & Mike Tsionas & Valentin Zelenyuk, 2020. "LASSO DEA for small and big data," CEPA Working Papers Series WP092020, School of Economics, University of Queensland, Australia.
    25. 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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