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A Monte Carlo Study on Multiple Output Stochastic Frontiers: Comparison of Two Approaches

  • Géraldine Henningsen

    ()

    (DTU Management Engineering, Technical University of Denmark)

  • Arne Henningsen

    ()

    (Department of Food and Resource Economics, University of Copenhagen)

  • Uwe Jensen

    ()

    (Institute for Statistics and Econometrics, University of Kiel)

In the estimation of multiple output technologies in a primal approach, the main question is how to handle the multiple outputs. Often an output distance function is used, where the classical approach is to exploit its homogeneity property by selecting one output quantity as the dependent variable, dividing all other output quantities by the selected output quantity, and using these ratios as regressors (OD). Another approach is the stochastic ray production frontier (SR) which transforms the output quantities into their Euclidean distance as the dependent variable and their polar coordinates as directional components as regressors. A number of studies have compared these specifications using real world data and have found significant differences in the inefficiency estimates. However, in order to get to the bottom of these differences, we apply a Monte-Carlo simulation. We test the robustness of both specifications for the case of a Translog output distance function with respect to different common statistical problems as well as problems arising as a consequence of zero values in the output quantities. Although, our results partly show clear reactions to statistical misspecifications, on average none of the approaches is superior. However, considerable differences are found between the estimates at single replications. In the case of zero values in the output quantities, the SR clearly outperforms the OD, although this advantage nearly vanishes when zeros are replaced by a small number.

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File URL: http://okonomi.foi.dk/workingpapers/WPpdf/WP2013/IFRO_WP_2013_7.pdf
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Paper provided by University of Copenhagen, Department of Food and Resource Economics in its series IFRO Working Paper with number 2013/7.

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Length: 31 pages
Date of creation: Apr 2013
Date of revision:
Handle: RePEc:foi:wpaper:2013_7
Contact details of provider: Web page: http://www.ifro.ku.dk/english/
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  1. Roibas, David & Arias, Carlos, 2004. "Endogeneity Problems in the Estimation of Multi-Output Technologies," Efficiency Series Papers 2004/06, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
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  5. Hugo Fuentes & Emili Grifell-Tatjé & Sergio Perelman, 2001. "A Parametric Distance Function Approach for Malmquist Productivity Index Estimation," Journal of Productivity Analysis, Springer, vol. 15(2), pages 79-94, March.
  6. Gong, Byeong-Ho & Sickles, Robin C., 1991. "Finite Sample Evidence on the Performance of Stochastic Frontiers and Data Envelopment Analysis Using Panel Data," Working Papers 91-12, C.V. Starr Center for Applied Economics, New York University.
  7. Perelman, Sergio & Santín, Daniel, 2009. "How to generate regularly behaved production data? A Monte Carlo experimentation on DEA scale efficiency measurement," European Journal of Operational Research, Elsevier, vol. 199(1), pages 303-310, November.
  8. Uwe Jensen, 2005. "Misspecification Preferred: The Sensitivity of Inefficiency Rankings," Journal of Productivity Analysis, Springer, vol. 23(2), pages 223-244, 05.
  9. Kumbhakar, Subal C. & Lien, Gudbrand D. & Hardaker, J. Brian, 2011. "Technical efficiency in competing panel data models: A study of Norwegian grain farming," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114673, European Association of Agricultural Economists.
  10. Tim Coelli & Sergio Perelman, 2000. "Technical efficiency of European railways: a distance function approach," Applied Economics, Taylor & Francis Journals, vol. 32(15), pages 1967-1976.
  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.
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