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A Monte Carlo study on multiple output stochastic frontiers: a comparison of two approaches

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  • Géraldine Henningsen

    ()

  • Arne Henningsen

    ()

  • Uwe Jensen

    ()

Abstract

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 show clear reactions to some statistical misspecifications, on average none of the approaches is clearly superior. However, considerable differences are found between the estimates at single replications. Taking average efficiencies from both approaches gives clearly better efficiency estimates than taking just the OD or the SR. In the case of zero values in the output quantities, the SR clearly outperforms the OD with observations with zero output quantities omitted and the OD with zero values replaced by a small positive number. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Géraldine Henningsen & Arne Henningsen & Uwe Jensen, 2015. "A Monte Carlo study on multiple output stochastic frontiers: a comparison of two approaches," Journal of Productivity Analysis, Springer, vol. 44(3), pages 309-320, December.
  • Handle: RePEc:kap:jproda:v:44:y:2015:i:3:p:309-320
    DOI: 10.1007/s11123-014-0416-9
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    References listed on IDEAS

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    1. Gong, Byeong-Ho & Sickles, Robin C., 1992. "Finite sample evidence on the performance of stochastic frontiers and data envelopment analysis using panel data," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 259-284.
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    5. 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.
    6. 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.
    7. Ruggiero, John, 1999. "Efficiency estimation and error decomposition in the stochastic frontier model: A Monte Carlo analysis," European Journal of Operational Research, Elsevier, vol. 115(3), pages 555-563, June.
    8. 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.
    9. 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.
    10. Subal Kumbhakar & Gudbrand Lien & J. Hardaker, 2014. "Technical efficiency in competing panel data models: a study of Norwegian grain farming," Journal of Productivity Analysis, Springer, vol. 41(2), pages 321-337, April.
    11. Yapo Genevier N’guessan & Allen Featherstone & Oluwarotimi Odeh & Sreedhar Upendram, 2017. "Choice of the empirical definition of zero in the translog multiproduct cost functional form," Applied Economics Letters, Taylor & Francis Journals, vol. 24(15), pages 1112-1120, September.
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    14. 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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    Citations

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    Cited by:

    1. Andor, Mark A. & Parmeter, Christopher & Sommer, Stephan, 2019. "Combining uncertainty with uncertainty to get certainty? Efficiency analysis for regulation purposes," European Journal of Operational Research, Elsevier, vol. 274(1), pages 240-252.
    2. Henningsen, Arne & Bělín, Matěj & Henningsen, Géraldine, 2017. "New insights into the stochastic ray production frontier," Economics Letters, Elsevier, vol. 156(C), pages 18-21.
    3. Garcia Suarez, F. & Quesada, G. Perez & Molina Ricetto, C., 2018. "Rangeland cattle production in Uruguay: single-output versus multi-output efficiency measures," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277178, International Association of Agricultural Economists.
    4. Tomasz Gerard Czekaj, 2013. "Measuring the Technical Efficiency of Farms Producing Environmental Output: Parametric and Semiparametric Estimation of Multi-output Stochastic Ray Production Frontiers," IFRO Working Paper 2013/21, University of Copenhagen, Department of Food and Resource Economics.
    5. Czekaj, Tomasz G., 2015. "Measuring the Technical Efficiency of Farms Producing Environmental Output: Semiparametric Estimation of Multi-output Stochastic Ray Production Frontiers," 2015 Conference, August 9-14, 2015, Milan, Italy 211555, International Association of Agricultural Economists.
    6. repec:kap:jproda:v:50:y:2018:i:3:d:10.1007_s11123-018-0539-5 is not listed on IDEAS

    More about this item

    Keywords

    Multiple outputs; SFA; Monte Carlo simulation; Stochastic ray production frontier; Output distance function; C21; C40; D24;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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