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Testing productivity change, frontier shift, and efficiency change

Author

Listed:
  • Mette Asmild

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

  • Dorte Kronborg

    (Center for Statistics, Department of Finance, Copenhagen Business School)

  • Anders Rønn-Nielsen

    (Center for Statistics, Department of Finance, Copenhagen Business School)

Abstract

Inference about productivity change over time based on data envelopment (DEA) has focused primarily on the Malmquist index and is based on asymptotic properties of the index. In this paper we propose a novel set of significance tests for DEA based productivity change measures based on permutations and accounting for the inherent correlations when panel data are observed. The tests are easily implementable and give exact significance probabilities as they are not based on asymptotic properties. Tests are formulated both for the geometric means of the Malmquist index, and also of its components, i.e. the frontier shift index and the eciency change index, which together enable analysis of not only the presence of differences, but also gives an indication of whether the productivity change is due to shifts in the frontiers and/or changes in the efficiency distributions. Simulation results show the power of, and suggest how to interpret the results of, the proposed tests. Finally, the tests are illustrated using a data set from the literature.

Suggested Citation

  • Mette Asmild & Dorte Kronborg & Anders Rønn-Nielsen, 2018. "Testing productivity change, frontier shift, and efficiency change," IFRO Working Paper 2018/07, University of Copenhagen, Department of Food and Resource Economics.
    • Handle: RePEc:foi:wpaper:2018_07
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    File URL: http://okonomi.foi.dk/workingpapers/WPpdf/WP2018/IFRO_WP_2018_07.pdf
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    References listed on IDEAS

    as
    1. Alois Kneip & Léopold Simar & Paul W. Wilson, 2016. "Testing Hypotheses in Nonparametric Models of Production," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 435-456, July.
    2. Rajiv D. Banker & Ram Natarajan, 2011. "Statistical Tests Based on DEA Efficiency Scores," International Series in Operations Research & Management Science, in: William W. Cooper & Lawrence M. Seiford & Joe Zhu (ed.), Handbook on Data Envelopment Analysis, chapter 0, pages 273-295, Springer.
    3. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2021. "Inference In Dynamic, Nonparametric Models Of Production: Central Limit Theorems For Malmquist Indices," Econometric Theory, Cambridge University Press, vol. 37(3), pages 537-572, June.
    4. Pastor, Jesus T. & Lovell, C.A. Knox, 2005. "A global Malmquist productivity index," Economics Letters, Elsevier, vol. 88(2), pages 266-271, August.
    5. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    6. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    7. Pastor, Jesús T. & Asmild, Mette & Lovell, C.A. Knox, 2011. "The biennial Malmquist productivity change index," Socio-Economic Planning Sciences, Elsevier, vol. 45(1), pages 10-15, March.
    8. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2015. "When Bias Kills The Variance: Central Limit Theorems For Dea And Fdh Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 31(2), pages 394-422, April.
    9. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    10. Mette Asmild & Fai Tam, 2007. "Estimating global frontier shifts and global Malmquist indices," Journal of Productivity Analysis, Springer, vol. 27(2), pages 137-148, April.
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    Cited by:

    1. Aigner, Lorenz & Asmild, Mette, 2023. "Identifying the most important set of weights when modelling bad outputs with the weak disposability approach," European Journal of Operational Research, Elsevier, vol. 310(2), pages 751-759.
    2. Anders Rønn-Nielsen & Dorte Kronborg & Mette Asmild, 2019. "Exact tests on returns to scale and comparisons of production frontiers in nonparametric models," IFRO Working Paper 2019/04, University of Copenhagen, Department of Food and Resource Economics.

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    More about this item

    Keywords

    Malmquist index; frontier shift; efficiency change; Data Envelopment Analysis (DEA); panel data; permutation tests; inference.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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