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Conical FDH Estimators of General Technologies, with Applications to Returns to Scale and Malmquist Productivity Indices

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  • Kneip, Alois

    (Universität Bonn)

  • Simar, Léopold

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Wilson, Paul W.

    (Clemson University)

Abstract

Nonparametric envelopment estimators are often used to estimate the attainable sets and its efficient boundary and to assess efficiency and changes in productivity. Kneip et al. (2015, 2016) provide asymptotic theory enabling inference about expected efficiency and testing constant versus variable returns to scale using these estimators, and Kneip et al. (2021) provide asymptotic results that can be used to make inference about expected changes in productivity measured by Malmquist indices. All of these results require convexity of the attainable set, but in a number of situations this assumption is questionable. Kneip et al. (2016) also provide a test of convexity versus non-convexity of a production set, and convexity is rejected in several recent studies. This paper extends the results mentioned above to allow for possibly nonconvex technologies. Properties of a nonparametric envelopment estimator of distance to the boundary of the cone spanned by a possibly non-convex attainable set are derived. These new results are then extended to make inference about geometric means of Malmquist indices and to test constant versus non-constant returns to scale when the production set is not convex.

Suggested Citation

  • Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2022. "Conical FDH Estimators of General Technologies, with Applications to Returns to Scale and Malmquist Productivity Indices," LIDAM Discussion Papers ISBA 2022024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2022024
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    References listed on IDEAS

    as
    1. Kerstens, Kristiaan & Vanden Eeckaut, Philippe, 1999. "Estimating returns to scale using non-parametric deterministic technologies: A new method based on goodness-of-fit," European Journal of Operational Research, Elsevier, vol. 113(1), pages 206-214, February.
    2. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    3. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, vol. 44(1), pages 49-61, January.
    4. Amy Apon & Linh Ngo & Michael Payne & Paul Wilson, 2015. "Assessing the effect of high performance computing capabilities on academic research output," Empirical Economics, Springer, vol. 48(1), pages 283-312, February.
    5. Daraio, Cinzia & Simar, Leopold & Wilson, Paul, 2018. "Central limit theorems for conditional efficiency measures and tests of the ‘separability’ condition in non-parametric, two-stage models of production," LIDAM Reprints ISBA 2018023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2018. "Central limit theorems for conditional efficiency measures and tests of the ‘separability’ condition in non‐parametric, two‐stage models of production," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 170-191, June.
    7. Caitlin T. O’Loughlin & Paul W. Wilson, 2021. "Benchmarking the performance of US Municipalities," Empirical Economics, Springer, vol. 60(6), pages 2665-2700, June.
    8. Wheelock, David C & Wilson, Paul W, 1999. "Technical Progress, Inefficiency, and Productivity Change in U.S. Banking, 1984-1993," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 31(2), pages 212-234, May.
    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. Wilson, Paul W., 2018. "Dimension reduction in nonparametric models of production," European Journal of Operational Research, Elsevier, vol. 267(1), pages 349-367.
    11. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2008. "Asymptotics And Consistent Bootstraps For Dea Estimators In Nonparametric Frontier Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1663-1697, December.
    12. Ball, V. Eldon & Lovell, C.A. Knox & Luu, H. & Nehring, Richard F., 2004. "Incorporating Environmental Impacts in the Measurement of Agricultural Productivity Growth," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 29(3), pages 1-25, December.
    13. Abdelaati Daouia & Léopold Simar & Paul W. Wilson, 2017. "Measuring firm performance using nonparametric quantile-type distances," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 156-181, March.
    14. 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.
    15. Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2018. "Central limit theorems for conditional efficiency measures and tests of the ‘separability’ condition in non‐parametric, two‐stage models of production," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 170-191, June.
    16. Kneip, Alois & Park, Byeong U. & Simar, Léopold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(6), pages 783-793, December.
    17. Guangshun Qiao & Zhan-ao Wang, 2021. "Vertical integration vs. specialization: a nonparametric conditional efficiency estimate for the global semiconductor industry," Journal of Productivity Analysis, Springer, vol. 56(2), pages 139-150, December.
    18. Park, B.U. & Jeong, S.-O. & Simar, L., 2010. "Asymptotic distribution of conical-hull estimators of directional edges," LIDAM Reprints ISBA 2010025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    More about this item

    Keywords

    Non-convex production sets ; FDH ; hypothesis test ; returns to scale ; Malmquist index ; productivity change;
    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
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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