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Statistical Inference for Hicks–Moorsteen Productivity Indices

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  • Simar, Léopold

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

  • Zelenyuk, Valentin
  • Zhao, Shirong

Abstract

The statistical framework for the Malmquist productivity index (MPI) is now welldeveloped and emphasizes the importance of developing such a framework for its alternatives. We try to fill this gap in the literature for another popular measure, known as Hicks–Moorsteen Productivity Index (HMPI). Unlike MPI, the HMPI has a total factor productivity interpretation in the sense of measuring productivity as the ratio of aggregated outputs to aggregated inputs and has other useful advantages over MPI. In this work, we develop a novel framework for statistical inference for HMPI in various contexts: when its components are known or when they are replaced with nonparametric envelopment estimators. This will be done for a particular firm’s HMPI as well as for the simple mean (unweighted) HMPI and the aggregate (weighted) HMPI. Our results further enrich the recent theoretical developments of nonparametric envelopment estimators for the various efficiency and productivity measures. We examine the performance of these theoretical results for the unweighted and weighted mean of HMPI using Monte-Carlo simulations and also provide an empirical illustration.

Suggested Citation

  • Simar, Léopold & Zelenyuk, Valentin & Zhao, Shirong, 2023. "Statistical Inference for Hicks–Moorsteen Productivity Indices," LIDAM Discussion Papers ISBA 2023032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2023032
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    References listed on IDEAS

    as
    1. Léopold Simar & Paul Wilson, 2011. "Inference by the m out of n bootstrap in nonparametric frontier models," Journal of Productivity Analysis, Springer, vol. 36(1), pages 33-53, August.
    2. Manh D. Pham & Léopold Simar & Valentin Zelenyuk, 2019. "Statistical Inference for Aggregation of Malmquist Productivity Indices," CEPA Working Papers Series WP082019, School of Economics, University of Queensland, Australia.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Hicks–Moorsteen Productivity Index ; Data Envelopment Analysis ; Aggregate ; Central Limit Theorem;
    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
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models

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