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Statistical Inference for the Aggregate Sources of Productivity Change Measured by Malmquist Productivity Indices

Author

Listed:
  • Simar, Léopold

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

  • Zelenyuk, Valentin
  • Zhao, Shirong

Abstract

The Malmquist productivity index (MPI) is one of the most widely used tools for measuring productivity change over time. A recent contribution by Pham et al. (2024) develops statistical inference procedures for the aggregate (or weighted) MPI of a group of firms. Building on this framework, the present paper develops statistical inference for the aggregate sources of productivity change measured by MPI. In particular, we derive the central limit theorems of the aggregated components, thereby enabling hypothesis testing for changes in technology, efficiency, and related sources. We illustrate the developed theoretical results by analyzing the sources of productivity change for 84 countries. Moreover, analogous theoretical results can be established for alternative productivity measures and their decompositions, including the Hicks–Moorsteen productivity index, the Luenberger productivity index, the Malmquist–Luenberger productivity index, etc.

Suggested Citation

  • Simar, Léopold & Zelenyuk, Valentin & Zhao, Shirong, 2026. "Statistical Inference for the Aggregate Sources of Productivity Change Measured by Malmquist Productivity Indices," LIDAM Discussion Papers ISBA 2026024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2026024
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    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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