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Central limit theorems and inference for sources of productivity change measured by nonparametric Malmquist indices

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  • Simar, Leopold
  • W. Wilson, Paul

Abstract

Malmquist indices are often used to measure productivity changes in dynamic settings and have been widely applied. The indices are typically estimated using data envelopment analysis (DEA) estimators. Malmquist indices are often decomposed into sub-indices that measure the sources of productivity change (e.g., changes in efficiency, technology or other factors). Recently, Kneip et al. (2018) provide new theoretical results enabling inference about productivity change for individual firms as well as average productivity changed measured in terms of geometric means. This paper extends those results to components of productivity change arising from various decompositions of Malmquist indices. New central limit theorems are developed to allow inference about arithmetic means of logarithms of the sub-indices as well as geometric means of (untransformed) sub-indices. The results are quite general and extend to other sub-indices not explicitly considered in this paper.
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Suggested Citation

  • Simar, Leopold & W. Wilson, Paul, 2019. "Central limit theorems and inference for sources of productivity change measured by nonparametric Malmquist indices," LIDAM Reprints ISBA 2019010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2019010
    Note: In : European Journal of Operational Research, vol. 277, no.2, p. 756-769 (2019)
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    Cited by:

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    3. Paul W. Wilson & Shirong Zhao, 2023. "Investigating the performance of Chinese banks over 2007–2014," Annals of Operations Research, Springer, vol. 321(1), pages 663-692, February.
    4. Pedro-José Martínez-Córdoba & Nicola Raimo & Filippo Vitolla & Bernardino Benito, 2020. "Achieving Sustainable Development Goals. Efficiency in the Spanish Clean Water and Sanitation Sector," Sustainability, MDPI, vol. 12(7), pages 1-13, April.
    5. Simar, Léopold & Wilson, Paul W., 2020. "Technical, allocative and overall efficiency: Estimation and inference," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1164-1176.
    6. Bigerna, Simona & D'Errico, Maria Chiara & Polinori, Paolo, 2020. "Heterogeneous impacts of regulatory policy stringency on the EU electricity Industry:A Bayesian shrinkage dynamic analysis," Energy Policy, Elsevier, vol. 142(C).
    7. Benito, Bernardino & Guillamón, María-Dolores & Martínez-Córdoba, Pedro-José, 2020. "Determinants of efficiency improvement in the Spanish public lighting sector," Utilities Policy, Elsevier, vol. 64(C).
    8. Léopold Simar & Paul W. Wilson, 2023. "Another look at productivity growth in industrialized countries," Journal of Productivity Analysis, Springer, vol. 60(3), pages 257-272, December.
    9. José Solana‐Ibáñez & Manuel Caravaca‐Garratón, 2021. "Stakeholder engagement and corporate social reputation: The influence of exogenous factors on efficiency performance (stakeholder engagement and exogenous factors): Stakeholder engagement and exogenou," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 28(6), pages 1891-1905, November.
    10. Daraio, Cinzia & Di Leo, Simone & Simar, Léopold, 2024. "Conical FDH Estimators of Directional Distances and Luenberger Productivity Indices for General Technologies," LIDAM Discussion Papers ISBA 2024009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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