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

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  • Simar, Léopold
  • 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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  • Simar, Léopold & W. Wilson, Paul, 2019. "Central limit theorems and inference for sources of productivity change measured by nonparametric Malmquist indices," European Journal of Operational Research, Elsevier, vol. 277(2), pages 756-769.
    • Handle: RePEc:eee:ejores:v:277:y:2019:i:2:p:756-769
    DOI: 10.1016/j.ejor.2019.02.040
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    1. Alin Marius Andries, 2011. "The Determinants of Bank Efficiency and Productivity Growth in the Central and Eastern European Banking Systems," Eastern European Economics, Taylor & Francis Journals, vol. 49(6), pages 38-59, November.
    2. William W. Cooper & Lawrence M. Seiford & Joe Zhu (ed.), 2011. "Handbook on Data Envelopment Analysis," International Series in Operations Research and Management Science, Springer, number 978-1-4419-6151-8, September.
    3. Ng, Ying Chu, 2011. "The productive efficiency of Chinese hospitals," China Economic Review, Elsevier, vol. 22(3), pages 428-439, September.
    4. Woo, Chungwon & Chung, Yanghon & Chun, Dongphil & Seo, Hangyeol & Hong, Sungjun, 2015. "The static and dynamic environmental efficiency of renewable energy: A Malmquist index analysis of OECD countries," Renewable and Sustainable Energy Reviews, Elsevier, vol. 47(C), pages 367-376.
    5. Simar, L. & Wilson, P.W., 1998. "Productivity Growth in Industrialized Countries," Papers 9810, Catholique de Louvain - Institut de statistique.
    6. Ray, Subhash C & Desli, Evangelia, 1997. "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries: Comment," American Economic Review, American Economic Association, vol. 87(5), pages 1033-1039, December.
    7. Simar, Léopold & Vanhems, Anne & Wilson, Paul W., 2012. "Statistical inference for DEA estimators of directional distances," European Journal of Operational Research, Elsevier, vol. 220(3), pages 853-864.
    8. Wilson, Paul W., 2018. "Dimension reduction in nonparametric models of production," European Journal of Operational Research, Elsevier, vol. 267(1), pages 349-367.
    9. 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.
    10. Maria Castro Lobo & Yasar Ozcan & Angela Silva & Marcos Lins & Roberto Fiszman, 2010. "Financing reform and productivity change in Brazilian teaching hospitals: Malmquist approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(2), pages 141-152, June.
    11. 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.
    12. C. Lovell, 2003. "The Decomposition of Malmquist Productivity Indexes," Journal of Productivity Analysis, Springer, vol. 20(3), pages 437-458, November.
    13. Alam, Ila M Semenick, 2001. "A Nonparametric Approach for Assessing Productivity Dynamics of Large U.S. Banks," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 33(1), pages 121-139, February.
    14. Emili Grifell-Tatjé & C.A. Knox Lovell & Robin Sickles & Laurens Cherchye & Bram de Rock & Antonio Estache & Marijn Verschelde, 2018. "The Oxford Handbook of Productivity Analysis," Post-Print hal-02573812, HAL.
    15. Ahn, Young-Hyo & Min, Hokey, 2014. "Evaluating the multi-period operating efficiency of international airports using data envelopment analysis and the Malmquist productivity index," Journal of Air Transport Management, Elsevier, vol. 39(C), pages 12-22.
    16. 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.
    17. 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.
    18. 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.
    19. Goksel Armagan & Altug Ozden & Selim Bekcioglu, 2010. "Efficiency and total factor productivity of crop production at NUTS1 level in Turkey: Malmquist index approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(3), pages 573-581, April.
    20. Simar, Leopold & Wilson, Paul W., 1999. "Estimating and bootstrapping Malmquist indices," European Journal of Operational Research, Elsevier, vol. 115(3), pages 459-471, June.
    21. Hedayet Chowdhury & Walter Wodchis & Audrey Laporte, 2011. "Efficiency and technological change in health care services in Ontario," International Journal of Productivity and Performance Management, Emerald Group Publishing Limited, vol. 60(7), pages 721-745, September.
    22. 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.
    23. Gilbert, R. Alton & Wilson, Paul W., 1998. "Effects of Deregulation on the Productivity of Korean Banks," Journal of Economics and Business, Elsevier, vol. 50(2), pages 133-155, March.
    24. Bert Balk, 2001. "Scale Efficiency and Productivity Change," Journal of Productivity Analysis, Springer, vol. 15(3), pages 159-183, May.
    25. Soltane Bassem, Ben, 2014. "Total factor productivity change of MENA microfinance institutions: A Malmquist productivity index approach," Economic Modelling, Elsevier, vol. 39(C), pages 182-189.
    26. Chang, Shyr-Juh & Hsiao, Hsing-Chin & Huang, Li-Hua & Chang, Hsihui, 2011. "Taiwan quality indicator project and hospital productivity growth," Omega, Elsevier, vol. 39(1), pages 14-22, January.
    27. Aly, Hassan Y, et al, 1990. "Technical, Scale, and Allocative Efficiencies in U.S. Banking: An Empirical Investigation," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 211-218, May.
    28. 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.
    29. A L Johnson & L F McGinnis, 2009. "The hyperbolic-oriented efficiency measure as a remedy to infeasibility of super efficiency models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1511-1517, November.
    30. Rolf Färe & Shawna Grosskopf & Dimitris Margaritis, 2011. "Malmquist Productivity Indexes and DEA," 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 127-149, Springer.
    31. Jose Zofio & C. A. Knox Lovell, 2001. "Graph efficiency and productivity measures: an application to US agriculture," Applied Economics, Taylor & Francis Journals, vol. 33(11), pages 1433-1442.
    32. Fare, Rolf & Grosskopf, Shawna & Norris, Mary, 1997. "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries: Reply," American Economic Review, American Economic Association, vol. 87(5), pages 1040-1043, December.
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    3. 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.
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    5. 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).
    6. 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.
    7. 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).
    8. 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.
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    10. 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).

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