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Forecasting the Malmquist Productivity Index

Author

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  • Daskovska, Alexandra
  • Simar, Léopold
  • Van Bellegem, Sébastien

Abstract

The Malmquist Productivity Index (MPI) suggests a convenient way of measuring the productivity change of a given unit between two consequent time periods. Until now, only a static approach for analyzing the MPI was available in the literature. However, this hides a potentially valuable information given by the evolution of productivity over time. In this paper, we introduce a dynamic procedure for forecasting the MPI. We compare several approaches and give credit to a method based on the assumption of circularity. Because the MPI is not circular, we present a new decomposition of the MPI, in which the time-varying indices are circular. Based on that decomposition, a new working dynamic forecasting procedure is proposed and illustrated. To construct prediction intervals of the MPI, we extend the bootstrap method in order to take into account potential serial correlation in the data. We illustrate all the new techniques described above by forecasting the productivityt index of 17 OCDE countries, constructed from their GDP, labor and capital stock.

Suggested Citation

  • Daskovska, Alexandra & Simar, Léopold & Van Bellegem, Sébastien, 2009. "Forecasting the Malmquist Productivity Index," TSE Working Papers 09-048, Toulouse School of Economics (TSE).
  • Handle: RePEc:tse:wpaper:22150
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    References listed on IDEAS

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    1. Léopold Simar & Paul Wilson, 2000. "Statistical Inference in Nonparametric Frontier Models: The State of the Art," Journal of Productivity Analysis, Springer, vol. 13(1), pages 49-78, January.
    2. Simar, L. & Wilson, P.W., 1998. "Productivity Growth in Industrialized Countries," Papers 9810, Catholique de Louvain - Institut de statistique.
    3. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, March.
    4. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers," Economic Journal, Royal Economic Society, vol. 92(365), pages 73-86, March.
    5. Oulton,Nicholas & O'Mahony,Mary, 1994. "Productivity and Growth," Cambridge Books, Cambridge University Press, number 9780521453455, March.
    6. Robert Summers & Alan Heston, 1991. "The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950–1988," The Quarterly Journal of Economics, Oxford University Press, vol. 106(2), pages 327-368.
    7. Van Bellegem, Sebastien & von Sachs, Rainer, 2004. "Forecasting economic time series with unconditional time-varying variance," International Journal of Forecasting, Elsevier, vol. 20(4), pages 611-627.
    8. Simar, Leopold & Wilson, Paul W., 1999. "Estimating and bootstrapping Malmquist indices," European Journal of Operational Research, Elsevier, vol. 115(3), pages 459-471, June.
    9. Finn R. FF8rsund, 2002. "On the circularity of the Malmquist productivity index," ICER Working Papers 29-2002, ICER - International Centre for Economic Research.
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    Cited by:

    1. Jakub Growiec, 2013. "On the measurement of technological progress across countries," Bank i Kredyt, Narodowy Bank Polski, vol. 44(5), pages 467-504.
    2. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    3. Florens, Jean-Pierre & Schwarz, Maik & Van Bellegem, Sébastien, 2010. "Nonparametric Frontier Estimation from Noisy Data," TSE Working Papers 10-179, Toulouse School of Economics (TSE).
    4. Andreas Mayer & Valentin Zelenyuk, 2014. "An Aggregation Paradigm for Hicks-Moorsteen Productivity Indexes," CEPA Working Papers Series WP012014, School of Economics, University of Queensland, Australia.
    5. Antonio Peyrache, 2013. "Multilateral productivity comparisons and homotheticity," Journal of Productivity Analysis, Springer, vol. 40(1), pages 57-65, August.
    6. Mayer, Andreas & Zelenyuk, Valentin, 2014. "Aggregation of Malmquist productivity indexes allowing for reallocation of resources," European Journal of Operational Research, Elsevier, vol. 238(3), pages 774-785.
    7. Benjamin Hampf, 2016. "Efficiency and productivity measurement with persistent benchmarks," Economics Bulletin, AccessEcon, vol. 36(3), pages 1715-1721.

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    Keywords

    Malmquist Productivity Index; circularity efficiency; smooth bootstrap;

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