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Forecasting the Malmquist productivity index

  • Alexandra Daskovska
  • Léopold Simar
  • Sébastien Bellegem


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.

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Article provided by Springer in its journal Journal of Productivity Analysis.

Volume (Year): 33 (2010)
Issue (Month): 2 (April)
Pages: 97-107

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Handle: RePEc:kap:jproda:v:33:y:2010:i:2:p:97-107
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  1. 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.
  2. Oulton,Nicholas & O'Mahony,Mary, 1994. "Productivity and Growth," Cambridge Books, Cambridge University Press, number 9780521453455, October.
  3. Simar, Leopold & Wilson, Paul W., 1999. "Estimating and bootstrapping Malmquist indices," European Journal of Operational Research, Elsevier, vol. 115(3), pages 459-471, June.
  4. Finn R. Førsund, 2002. "On the circularity of the Malmquist productivity index," ICER Working Papers 29-2002, ICER - International Centre for Economic Research.
  5. SIMAR, Léopold & WILSON, Paul W., 1998. "Productivity growth in industrialized countries," CORE Discussion Papers 1998036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Summers, Robert & Heston, Alan, 1991. "The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950-1988," The Quarterly Journal of Economics, MIT Press, vol. 106(2), pages 327-68, May.
  7. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, October.
  8. 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.
  9. 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.
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