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An aggregate quantity framework for measuring and decomposing productivity change


  • C. O’Donnell



Total factor productivity (TFP) can be defined as the ratio of an aggregate output to an aggregate input. This definition naturally leads to TFP indexes that can be expressed as the ratio of an output quantity index to an input quantity index. If the aggregator functions satisfy certain regularity properties then these TFP indexes are said to be multiplicatively complete. This paper formally defines what is meant by completeness and reveals that (1) the class of multiplicatively complete TFP indexes includes Laspeyres, Paasche, Fisher, Törnqvist and Hicks-Moorsteen indexes, (2) the popular Malmquist TFP index of Caves et al. (Econometrica 50(6):1393–1414, 1982a ) is incomplete, implying it cannot always be interpreted as a measure of productivity change, (3) all multiplicatively complete TFP indexes can be exhaustively decomposed into measures of technical change and efficiency change, and (4) the efficiency change component can be further decomposed into measures of technical, mix and scale efficiency change. Artificial data are used to illustrate the decomposition of Hicks-Moorsteen and Fisher TFP indexes. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • C. O’Donnell, 2012. "An aggregate quantity framework for measuring and decomposing productivity change," Journal of Productivity Analysis, Springer, vol. 38(3), pages 255-272, December.
  • Handle: RePEc:kap:jproda:v:38:y:2012:i:3:p:255-272
    DOI: 10.1007/s11123-012-0275-1

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    References listed on IDEAS

    1. D. W. Jorgenson & Z. Griliches, 1967. "The Explanation of Productivity Change," Review of Economic Studies, Oxford University Press, vol. 34(3), pages 249-283.
    2. C. Lovell, 2003. "The Decomposition of Malmquist Productivity Indexes," Journal of Productivity Analysis, Springer, vol. 20(3), pages 437-458, November.
    3. Robert G. Chambers & Rulon D. Pope, 1996. "Aggregate Productivity Measures," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 78(5), pages 1360-1365.
    4. Bjurek, Hans, 1996. " The Malmquist Total Factor Productivity Index," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 303-313, June.
    5. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, May.
    6. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    7. Bert Balk, 2001. "Scale Efficiency and Productivity Change," Journal of Productivity Analysis, Springer, vol. 15(3), pages 159-183, May.
    8. Ray, Subhash C & Mukherjee, Kankana, 1996. "Decomposition of the Fisher Ideal Index of Productivity: A Non-parametric Dual Analysis of US Airlines Data," Economic Journal, Royal Economic Society, vol. 106(439), pages 1659-1678, November.
    9. Timo Kuosmanen & Timo Sipiläinen, 2009. "Exact decomposition of the Fisher ideal total factor productivity index," Journal of Productivity Analysis, Springer, vol. 31(3), pages 137-150, June.
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    Cited by:

    1. Laurenceson, James & O'Donnell, Christopher, 2014. "New estimates and a decomposition of provincial productivity change in China," China Economic Review, Elsevier, vol. 30(C), pages 86-97.
    2. Ipatova, Irina, 2015. "The dynamics of total factor productivity and its components: Russian plastic production," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 38(2), pages 21-40.
    3. See, Kok Fong & Li, Fei, 2015. "Total factor productivity analysis of the UK airport industry: A Hicks-Moorsteen index method," Journal of Air Transport Management, Elsevier, vol. 43(C), pages 1-10.
    4. Karagiannis, Giannis & Knox Lovell, C.A., 2016. "Productivity measurement in radial DEA models with a single constant input," European Journal of Operational Research, Elsevier, vol. 251(1), pages 323-328.
    5. Rosenkranz, Lydia & Seintsch, Björn & Dieter, Matthias, 2015. "Decomposition analysis of changes in value added. A case study of the sawmilling and wood processing industry in Germany," Forest Policy and Economics, Elsevier, vol. 54(C), pages 36-50.


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