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An aggregate quantity framework for measuring and decomposing productivity change

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  • C. O’Donnell

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Abstract

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

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File URL: http://hdl.handle.net/10.1007/s11123-012-0275-1
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Bibliographic Info

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

Volume (Year): 38 (2012)
Issue (Month): 3 (December)
Pages: 255-272

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Handle: RePEc:kap:jproda:v:38:y:2012:i:3:p:255-272

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Web page: http://www.springerlink.com/link.asp?id=100296

Related research

Keywords: Index numbers; Total factor productivity; Efficiency; Malmquist index; Hicks-Moorsteen index; Fisher index;

References

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  1. 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.
  2. Bert Balk, 2001. "Scale Efficiency and Productivity Change," Journal of Productivity Analysis, Springer, vol. 15(3), pages 159-183, May.
  3. 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 1659-78, November.
  4. 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.
  5. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, October.
  6. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
  7. Bjurek, Hans, 1996. " The Malmquist Total Factor Productivity Index," Scandinavian Journal of Economics, Wiley Blackwell, vol. 98(2), pages 303-13, June.
  8. C. Lovell, 2003. "The Decomposition of Malmquist Productivity Indexes," Journal of Productivity Analysis, Springer, vol. 20(3), pages 437-458, November.
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