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A primal Divisia technical change index based on the output distance function

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  • Feng, Guohua
  • Serletis, Apostolos

Abstract

We derive a primal Divisia technical change index based on the output distance function and further show the validity of this index from both economic and axiomatic points of view. In particular, we derive the primal Divisia technical change index by total differentiation of the output distance function with respect to a time trend. We then show that this index is dual to the Jorgenson and Griliches (1967) dual Divisia total factor productivity growth (TFPG) index when both the output and input markets are competitive; dual to the Diewert and Fox (2008) markup-adjusted revenue-share-based dual Divisia technical change index when market power is limited to output markets; dual to the Denny et al. (1981) and Fuss (1994) cost-elasticity-share-based dual Divisia TFPG index when market power is limited to output markets and constant returns to scale is present; and also dual to a markup-and-markdown-adjusted Divisia technical change index when market power is present in both output and input markets. Finally, we show that the primal Divisia technical change index satisfies the properties of identity, commensurability, monotonicity, and time reversal. It also satisfies the property of proportionality in the presence of path independence, which in turn requires separability between inputs and outputs and homogeneity of subaggregator functions.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 159 (2010)
Issue (Month): 2 (December)
Pages: 320-330

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Handle: RePEc:eee:econom:v:159:y:2010:i:2:p:320-330

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Output distance function Divisia technical change index Imperfect competition Axiomatic properties Path independence;

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References

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  1. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
  2. Kevin J. Fox & W. Erwin Diewert, 2004. "On the Estimation of Returns to Scale, Technical Progress and Monopolistic Markups," Econometric Society 2004 Australasian Meetings 310, Econometric Society.
  3. Melvyn A. Fuss, 1994. "Productivity Growth in Canadian Telecommunications," Canadian Journal of Economics, Canadian Economics Association, vol. 27(2), pages 371-92, May.
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  7. Star, Spencer & Hall, Robert E, 1976. "An Approximate Divisia Index of Total Factor Productivity," Econometrica, Econometric Society, vol. 44(2), pages 257-63, March.
  8. J. Peter Neary, 1996. "Rationalising the Penn World Table - True Multilateral Indices for International Comparisons of real Income," Working Papers 199622, School Of Economics, University College Dublin.
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  10. Small, Kenneth A., 1999. "Economies of scale and self-financing rules with non-competitive factor markets," Journal of Public Economics, Elsevier, vol. 74(3), pages 431-450, December.
  11. W. Diewert & Kevin Fox, 2010. "Malmquist and Törnqvist productivity indexes: returns to scale and technical progress with imperfect competition," Journal of Economics, Springer, vol. 101(1), pages 73-95, September.
  12. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-25, November.
  13. Susanto Basu & John G. Fernald, 1996. "Returns to scale in U.S. production: estimates and implications," International Finance Discussion Papers 546, Board of Governors of the Federal Reserve System (U.S.).
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  15. W. Diewert & Alice Nakamura, 2003. "Index Number Concepts, Measures and Decompositions of Productivity Growth," Journal of Productivity Analysis, Springer, vol. 19(2), pages 127-159, April.
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  17. C. Lovell, 2003. "The Decomposition of Malmquist Productivity Indexes," Journal of Productivity Analysis, Springer, vol. 20(3), pages 437-458, November.
  18. Diewert, Erwin & Fox, Kevin J., 2010. "Malmquist and Törnqvist Productivity Indexes: Returns to Scale and Technical Progress with Imperfect Competition," Economics working papers erwin_diewert-2010-5, Vancouver School of Economics, revised 13 Jul 2010.
  19. Charles R. Hulten, 2009. "Growth Accounting," NBER Working Papers 15341, National Bureau of Economic Research, Inc.
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Cited by:
  1. Guohua Feng & Apostolos Serletis, 2013. "Undesirable Outputs and a Primal Divisia Productivity Index Based on the Directional Output Distance Function," Working Papers 2013-15, Department of Economics, University of Calgary.
  2. Feng, Guohua & Zhang, Xiaohui, 2012. "Productivity and efficiency at large and community banks in the US: A Bayesian true random effects stochastic distance frontier analysis," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1883-1895.

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