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A Primal Divisia Technical Change Index Based on the Output Distance Function

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  • Guohua Feng

    ()

  • Apostolos Serletis

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

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 7/10.

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Length: 31 pages
Date of creation: 05 Mar 2010
Date of revision:
Handle: RePEc:msh:ebswps:2010-7

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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. 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.
  2. Charles R. Hulten, 2009. "Growth Accounting," NBER Working Papers 15341, National Bureau of Economic Research, Inc.
  3. Small, Kenneth A., 1996. "Economies of Scale and Self-Financing Rules with Noncompetitive Factor Markets," University of California Transportation Center, Working Papers qt70m3c7hh, University of California Transportation Center.
  4. 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.
  5. Caves, Douglas W & Christensen, Laurits R, 1980. "The Relative Efficiency of Public and Private Firms in a Competitive Environment: The Case of Canadian Railroads," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 958-76, October.
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  7. Melvyn A. Fuss, 1994. "Productivity Growth in Canadian Telecommunications," Canadian Journal of Economics, Canadian Economics Association, vol. 27(2), pages 371-92, May.
  8. Luis Orea, 2002. "Parametric Decomposition of a Generalized Malmquist Productivity Index," Journal of Productivity Analysis, Springer, vol. 18(1), pages 5-22, July.
  9. 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.
  10. Star, Spencer & Hall, Robert E, 1976. "An Approximate Divisia Index of Total Factor Productivity," Econometrica, Econometric Society, vol. 44(2), pages 257-63, March.
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  12. Robert Chambers & Rolf Färe, 1993. "Input-output separability in production models and its structural consequences," Journal of Economics, Springer, vol. 57(2), pages 197-202, June.
  13. Barnett, William A., 1980. "Economic monetary aggregates an application of index number and aggregation theory," Journal of Econometrics, Elsevier, vol. 14(1), pages 11-48, September.
  14. Feng, Guohua & Serletis, Apostolos, 2008. "Productivity trends in U.S. manufacturing: Evidence from the NQ and AIM cost functions," Journal of Econometrics, Elsevier, vol. 142(1), pages 281-311, January.
  15. J. Peter Neary, 2004. "Rationalizing the Penn World Table: True Multilateral Indices for International Comparisons of Real Income," American Economic Review, American Economic Association, vol. 94(5), pages 1411-1428, December.
  16. 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.
  17. C. Lovell, 2003. "The Decomposition of Malmquist Productivity Indexes," Journal of Productivity Analysis, Springer, vol. 20(3), pages 437-458, November.
  18. Bert M. Balk, 2005. "Divisia price and quantity indices: 80 years after," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(2), pages 119-158.
  19. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
  20. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-25, November.
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Citations

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Cited by:
  1. 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.
  2. 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.

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