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The Econometric Specification of Input Demand Systems Implied by Cost Function Representations

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  • Keith R. McLaren
  • Xueyan Zhao

Abstract

In the case of input demand systems based on specification of technology by a Translog cost function, it is common to estimate either a system of share equations alone, or to supplement them by the cost function. By adding up, one of the share equations is excluded. In this paper it is argued that a system of n-1 share equations is essentially incomplete, whereas if the n-1 share equations are supplemented by the cost function the implied error structure is inadmissible. Similarly, if the technology is specified by a normalized quadratic cost function, it is common to estimate either a system of n-1 demand equations alone, or to supplement them by the cost function. In both cases, the implied error structure is again inadmissible.

Suggested Citation

  • Keith R. McLaren & Xueyan Zhao, 2009. "The Econometric Specification of Input Demand Systems Implied by Cost Function Representations," Monash Econometrics and Business Statistics Working Papers 3/09, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2009-3
    as

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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2009/wp3-09.pdf
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    References listed on IDEAS

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    6. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-383, June.
    7. Halvorsen, Robert & Smith, Tim R, 1986. "Substitution Possibilities for Unpriced Natural Resources: Restricted Cost Functions for the Canadian Metal Mining Industry," The Review of Economics and Statistics, MIT Press, vol. 68(3), pages 398-405, August.
    8. C. Richard Shumway, 1983. "Supply, Demand, and Technology in a Multiproduct Industry: Texas Field Crops," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 65(4), pages 748-760.
    9. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
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    Cited by:

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    2. Vicente Ruiz, 2016. "Groundwater Overdraft, Electricity, and Wrong Incentives: Evidence from Mexico," Working Papers 2016.05, FAERE - French Association of Environmental and Resource Economists.

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    More about this item

    Keywords

    Cost Function; Input demands; Share equations; Translog; Normalized Quadratic; Error specification.;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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