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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

    as
    1. Diewert, W E & Wales, T J, 1988. "Normalized Quadratic Systems of Consumer Demand Functions," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 303-312, July.
    2. 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.
    3. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    4. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, January.
    5. Giancarlo Moschini, 1988. "A Model of Production with Supply Management for the Canadian Agricultural Sector," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 70(2), pages 318-329.
    6. 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.
    7. 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.
    8. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
    9. Fuss, Melvyn A., 1977. "The demand for energy in Canadian manufacturing : An example of the estimation of production structures with many inputs," Journal of Econometrics, Elsevier, vol. 5(1), pages 89-116, January.
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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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