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


  • Keith R. McLaren


  • Xueyan Zhao



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

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    References listed on IDEAS

    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. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    3. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, March.
    4. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
    5. 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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    More about this item


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

    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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