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Least squares estimation of joint production functions by the Differential Evolution method of global optimization

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Abstract

In the economics of joint production one often distinguishes between the two cases: the one in which a firm produces multiple products each produced under separate production process, and the other “true joint production” where a number of outputs are produced from a single production process, where each product shares common inputs. In the econometric practice the first case has often been dealt with by aggregation of individual production functions into a macro production function. The second case has often called for estimation of an implicit aggregate production function. Most of the studies relating to estimation of joint production functions have noted two difficulties: first that allocation of inputs to different outputs are not known, and the second that a method of estimation (such as the Least Squares) cannot have more than one dependent variable. Construction of a composite (macro) output function is at least partly motivated by the inability of the estimation methods to deal with multiple dependent variables and different forms of production function for different outputs. This study has conducted some simulation experiments on joint estimation of the CES, the Transcendental and the Nerlove-Ringstad functions. Allocation parameters (of inputs) across the products have been introduced. Estimation has been done jointly, but without constructing a composite macro production function or an output transformation function. We use nonlinear least squares based on the Differential Evolution method of global optimization that permits fitting multiple production functions simultaneously.

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  • Mishra, SK, 2007. "Least squares estimation of joint production functions by the Differential Evolution method of global optimization," MPRA Paper 4813, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:4813
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    References listed on IDEAS

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    1. Vinod, Hrishikesh D, 1969. "Econometrics of Joint Production-A Reply," Econometrica, Econometric Society, vol. 37(4), pages 739-740, October.
    2. Dhrymes, Phoebus J & Mitchell, B M, 1969. "Estimation of Joint Production Functions," Econometrica, Econometric Society, vol. 37(4), pages 732-736, October.
    3. K. Sato, 1967. "A Two-Level Constant-Elasticity-of-Substitution Production Function," Review of Economic Studies, Oxford University Press, vol. 34(2), pages 201-218.
    4. Chetty, V Karuppan, 1969. "Econometrics of Joint Production: A Comment," Econometrica, Econometric Society, vol. 37(4), pages 731-731, October.
    5. Chizmar, John F & Zak, Thomas A, 1983. "Modeling Multiple Outputs in Educational Production Functions," American Economic Review, American Economic Association, vol. 73(2), pages 17-22, May.
    6. Vinod, H. D., 1976. "Canonical ridge and econometrics of joint production," Journal of Econometrics, Elsevier, vol. 4(2), pages 147-166, May.
    7. Diewert, W E, 1971. "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, University of Chicago Press, vol. 79(3), pages 481-507, May-June.
    8. Rao, Potluri, 1969. "A Note on Econometrics of Joint Production," Econometrica, Econometric Society, vol. 37(4), pages 737-738, October.
    9. Mishra, SK, 2007. "Performance of Differential Evolution Method in Least Squares Fitting of Some Typical Nonlinear Curves," MPRA Paper 4634, University Library of Munich, Germany.
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    Cited by:

    1. S K Mishra, 2010. "A Brief History of Production Functions," The IUP Journal of Managerial Economics, IUP Publications, vol. 0(4), pages 6-34, November.

    More about this item

    Keywords

    Joint production; multiple output; allocation parameters; nonlinear least squares; Differential Evolution; Nerlove-Ringstad; Transcendental; CES; macro; implicit; composite production function; transformation function; canonical correlation; multiple dependent variables;

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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