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Estimation of Zellner-Revankar Production Function Revisited

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Abstract

Arnold Zellner and Nagesh Revankar in their well-known paper “Generalized Production Functions” [The Review of Economic Studies, 36(2), pp. 241-250, 1969] introduced a new generalized production function, which was illustrated by an example of fitting the generalized Cobb-Douglas function to the U.S. data for Transportation Equipment Industry. For estimating the parameters of their production function, they used a method in which one of the parameters (theta) is chosen at the trial basis and other parameters relating to elasticity and returns to scale are estimated so as to maximize the likelihood function. Repeated trials are made with different values of theta so as to obtain the global maximum of the likelihood function. In this paper we show that the method suggested and used by Zellner and Revankar (ZR) may easily be caught into a local optimum trap. We also show that the estimated parameters reported by them are grossly sub-optimal. Using the Differential Evolution (DE) and the Repulsive Particle Swarm (RPS) methods of global optimization, the present paper re-estimates the parameters of the ZR production function with the U.S. data used by ZR. We find that the DE and the RPS estimates of parameters are significantly different from (but much better than) those estimated by ZR. We also find that the returns to scale do not vary with the size of output as reported by ZR.

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  • Mishra, SK, 2006. "Estimation of Zellner-Revankar Production Function Revisited," MPRA Paper 1172, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:1172
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    as
    1. SK Mishra, 2007. "Estimation of Zellner-Revankar Production Function Revisited," Economics Bulletin, AccessEcon, vol. 3(14), pages 1-7.
    2. Mishra, SK, 2006. "A Note on Numerical Estimation of Sato’s Two-Level CES Production Function," MPRA Paper 1019, University Library of Munich, Germany, revised 02 Dec 2006.
    3. A. Zellner & N. S. Revankar, 1969. "Generalized Production Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(2), pages 241-250.
    4. Mishra, SK, 2006. "Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions," MPRA Paper 1005, University Library of Munich, Germany.
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    1. SK Mishra, 2007. "Estimation of Zellner-Revankar Production Function Revisited," Economics Bulletin, AccessEcon, vol. 3(14), pages 1-7.
    2. repec:ebl:ecbull:v:3:y:2007:i:14:p:1-7 is not listed on IDEAS
    3. S K Mishra, 2007. "Globalization and Structural Changes in the Indian Industrial Sector: An Analysis of Production Functions," The IUP Journal of Managerial Economics, IUP Publications, vol. 0(4), pages 56-81, November.
    4. 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.

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    More about this item

    Keywords

    Zellner-Revankar production function; maximum likelihood; global optimization; Repulsive Particle Swarm; Differential Evolution; U.S. Data; Transport Equipment Industry; variable Returns to scale; sub-optimality;
    All these keywords.

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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