Estimation of Zellner-Revankar Production Function Revisited

Mishra, SK (2006): Estimation of Zellner-Revankar Production Function Revisited. Unpublished.

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. A Fortran program for estimation of ZR production function by the Particle Swarm and the Differential Evolution has been appended.

• Item Type: MPRA Paper
• Institution: North-Eastern Hill University, Shillong (India)
• Language: English
• Keywords: Zellner-Revankar production function; maximum likelihood; global optimization; Repulsive Particle Swarm; Differential Evolution; U.S. Data; Transport Equipment Industry; Fortran Program; variable Returns to scale; sub-optimality
• Subjects: D - Microeconomics > D2 - Production and Organizations > D24 - Production; Cost; Capital and Total Factor Productivity; Capacity; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C61 - Optimization Techniques; Programming Models; Dynamic Analysis; C - Mathematical and Quantitative Methods > C3 - Econometric Methods: Multiple; Simultaneous Equation Models; Multiple Variables; Endogenous Regressors > C31 - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C63 - Computational Techniques; Simulation Modeling

References

· Box, G.E.P. and Cox, D.R. “An Analysis of Transformations”, Journal of the Royal Statistical Society, SeriesB, 26, pp. 566-578, 1963. · Eberhart R.C. and Kennedy J.: “A New Optimizer using Particle Swarm Theory”, Proceedings Sixth Symposium on Micro Machine and Human Science, pp. 39–43. IEEE Service Center, Piscataway, NJ, 1995. · Mishra, SK. "Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions", Social Science Research Network, http://ssrn.com/abstract=933827 , 2006 (a) · Mishra, S. K., "A Note on Numerical Estimation of Sato's Two-Level CES Production Function" Social Science Research Network, http://ssrn.com/abstract=947307, 2006(b). · Storn, R. and Price, K. "Differential Evolution - A Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces": Technical Report, International Computer Science Institute, Berkley, 1995. · Zellner, A. and Revankar, N.S. “Generalized Production Functions”, The Review of Economic Studies, 36(2), pp. 241-250, 1969.