A Note on Numerical Estimation of Sato's Two-Level Ces Production Function
14 Pages Posted: 28 Nov 2006
Date Written: November 26, 2006
Abstract
In this paper Sato's two-level CES production function has been estimated by nonlinear regression carried out through five different methods of optimization, namely, the Hooke-Jeeves Pattern Moves (HJPM), the Hooke-Jeeves-Quasi-Newton (HJQN), the Rosenbrock-Quasi-Newton (RQN), the Differential Evolution (DE) and the Repulsive Particle Swarm methods (RPS). The last two methods are particularly suited to optimization of extremely nonlinear (often multimodal) objective functions.
While data may be containing outliers, the method of least squares has a clear disadvantage as it may be pulled by extremely small or large errors. The absolute deviation estimation of parameters is more suitable in such cases. This paper has made an attempt to estimation of parameters of Sato's two-level CES production function by minimizing the sum of absolute errors. While the HJPM and the HJQN perform poorly at minimizing the sum of absolute deviations, the RQN performs much better. The DE and the RPS perform very well in estimating the parameters. We also estimate the parameters of a production function in which the output is determined by capital, labour and energy. The model is in the family of the Linear exponentials (LINEX) type. To estimate this model, we use German Sector "Market-determined Services" data for the years 1960-1989. Using the same data, we also estimate Sato's function with constant as well as variable returns to scale. Estimation has been done by minimization of the absolute deviations. Minimization has been done by Particle Swarm and Differential Evolution methods. The models fit extremely well to the data.
Keywords: Sato's productions function, CES, constant elasticity of substitution, two-level, Linear exponential, LINEX, Hooke Jeeves, Quasi-Newton, Rosenbrock, Repulsive Particle swarm, Differential Evolution, Global Optimization, Outliers, Least absolute deviation, Service Production function, German Data
JEL Classification: C13, C15, C63
Suggested Citation: Suggested Citation
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