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A Note on Numerical Estimation of Sato’s Two-Level CES Production Function


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  • Mishra, SK


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. The minimization has been done by the five methods noted above. 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.As an exercise on real data, the German Sector "Merket-Determined Services" production function has been estimated with three inputs: Capital, Labour and Energy. The Linear Exponential (LINEX) and Sato's two-level specifications of the "Service Function" have been estimated.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 1019.

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Date of creation: 26 Nov 2006
Date of revision: 02 Dec 2006
Handle: RePEc:pra:mprapa:1019

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Keywords: Sato’s productions function; CES; constant elasticity of substitution; two-level; nonlinear regression; Hooke Jeeves; Quasi-Newton; Rosenbrock; Repulsive Particle swarm; Differential Evolution; Global Optimization; Econometrics; Estimation; Outliers; Least absolute deviation; error; German Sector Market-Determined Services; Service Production function; LINEX; Linear Exponential specification;

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Cited by:
  1. Mishra, SK, 2007. "A Brief History of Production Functions," MPRA Paper 5254, University Library of Munich, Germany.
  2. Keting Shen & John Whalley, 2013. "Capital-Labor-Energy Substitution in Nested CES Production Functions for China," NBER Working Papers 19104, National Bureau of Economic Research, Inc.
  3. repec:ebl:ecbull:v:3:y:2007:i:14:p:1-7 is not listed on IDEAS
  4. SK Mishra, 2007. "Estimation of Zellner-Revankar Production Function Revisited," Economics Bulletin, AccessEcon, vol. 3(14), pages 1-7.
  5. Arne Henningsen & Géraldine Henningsen, 2011. "Econometric Estimation of the “Constant Elasticity of Substitution" Function in R: Package micEconCES," IFRO Working Paper 2011/9, University of Copenhagen, Department of Food and Resource Economics.


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