Mishra, SK (2006): A Note on Numerical Estimation of Sato’s Two-Level CES Production Function.
Download (185Kb) | Preview
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.
|Item Type:||MPRA Paper|
|Institution:||North-Eastern Hill University, Shillong (India)|
|Original Title:||A Note on Numerical Estimation of Sato’s Two-Level CES Production Function|
|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|
|Subjects:||D - Microeconomics > D2 - Production and Organizations > D20 - General
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
C - Mathematical and Quantitative Methods > C2 - Single Equation Models; Single Variables > C20 - General
|Depositing User:||Sudhanshu Kumar Mishra|
|Date Deposited:||04. Dec 2006|
|Last Modified:||21. Feb 2013 00:39|
· Arrow K.J., Chenery H.B., Minhas B.S. and Solow R.M.: “Capital-Labor Substitution and Economic Efficiency”, Review of Economics and Statistics. 43: pp. 225-50, 1961 · Charnes, A., Cooper, W.W. and Ferguson, R.O.: “Optimal Estimation of Executive Compensation by Linear Programming”, Management Science, 1, pp. 138-151, 1955. · Dasgupta, M. and Mishra, S.K.,: "Least Absolute Deviation Estimation of Linear Econometric Models: A Literature Review". SSRN, http://ssrn.com/abstract=552502, 2004. · 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. · Fair, R.C.: "On Robust Estimation of Econometric Models", Annals of Economic and Social Measurement, 3, pp. 667-678, 1974. · Felipe, J. and Fisher, F.M.:"Aggregation in Production Functions: What Applied Economists Should Know" . Metroeconomica, 54, pp. 208-262, 2001. Available at Social Science Research Network (SSRN) http://ssrn.com/abstract=422067. · Fisher, F.M.: Aggregation. Aggregate Production Functions and Related Topics. The MIT Press, Cambridge, MA, 1993. · Griliches, Z.: “Capital-Skill Complementarity”, Review of Economics and Statistics, 6, pp. 465-468, 1969. · Intriligator, M.D.: Econometric Models, Techniques and Applications, Prentice Hall, Inc. New Jersey, 1978. · Kmenta, J.: “On Estimation of the CES Production Function”, International Economic Review, 8, pp. 180-189, 1967. · Kmenta, J.: Elements of Econometrics, Macmillan Publishing Co. Inc. New York, 1971. · Kümmel, R.: “The Impact of Energy on Industrial Growth”, Energy - The International Journal, 7, pp. 189-203, 1982. · Kümmel R, Strassl W, Gossner A, Eichhorn W.: “Technical Progress and Energy Dependent Production Functions”, Journal of Economics, 45, pp. 285-311, 1985. · Leontief, W.W.: “Introduction to a Theory of the Internal Structure of Functional Relationships” Econometrica, 15, 4. pp. 361-73, 1947. · Lindenberger, D.: “Service Production Functions”, EWI Working Paper No. 03.02, Institute of Energy Economics, University of Cologne (EWI), Cologne, http://www.ewi.uni-koeln.de/ewi/content/e266/e283/e281/Ewiwp0302_ger.pdf , 2003. · Mishra, S.K.: “Performance of Repulsive Particle Swarm Method in Global Optimization of Some Important Test Functions: A Fortran Program” , Social Science Research Network (SSRN), Working Papers Series, http://ssrn.com/abstract=924339 , 2006 (a). · 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 (b) · Papageorgiou, C and Saam, M.: “Two-Level CES Production Technology in the Solow and Diamond Growth Models”, Working Paper 2005-07, Department of Economics Louisiana State Univ, http://www.bus.lsu.edu/economics/papers/pap05_07.pdf , 2005 · Sato, K.: “A Two-Level Constant-Elasticity-of-Substitution Production Function”, Review of Economic Studies, 43, pp. 201-218, 1967. · Schlossmacher, E.J.: "An Alternative Technique for Absolute Deviations Curve Fitting", Journal of the American Statistical Association, 68, pp. 857-859, 1973. · 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. · Taylor, L.D.: “Estimation by Minimizing the Sum of Absolute Errors”, in Zarembka, P. (Ed) Frontiers of Econometrics, Academic Press, New York, 1974.