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

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.