On estimation of the CES production function—Revisited

Abstract

Highlights-We propose three solutions to avoid serious problems when estimating CES functions.-Removing discontinuities by using the limits of the CES function and its derivatives.-Circumventing large rounding errors by local linear approximations.-Handling ill-behaved objective functions by a multi-dimensional grid search. Highlights On Estimation of the CES Production Function-Revisited AbstractEstimation of the non-linear Constant Elasticity of Scale (CES) function is generally considered problematic due to convergence problems and unstable and/or meaningless results. These problems often arise from a non-smooth objective function with large flat areas, the discontinuity of the CES function where the elasticity of substitution is one, and possibly significant rounding errors where the elasticity of substitution is close to one. We suggest three (combinable) solutions that alleviate these problems and improve the reliability and stability of the results.JEL classification: C13, C51, D22, E23

Energy-Extended CES Aggregate Production: Current Aspects of Their Specification and Econometric Estimation

“…However, since the Kmenta approximation cannot be used to linearise CES production functions with more than two factors of production [176], it is found only in our samples for two factor (capital-labour) studies [6,74,85], and is therefore not a valid estimation technique for the energy-extended (capital-labour-energy) CES function.…”

“…Though complex, its popularity appears to be increasing, which may be due to the increased availability of econometric guidance [175], off-the-shelf programmes [30], and advances in computing power. A common method is a grid based search over relevant parameter ranges, such as that set out by Henningsen and Henningsen [30,176], and used by Heun et al [35]. Though non-linear techniques appear attractive to solve the inherently non-linear CES function, and have been found to perform better than linear alternatives [46]-care needs to be taken: for example Papageorgiou et al [171] (p. 26) note that "results of non-linear estimation procedures maybe sensitive to the choice of starting values of the estimation parameters".…”

Energy Rebound as a Potential Threat to a Low-Carbon Future: Findings from a New Exergy-Based National-Level Rebound Approach

“…Last, we obtain values for the six unknown parameters: θ, λ, δ, δ 1 , ρ, ρ 1 , by econometrically fitting Equation (6) using a customised version of the iterative, non-linear technique developed by Henningsen and Henningsen [90,91]. Two steps are completed.…”

Selection behavior of the global container shipping industry for carrier-owned and leased containers

“…Meanwhile, the estimation of the CES function by using non-linear methods cannot be performed very well due to the large flat surface of the objective function causing local minima, the discontinuity of the CES function, and considerable rounding errors of specific parameters, etc. (Henningsen and Henningsen, 2012).…”