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Intrinsically nonlinear models are models that cannot be made linear irrespective of the linearization method employed. Statisticians are often interested in estimating the parameters of nonlinear models but are faced with great difficulties since some nonlinear models cannot be solved analytically however, researchers have developed a way out of this difficulty using the Gauss-Newton Method via Kmenta approximation. This paper made use of classical and Bayesian approaches to estimate the Constant Elasticity of Substitution (CES) production function. The Metropolis-within Gibbs Algorithm was used to carry out the analysis as shown in the empirical illustrations and the result showed that the Numerical Standard Error (NSE) is minimal while the posterior estimates converged to the region of the true values making the Bayesian approach more preferred.

Effects of varying substitution parameter (ρ) of the CES production function on the estimation methods: Bayesian and frequentist approaches