A Bayesian Perspective on Error-Driven Cobb-Douglas Models: Revisiting Intrinsic Linearity

Non-linear models in the classical approach have been used by different researchers in the estimation of production function (case study: Cobb-Douglas), which is intrinsically linear. Bayesian approach to non-linear models had gained much ground but little attention had been paid towards using independent Normal-Gamma prior. This study aimed at investigating the behaviour of the parameters in the Cobb-Douglas Model using Bayesian approach. Metropolis–Within-Gibbs Algorithm (Posterior simulator) with non-informative prior was adopted to generate posterior estimates in this work. The results obtained from the simulation study showed that as sample size increases, the true values are significantly close to the posterior estimates. Also, the estimated standard deviations and the numerical standard errors decreased consistently when production function is “less one†, “greater than one†and “equal to one†. As the prior changed in all measures of return to scale, the considered criteria remained unchanged using the Geweke’s convergence diagnostics tool to show the good performance of non-informative prior of the error precision.