MCMC Algorithm for Bayesian Heterogeneous Coefficients of Panel Data Model

Panel data models have been applied widely in many subject areas related to economic, social, and epidemiology. In some cases (e.g. epidemiology studies), the phenomena encountered have a complex relationship structured. The risk factors such as house index, healthy behaviour index, rainfall and the other risk factors of particular infectiouse disease may have different effect on the outcome due to the heterogeneity of crossection units. The effect of the covariates on outcome could vary over individual and time units. This condition is called as a non-stationary or instability relationship problem. This problem leads to bias and inefficient of the estimators. It is important to examine the heterogeneous coefficients model for avoiding inefficient estimator. We present in detail a statistical estimation procedure of the heterogeneous coefficients for fixed effect panel data model by means of the hierarchical Bayesian estimation approach. The challenges of the Bayesian approaches are finding the joint posterior distribution and developing the algorithm for estimating the parameters of interest. We find that the joint posterior distribution of the heterogeneous coefficients fixed effect panel data model does not follow any standard known distribution form. Consequently, the analytical solution cannot be applied and simulation approach of Markov Chain Monte Carlo (MCMC) was used. We present the MCMC procedure covering the derivation of the full conditional distribution of the parameters model and present step-by-step the Gibbs sampling algorithm. The idea of this preliminary research can be applied in various fields to overcome the non-stationarity problem.