Comparison of Bayesian and Sample Theory Semi-Parametric Binary Response Model

A Bayesian semi-parametric estimation of the binary response model using Markov Chain Monte Carlo algorithms is proposed. The performances of the parametric and semi-parametric models are presented. The mean squared errors, receiver operating characteristic curve, and the marginal effect are used as the model selection criteria. The graphic processing computing is implemented to estimate the optimal bandwidth within the kernel density estimation for the semi-parametric model. Simulated data and Monte Carlo experiments show that unless the binary data is extremely unbalanced the semi-parametric and parametric models perform equally well. However, if the data is extremely unbalanced the maximum likelihood estimation does not converge whereas the Bayesian algorithms do. Finally, an application to evaluated the unemployment rate based on the PSID data is presented