Bayesian Empirical Likelihood Estimation for Kink Regression with Unknown Threshold

Abstract

Bayesian inference provides a flexible way of combining data with prior information from our knowledge. However, Bayesian estimation is very sensitive to the likelihood. We need to evaluate the likelihood density, which is difficult to evaluate, in order to use MCMC. Thus, this study considers using the Bayesian empirical likelihood(BEL) approach to kink regression. By taking the empirical likelihood into a Bayesian framework, the simulation results show an acceptable bias and MSE values when compared with LS, MLE, and Bayesian when the errors are generated from both normal and non-normal distributions. In addition, BEL can outperform the competing methods with quite small sample sizes under various error distributions. Then, we apply our approach to address a question: Has the accumulation of foreign reserves effectively protected the Thai economy from the financial crisis? The results demonstrate that foreign reserves provide both positive and negative effects on economic growth for high and low growth regimes of foreign reserve, respectively. We also find that foreign reserves seem to have played a role in offsetting the effect of the crisis when the growth rate of foreign reserves is less than 2.48%.