The Empirical Application Of Bayesian Quantile Regression Method Via MCMC Algorithms

The theory of quantile regression has made up the defects of the ordinary least squares method in regression analysis, since Koenker and Bassett proposed in 1978. According to the conditional quantile of dependent variables, we make a regression for independent variables, then we can get all the quantile regression models. For the situation of small sample size, general quantile regression methods is difficult to ensure a good statistical properties of estimators, and when the objective functions is non-convex or no derivable, it is difficult to obtain a global optimal solution. With the promotion of Bayes’ theorem, it was discovered that the Bayesian method can estimate the model parameters under the small sample conditions well. Yu and Moyeed firstly proposed quantile regression in 2001, which based on Bayesian inference, in the mean while, many researchers was attracted.The second chapter in this article mainly elaborates the application of Bayesian inference in quantile regression models. The core idea of the method is that, turning the optimal solution of quantile regression to a density of Asymmetric Laplace distribution(ALD) maximum likelihood function. Through the MCMC algorithm(the sampling algorithm is M-H sampling), we can obtain the posterior distribution of the parameters.This article had made simulation and empirical applications for this method, which based on the theoretical method. In the empirical application, we had selected the sample datas from 1926 countries, and according to general area, our contry is divided into eastern, central and western, then this paper analyzed the relationship of all the eastern, central and western, including the gap between urban and rural areas, economic growth and financial development. At the same time, we had found the evidence that, the inverted U relationship between the financial development and the gap between urban and rural areas had a existence of statistical signifiance. However, there is no statistical significance in our sample regional economy according to the inverted U hypothesis of economic growth and the gap between urban and rural, which proposed by Kuznets. As a result of this research, Bayesian quantile regression has better accuracy and significance. According to the empirical results of there subregions, we got there conclusions.The last part of the paper is conclusion. Based on the theoretical and empirical methods, we had this summary. In the mean while, The paper try to pointed the research directions in the future.