Research On Bayesian Analysis Of Quantile Regression Econometric Models Based On MCMC And Its Application

Quantile regression method is a regression technique based on minimization problem to obtain sample quantile. The approach can capture systematic influences of covariates on the location, scale and shape of the conditional distribution of the response. Comparing it with ordinary least squares method, quantile regression method can not only measure the central tendency of the response but also its tail behavior. Therefore, quantile regression is an important approach in econometric analysis and economic applications. Under the framework of Bayesian theory, this paper discusses random coefficient quantile autoregression, Markov-switching random coefficient quantile autoregression, nonparametric quantile regression based on Fourier series and their applications to economic growth in China. The main achievements of this work are listed as follows.First, the distribution feature of time series could not always be described easily, due to its skewness, fat-tail and multimodal, this paper proposes a random coefficient quantile autoregressive models and exploits its heteroscedastics. The likelihood function based on the asymmetric Laplace distribution was employed irrespective of the original distribution of the data. To carry out Bayesian inference on the quantile autoregression, the Metropolis-Hastings algorithm was utilized to simulate the posterior marginal distribution of quantile autoregressive parameters, which resolved the difficulties of the high dimension numerical integral. The simulation result shows that the model can comprehensively describe how the lag variables influence on the location, scale and shape of the conditional distribution of the response.Second, considering the nonlinear of the tail behavior of economic variables, this paper is concerned with mixture conditional distribution in which a latent discrete state variable that indicates the regime from which a particular observation has been drawn. This state variable is specified to evolve according to a discrete-time discrete-state Markov process. A new full Bayesian approach based on the method of Gibbs sampling is developed by data augmentation. The state variables, one for each observation, can be simulated from their joint distribution given the data and the remaining parameters. This result serves to accelerate the convergence of the Gibbs sample. The simulation shows that the method performs very well in quantile regime switching models and can forecast the change points in future. Third, a method of estimating conditional quantile functions via Fourier series is proposed from a Bayesian perspective, which involves fewer smoothing parameter selection than that of spline-based and kernel-based quantile regression. The analytic posterior estimator of conditional quantile function is obtained by a mixture representation of asymmetric Laplace distribution. In addition, the MISE of the estimator at different quantiles converges to0and its convergence rate is faster than that of kernel method. The simulation shows that Fourier series is effective to fit quantile curves and its performance is better than splines approach.At last, the proposed models and approaches discussed in this paper can be used to analyze the volatility and convergence of economic growth based on economic theory in China. From the empirical results, the feature distribution of economic growth rate is skewness and fat-tail, and it is a heteroskedatic time series from period1971to2009; in our application to the GDP growth rates of every province in China after the reform and opening-up, the results show that there exist homogeneity of growth before the shareholding system reform on an enlarged scale but not after that; in our application to the influence of policy variable for economic growth, it shows that physical capital and human capital is nonlinear positive proportional to economic growth, but population rate is negative proportional to economic growth in the poor province but not for the rich province. The findings support that the underlying growth model for cross-provinces is of neoclassical growth type. Based on the above analysis, the paper presents the corresponding policy to promote China’s regional economic development coordinately.