Bayesian Spatial Quantile Panel Regression Model And Its Application

Spatial econometrics is one of an important topic in areas of econometrics. Spatial econometrics model can be used to measure the spillover effects among countries. Considering the spatial spillover effects is important, especially in the economic globalization and integration, capital flows, international trade and technology spillovers and other activities greatly improves the degree of dependency between various regions. At the same time, the economic and financial data often exhibit non-normal and non-symmetrical features, these characteristics make the traditional mean regression model assumptions hard to be satisfied, the quantile regression theory provides a powerful tool for solving this problem. It relaxes the assumptions of the model and has a good fitting effect for the non-normal and heteroscedasticity data; meanwhile, the quantile regression model can provide a more comprehensive description for the effect of the independent variables on the dependent at different quantiles. Therefore, spatial econometric model and quantile regression become the main focus of current research. In this paper, we combine the spatial econometric theory with quantile regression model and develop the Bayesian spatial quantile regression model. Spatial quantile regression model can be used to consider regional spatial dependence advantage, and the quantile regression method which not only can be used to describe the central tendency of the response variables, but also can characterize the variable has the advantages of extreme quantile behavior, so as to more fully describe the relationships between the dependent variable and the independent variables. Bayesian spatial quantile regression model can be used to provide technical support for the quantitative analysis of economic management and scientific decision in practice.Considering the spatial spillover effect between regions, this paper proposes Bayesian spatial panel data model using eigen value transform method. The method can effectively avoid the converted model has no closed form expression for the likelihood function, which is difficult for Bayesian analysis. By inferring the fully posterior probability distribution of parameters in model, developing the corresponding Gibbs and M-H algorithm to estimate and test the parameters. At the same time, we check the effectiveness of the method by the simulation experiment.Economic and financial variables often present the dynamic characteristic. This paper introduces the lag dependent variable to describe it. This model is a Bayesian spatial dynamic panel data model. After defining the space effect and time effect filter matrix respectively and then calculate the Kronecker product, spatial-temporal filter matrix is constructed to transform the model. According to the transformed model, this paper studies the model when the initial value is exogenous or endogenous. After deducing the full posterior probability density distribution of the parameters, we design the corresponding MCMC algorithm to estimate the model parameters, and finally we check the validity of the model by Monte Carlo simulation.Economic and financial data often exhibit non-normal and non-symmetrical features, these characteristics make the traditional mean regression model assumptions hard to be satisfied. Unlike the mean regression, quantile regression model relaxes the assumptions of the model and thus can be used to handle with the non-normal and heteroscedasticity data; meanwhile, quantile regression model can be used to comprehensively describe the effect of the independent variables on the dependent variable at different quantiles. Using the Bayesian quantile regression method, the asymmetric Laplace distribution is expressed as a linear combination of exponential distribution and normal distribution. We can obtain the analytical expressions of the conditions of quantile function posterior estimator, and we design the Gibbs and the M-H sampling algorithm to estimate the model parameters. At the same time, the experimental results of Monte Carlo simulation show that Bayesian spatial quantile model can provide a more comprehensive understand the relationship between the independent variables and the dependent variable.Using the Bayesian spatial quantile regression model, we study the causes of regional differences of energy intensity in the Chinese provinces using the panel data of 30 provinces during 1997-2006. We study the impact of economic development, industrial structure, trade openness and government expenditure on energy intensity. The results show that the importance of spatial dependence. The relationship between independent variables and dependent variable is different across different quantiles. The empirical results verify the feasibility of quantile econometric model.