Bayesian Spatial Quantile Econometrics Model And Its Application

Spatial econometrics is one of the frontiers in the field of Econometrics.As any economic individuals cannot exist independently,it has various relations to the adjacent individual economy,which makes the theory and application of spatial econometrics has attracted widespread attention in academic circles.Spatial econometrics introduces the spatial effect and spatial dependence into the traditional econometric models and statistical methods,providing a theoretical framework and new analysis method for solving the spatial dependence and spatial heterogeneity problems in management and economic activities.In addition,we add the spatial weight matrix into the model analysis,which can measure the spatial effect of the individuals.Especially under the background of economic globalization and integration,international trade,capital flows and other activities can greatly improve the financial dependence among various countries and regions.The co-movements among the global stock markets are significantly increased,it is particularly important to consider the spatial spillover effects of the stock markets.As the sharp and tail feature of spatial financial data,the classical mean regression model is difficult to satisfy the assumptions.But quantile regression theory provides an effective tool to solve this problem.The quantile regression model could completely characters the center position and tail behavior tendency of explained variable.It also provides methods and effective support tools to fully describe the causal relationship between explanatory variables and explained variable.When the Bayesian theory is introduced,we can consider the uncertainty risk of the parameters.It expands the research methods and perspectives of spatial econometrics in theory,and provides technical support for decision-making analysis of economic and management in practice.To the spatial dependence in spatial data,we describe the asymmetric Laplace distribution as a mixed form of the classical Gauss distribution and exponential distribution in this paper.The spatial dependence is integrated into the asymmetric Laplace process by the mixed expression.Then,the conditional quantile model is used to estimate the quantile multiple regression model,which can depict the heterogeneity influence of the independent variables on the dependent variables.Under three kinds of mixed expressions,we derive the properties of Bayesian spatial quantile autoregressive models.Finally,a simulation analysis is given to demonstrate the properties of Bayesian spatial quantile autoregressive model.At present,only the geographically weighted regression model is employed to deal with the spatial dependence and spatial heterogeneity of cross sectional data from the local perspective.However,there are three main limitations in the estimation of geographically weighted regression models.Firstly,the random error term is subject to normal distribution or other known distribution;secondly,enormous computing;finally,it can only describe the central tendency between the response and the covariate variable,but cannot depict the tail property.In this paper,Bayesian theory and quantile regression method are used to estimate the geographically weighted regression model,and the mathematical derivation and statistical inference of geographically weighted regression model are also discussed.Finally,the simulation study and parameter estimation are carried out to the geographically weighted regression model,Bayesian geographically weighted regression model and M-quantile geographically weighted regression model.In this paper,a Bayesian spatial panel quantile regression model is developed,which not only fit the non-normal and heteroscedastic data,but also describe the marginal effects of the explanatory variables on the explained variables under different quantiles.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 design the Gibbs and the M-H sampling algorithm to estimate the model parameters.Finally,Monte Carlo simulation is used to test the proposed model and method.The research of stock market co-movement has been a hot issue in financial research.We choose the stock market data of forty-one countries,and treat the stock market return as the response variable.The exchange rate volatility,the GDP growth rate and the sovereign default rate are covariates.Firstly,the spatial dependence of the global stock markets is estimated by the first order spatial mixed regression model.Secondly,the two order spatial mixed regression model is employed to study the spatial effects of stock returns and how external shocks are transmitted through the spatial system.Finally,we explore the robustness of each model.