Empirical Likelihood Inference For Spatial Panel Quantile Regression Model

This paper studies spatial panel quantile model, mainly involving the following three aspects: the Spatial Econometrics, the structure of the panel data and the Quantile regression. Spatial Econometrics is the study of the relationship of the economic development between different regions, it can measure the relations of inter-regional economic development through spatial effect. However, the sectional spatial econometric model ignores the inner characteristics and the correlation of the time series of the object. With the development of spatial econometrics, it can both control the individual heterogeneity and consider the spatial correlation of the sectional latitude on the same time by incorporating the spatial effect into the panel data models. But it may lose some important information by only conducting the parameterized estimation under conditional mean model. The information it tries to convey is probably inaccurate especially under the condition of imbalanced regional economic development level. As a consequence, the Space panel quantile regression, combining the spatial panel model and quantile regression, can describe the relationship between the response variable and the covariates under various quantile.In order to closely combine Spatial Panel Model and the quantile regression, we use the empirical likelihood method to obtain the inner correlation of the spatial panel model, by absorbing the auxiliary information we get from the empirical likelihood method. We achieve the goal to combine these two kind of models. In the spatial panel quantile regression model, there exists endogenous problems in the spatial lag. To tackle the spatial lag factor, we introduce the instrumental variable. Through three-step estimation method, we get the consistent estimation of the spatial lag factor. This paper mainly contains the following three parts:First, this paper first describes the theoretical framework of the classical spatial econometric model and quantile regression model, as well as the advantages of the two theories in the field of the respective fields and the complementary points. Then the process and theoretical basis of the combination of spatial panel model and quantile regression are discussed in detail. From the structural aspects of the model, it not only considers the intrinsic correlation between the panel data, spatial dependence and individual effect, but also combines the characteristics of quantile regression to study the influence of different points, so that the model can reflect the development of things more comprehensively.Second, this paper uses the method of instrumental variables and empirical likelihood method to deal with the problem of the inherent problem of spatial lag factors. Using the empirical likelihood method, the panel data is introduced into the spatial panel quantile regression, and the parameter estimation of the spatial panel quantile regression model is solved by using weighted quantile regression. When we deal with the individual effects of panel data, we assume that the individual effect does not change with the variation of the points, so that we can handle the individual effects in the mean model and return to the case without the individual effects.Third, the empirical analysis of the theory of this paper is applied to the modern service industry in the Yangtze River Delta, which can help us understand the development of modern service industry in the Yangtze River Delta Urban Agglomeration in different points, and it is more abundant than that of the spatial econometric model or quantile regression model.