Estimation Of Semi-parametric Varying-coefficient Spatial Autoregressive Panel Data Models

Panel data refers to the two-dimensional data set observed by continuously tracking the same group of individuals for multiple periods.Panel data analysis has received extensive attention during the past two decades due to its application in many disciplines such as Economics,Finance and Biology.Panel data can provide researchers with expanded modeling possibilities as compared to purely time-series or cross-sectional data.They control more information.In this paper,we study the estimation of a semi-parametric variable coefficient spatial panel data model with fixed effects.First,the difference method is used to eliminate the influence of the fixed effects,and then based on B-spline function expansion method,the unknown nonparametric components in the model are approximated,and the model is further transformed into a parametric model.Then,the tool variable method is used to estimate the unknown parameter components.Further,the empirical likelihood method is used to construct the confidence interval of unknown parameters.The asymptotic normality and convergence rate of the estimator are proved under appropriate conditions,and the numerical simulation results show that the proposed estimation method performs well.This paper's arrangement is as follows.Chapter 1,the semi-parametric varying-coefficient spatial autoregressive panel data model with fixed effects is proposed.The correlated knowledge of this model and the main work of this paper are introduced.Chapter 2,we give the two-stage least squares estimation of the model and the empirical log-likelihood ratio function of the parameters.Chapter 3,we give the model assumptions and related theorems.Chapter 4 reports some Monte Carlo simulation results.Chapter 5 gives the detailed proof process of the theorem.