Statistical Inference Of Partially Linear Varying-coefficient Spatial Panel Regression Model

Panel data includes both cross-sectional data and time series,which is one of the hot research topics in econometrics and statistics recent years.The partially linear varying-coefficient regression model combines the characteristics of the parameter model and the non-parametric model,and it has the advantages of flexibility and ease of explanation.Compared with the classical model,the partially linear varying-coefficient regression model has a better fitting effect and is widely discussed and applied in the fields of statistics and econometrics.Usually in real problems,there are spatial correlations among the individuals and interaction of explanatory variables.Therefore,this paper introduces a partially linear varyingcoefficient panel regression model with the assumption that there are a fixed effect and endogeneity.The main focus of this paper is statistical inference to the proposed new model,which includes the estimation of parameters and varying-coefficient functions.In this paper,the first order difference is used to eliminate the fixed effect and the spline method is used to approximate the varying-coefficient part.Then,the two-stage least square method is used to deal with the endogeneity problem of the model and results in the estimators.Meanwhile,the asymptotic normality of estimator for parametric part and convergence rate as well as asymptotic properties for the varying-coefficient estimators are given.Furthermore,the consistent estimation for asymptotic covariance matrix of these estimators is also considered.Finally,the Monte Carlo simulation is used to show the small sample performance of the proposed estimation method.