Estimation And Application Of Panel Data Fixed Effect Varying Coefficient Model Based On Auxiliary Regression

Panel data is a generalization of the static cross-sectional data and the homogeneity of time series data,which can not only reveal the dynamic behavior of individual differences,but also discover the differences of individual dynamic behavior.Under the background of increasingly complicated economic activities,it is of great significance to model and analyze panel data,among which parametric panel data model is the most common.Parametric model has the advantages of easy estimation and easy explanation,but it ignores the dynamic characteristics in the data,resulting in inaccurate estimation.Varying coefficient model is developed from parametric model,which not only retains the interpretability of parametric model,but also has the flexibility of nonparametric model.Therefore,the panel data varying coefficient model can effectively fit the data and explore the dynamic data characteristics,which is a powerful tool to study the dynamic characteristics of regression relations.In this thesis,a more effective estimation method is proposed for the panel data fixed effect varying coefficient model,and the method is used to an example.For the estimation process of the model,the relationship between the fixed effect and the covariate is explained by introducing auxiliary regression which linear regression of fixed effects to the mean of covariates,and the panel data varying coefficient model with fixed effect is transformed into a partial linear varying coefficient model without effect term.Then,combined with orthogonal projection method,the estimation of interest coefficient function is obtained by local linear method.Meanwhile,the asymptotic normality of the estimator obtained by this method is discussed under certain regular conditions,and the proof process of the theorem is given.The merits and demerits of this method are compared with the local linear dummy varying method through numerical simulation.Simulation results indicate that this method is superior to the local linear dummy varying method,especially has obvious advantages in the case of small samples size,and it is also applicable to random effect models.In the empirical analysis part,the method proposed in this thesis is applied to the study of the influential factors of household income,combining personal factors with macroeconomic environment,and based on micro-survey data CFPS,the factors influencing household income of Chinese residents are analyzed on a household basis.Combined with the actual situation and the availability of data,an index system affecting household income is established,and CFPS data is cleaned and preprocessed according to this index system to obtain balanced panel data.Subsequently,the correlation relationship of the selected variables is determined by correlation analysis,and the varying coefficient model of panel data is established accordingly.Furthermore,the estimation results of the coefficient function of the model are obtained by using the method proposed in this thesis,and it is found that family size,male proportion of households,highest household education,minimum household health and regional GDP are nonlinear influencing factors affecting household income,and the influence of these factors on household income fluctuates with the increase of average family age.