Estimating, Testing And Model Selection In Semi-Parametric Panel Data Models

Panel data traces information on each individual unit across time, such two-dimensional information set has advantages over cross section data and time series data. It plays an important role in applied work. Semi-parametric panel data models which combine characteristics of parametric and nonparametric models avoid the strong restrictions and'curse of dimensionality'problem. Semi-parametric panel data models have gained wide attention in recent years.This paper considers the estimation for semi-parametric panel data models, which include partially linear models and varying coefficient models. Profile least squares method and modified local constant least squares method are used to estimate the unknown components.As we all know, there are differences in method and estimator for random effects model and fixed effects model. In partially linear panel data models, we propose parametric Hausman test and nonparametric Hausman test to improve the accuracy of estimation and prediction. The parametric Hausman test is proved to follow asymptotically chi-square distribution under the null hypothesis of random effects, and the nonparametric Hausman test is proved to be asymptotically normally distributed under the null hypothesis. Monte Carlo simulations show that the parametric Hausman test behaves quite well, and in the same circumstances the parametric Hausman test performs better than the nonparametric Hausman test. Moreover, we apply the parametric Hausman test method into the empirical study of regional GDP's influence factors.The numerical simulation results have shown the uncertainty of the Hausman test statistic in small sample. To avoid the inaccurate inference, we adopt the Bootstrap-sampling method. The parametric Bootstrap-Hausman test and the nonparametric Bootstrap-Hausman test are proposed. We obtain the quantiles of the test statistics and subsequently construct the rejection regions. Simulations indicate that the parametric Bootstrap-Hausman test performs better than the nonparametric Bootstrap-Hausman test. Finally, an empirical application based on the economic growth and household consumption are conducted.