Statistical Inference For The Panel Data Models

Panel data models are linear mixed-effects models which have been widely used in economics,medicine,sociology,etc.,and hence enjoy their popularity among statistical modeling.In this article,we focus on the statistical inference for the regression coefficients of the one-way error component regression model and two-way error component regression model.In the paper,the following aspects are interested.1.For the classical two-way error component regression model,the nonhomogeneous linear hypothesis testing of the regression coefficients is interested,a parametric bootstrap(PB)approach is proposed.Simulation results indicate that the PB test,regardless of the sample sizes,maintains the Type I error rates very well and outperforms the existing generalized variable test,which may far exceed the intended significance level when the sample sizes are small or moderate.Real data examples illustrate the proposed approach work satisfactorily.In the remainder of the paper,the confidence ellipsoid is constructed.By the Monte Carlo simulation,the effectiveness of our proposed procedure is assessed.2.For the two-way error component regression model with errors in variables,the nonhomogeneous linear hypothesis testing of the regression coefficients is considered.Firstly,a corrected least squares estimation and restricted estimation are presented,as well as its asymptotic normalities.Secondly,a test statistic based on the difference between the corrected residual sum of squares under the null and alternative hypotheses is constructed,and its limiting distribution is showed as a standard chi-squared distribution.Using the results,an approximate test is proposed.Finally,some simulation studies illustrate the proposed approach are conducted.3.For the testing equality problem of regression coefficients in several one-way error component regression models,a parameter bootstrap is proposed.Some simulated numerical results indicate that the PB test,regardless of the sample sizes,values of the variance components,number of the models,dimensions of regression coefficients,performs well.