Testing For Panel Data Models With Fixed Effects

Panel data is a data set formed by drawing observations on different cross-sectional units for different periods,and panel data involves two dimensions:a cross-sectional dimension and a time series dimension.In the panel data model analysis,because the model uses both cross-section data and time series data,it makes full use of the sample information and meet the needs of economic analysis as much as possible.In addition,when using panel data model to deal with economic research,it is necessary to con-sider the model error variance structure.One of the standard methods is to introduce unobservable effects into the error structure.These unobservable effects are random variables,which are called fixed effects if they are related to covariates.If the unob-servable effects in the panel data model are fixed effects,the model can be called panel data model with fixed effectsWith the development of panel data,panel data models attract the attention of economists and statisticians.On the one hand,nonparametric and semiparametric mod-els are introduced to fit the panel data very well.On the other hand,with the rapid development of science and technology,the more complex data sets can be stored.So the study on high-dimensional data models is worthy of attention.In this thesis,the studies are expanded surrounding aforementioned problems.The main contents con-tain the testing for heteroskedasticity and the testing for covariance matrices for a class of panel data models including panel data model with interactive fixed effects,non-parametric panel data model with fixed effects and time-varying coefficient panel data model with fixed effectsFirstly,we focus on the testing variance components in panel data model with interactive fixed effects.For the problem of testing heteroskedasticity,we propose a test statistic based on an artificial regression constructed by the residual estimation.We further propose another test statistic based on the different artificial regression in order to decide the source of heteroskedasticity.Under both the null hypothesis and the alternatives,we establish the asymptotic distributions of the proposed test statistics under by assuming some regularity conditions,and we further show that the proposed tests are distribution free.Subsequently simulations suggest that the proposed tests perform well.Secondly,we focus on the testing variance components in nonparametric panel data model with fixed effects.Based on the nonparametric version of the least-squares dummy variable approach,we obtain the estimators of the unknown functions.For the problem of testing heteroskedasticity,we propose test statistics based on difference artificial regressions constructed by the nonparametric estimation,when the time series is finite or infinite,and the test statistics are modified to improve the test efficiency as the time series is finite.We further propose another test statistic based on the different artificial regression in order to decide the source of heteroskedasticity.Under both the null hypothesis and the alternatives,we establish the asymptotic distributions of the proposed test statistics under by assuming some regularity conditions,and we further show that the proposed tests are distribution free.Subsequently simulations suggest that the proposed tests perform well.Thirdly,we focus on the tests for covariance matrices in panel data model with in-teractive fixed effects.For the problem of testing identity and sphericity of covariance matrices,we propose test statistics based on the estimators of the trace of covariance matrices.Under both the null hypothesis and the alternatives,we establish the asymp-totic distributions of the proposed test statistics under some regularity conditions,and we further show that the proposed tests are distribution free.Subsequently simulation studies suggest that the proposed tests perform well under the high dimensional panel data.Finally,we study the tests for sphericity and identity of covariance matrices in time-varying coefficient high-dimensional panel data models with fixed effects.In order to construct the effective test statistics and avoid the influence of the unknown fixed effects,we apply the difference method to eliminate the dependence of the residual sample,and further construct test statistics using the trace estimators of the covariance matrices.For the estimators of the coefficient functions,we use the local linear dummy variable method.Under some regularity conditions,we study the asymptotic property of the estimators and establish the asymptotic distributions of our proposed test statistics without specifying an explicit relationship between the cross-sectional and the time series dimensions.We further show that the test statistics are asymptotic distribution-free.Subsequently simulation studies are carried out to evaluate our proposed methods In order to assess the performance of our proposed test method,we compare with the existing test methods in panel data linear models with fixed effects.The following is a brief summarization about the merits in this thesis.(1)For the panel data model with interactive fixed effects,the studies in the current literature discuss mostly the estimation of the unknown parametric.In this thesis,we focus on the testing of variance in the model.We study the testing for variance compo-nents.Not only that,study the testing for sphericity and identity of covariance matrices when(N,T)?? and N/T???(0,?).(2)As far as we know,there are few works about the test for heteroskedastici-ty in nonparametric panel data model with fixed effects.In this thesis,when T tends to infinite or T is fixed,we present different test statistics to test the existence of het-eroskedasticity in the model.(3)In this thesis,we study the tests for sphericity and identity of covariance matri-ces in time-varying coefficient high-dimensional panel data models with fixed effects When(N,T)?? and without specifying an explicit relationship between N and T,we test for high-dimensional covariance matrices.In order to construct the effective test statistics and avoid the influence of the unknown fixed effects,we apply the difference method.We further construct the test statistics by U test statistics.