Estimation And Tests For A Class Of Panel Data Models

Since the middle period of last century,due to the advantage of model set-ting and data structure,the Panel Data model has become one of the important research direction in the field of econometrics.In this thesis,we are mainly inter-ested in the analysis of estimation and hypothesis testing for a class of panel data models,including nested error components regression model,high-dimensional panel data model,time-varying coefficients panel data model with fixed effects and partially linear time-varying coefficients panel data model with fixed effects.For nested error component regression model with several random effects and nested effects,some new exact tests and confidence intervals of hypothesis testing of variance components are developed by using the concept of generalized p-value and generalized confidence interval.Compared to likelihood method,this method has the features that are convenient to compute and are easy to apply to small sample problems.In addition,from theoretical view,invariance of these tests and confidence intervals under scale transformation is discussed.At last,some simulation results on the type I error probability and power of the proposed test are reported.For one-way panel data regression model,this paper investigates asymptotic property of FW statistic[74]when the dimension of covariates grows as sample size grows.With the help of spectral theory of large-dimension random matrix,the asymptotic normality and asymptotic power of the FW-statistic are obtained under some regular conditions.It is worth noting that the inference approach does not require any specification of the error distribution.At last,some simulation studies and a real example are conducted to examine the finite sample performance for the test.In chapter 4 we investigate partially linear time-varying coefficient panel da-ta model with fixed effects,which can fit the characteristics of the data itself better and characterize non-linear and trending phenomenon in a partially lin-ear panel data model.The cross-sectional average method and profile dummy variable approach are took to eliminate the fixed effects.Then we derive point es-timations for both the parametric components and non-parametric trend function with the help of local linear expansion and profile least square method.Further-more,asymptotic normality of the estimation are derived when the error terms are correlated across time points.The asymptotic theory reveals that the para-metric component(non-parametric coefficient function)estimates based on local linear dummy variable approach have a rate of convergence that is faster than that based on cross-sectional average.Secondly,because there are unknown de-pendent structures in asymptotic variance of estimators and intraclass correlation in the model,block bootstrap method is used to construct confidence interval and pointwise confidence interval for parametric and nonparametric components,re-spectively.At last,some simulation studies are conducted to examine the finite sample performance for the proposed methods and a real data example is analyzed.In chapter 5,for nonparametric time-varying coefficient panel data models with fixed effects,we propose tests for the null of sphericity and identity matrix.Firstly,based on the local linear smoothing technique,the estimators of the un-known coefficient functions and model residuals are obtained.Secondly,proper test statistics are proposed aiming at tests for sphericity or identity matrix with a large number of cross-sectional units and time series observations.In addition,the limiting distributions of the proposed test statistics are derived based on random matrix theory.At last,their finite sample properties are examined using Monte Carlo simulations.At last we conduct comparisons for several Pareto distributions based on record values by using generalized p-value method.With the help of properties of Pareto distribution under record values,we construct generalized pivot quantity for characteristic quantities including mean,quantity and reliability function and obtained corresponding generalized p-value.Furthermore,we conduct parametric bootstrap-based tests for comparison.Simulation studies demonstrate that gen-eralized p-value-based tests outperform the parametric bootstrap-based tests in most cases.