Test Of Panel Data Models With Interactive Fixed Effects

Panel data is the data that needs to be considered both in time and in individuals.Compared with time or individual single dimension data,it can describe more complex actual situation,and get better parameter estimation effects in the established model.This thesis considers the test of panel data models with interactive fixed effects.Different from the traditional panel data models,the time-varying common factor and the individual variable factor load are considered in the interactive fixed effects models.Therefore,the interactive fixed effects models have obvious advantages in model fitting.In the era of rapid development of modern high technology,data acquisition and storage become easier,and high-dimensional data is becoming more and more common,so it is necessary and meaningful to study high-dimensional panel data.This thesis mainly studies the model test method with dimension reduction effect under panel data.Firstly,Gaussian quasi maximum likelihood estimation is used to estimate the parameters of the panel data models with interactive fixed effects,and the error estimation of the model is obtained.The residual empirical process is constructed by using the obtained error estimation.On this basis,the test statistics of this thesis are proposed.It is concluded that the core idea of the test statistic is to use the projection method to reduce the dimension of highdimensional covariates,so as to transform them into one-dimensional variables for calculation.Secondly,the asymptotic distribution of test statistics when the null hypothesis is true is analyzed and proved theoretically.Compared with the method of constructing test statistics based on kernel estimation,the method proposed in this thesis avoids the curse of dimensionality and the problem of choosing bandwidth.Then,the critical value of the test statistic is calculated.In the part of numerical simulation,it is discussed when the covariates are low dimension and high dimension,and the error terms are homoscedasticity and heteroscedasticity.Simulation results show that the proposed method can well control the probability of making the first type of error near the significance level under the null hypothesis.Under the alternative hypothesis,the power tends to 1 as the deviation of the model from the null hypothesis increases.In addition,the proposed method is better applicated in terms of error term and covariate dimension.Finally,the rationality of this method is illustrated by empirical analysis.