Testing For Sphericity In A Fixed Effects Panel Data Model With Time-Varying Variances

Classical linear regression model assumes the property of homoskedasticity.But in real life,it doesn't accord with reality.When there is heteroscedasticity,the OLS estimation is not the best.The variance of the OLS estimation is not the smallest among that of all the linear unbiased estimations.Now the economy of the world is in closely connection.Panel data model always exists cross-sectional dependence.Ignoring the cross-sectional dependence will influence the correction of the estimations.What's more,if there are time series dependency and cross-sectional dependence in the model,the estimation will be unconsistent.Ignoring the time series dependency and cross-sectional dependence will lead to the uneffcient and unconsistent estimation.Considering the difficulty and the deficiency of the recent studies,this paper pro-poses a test for the null of sphericity in a fixed effects panel data model with time-varying variances.Firstly,this paper reviews the research in the sphericity test field.Then we discuss the model and hypothesis of this paper,and propose a new statistics.Later,We derive the asymptotic distributions of the tests under the null.In the end,we conduct Monte Carlo simulations to assess the empirical size and power of the statistics proposed in this paper.We also report those of other statistics for comparison.The results show that the statistics proposed in this paper,J_new,converges to the standard normal distribution,when(n,t)??,n/T?c?(0,?).From the Monte Carlo simulations,we know that the size of J_newis good,but J_{BF K}and J_BKPhave size distortion.When n is larger than T,the statistics J_newhave a relevant higher size.In the factor model and SAR(1)model,the power increases with n and T.The statistics J_newis robust to time-varying variance model.