Testing for Covariance Matrices in Panel Data Models with Interactive Fixed Effect

In this paper, we focus on the tests for covariance matrices in panel data model with interactive fixed effects. For the problem of testing identity and sphericity of covariance matrices, we first propose test statistics based on the estimators of the trace of covariance matrices. Under both the null hypothesis and the alternatives, we establish the asymptotic 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.