A bias-corrected Srivastava-type test for cross-sectional independence

This paper proposes a test for cross-sectional independence with high dimensional panel data. It uses the random matrix theory based approach of Srivastava (2005) in the presence of a large number of cross-sectional units and time series observations. Because the errors are unobservable, the residuals from the regression model for panel data are used. We develop a bias-corrected test after adjusting for the contribution from the regressors. With the aid of the martingale central limit theorem, we prove that the limiting null distribution of the proposed test statistic is normal under mild conditions as cross-sectional dimension and time dimension go to infinity together. We further study the asymptotic relative efficiency of our proposed test with respect to the state-of-art Lagrange multiplier test. An interesting finding is that the newly proposed test can have substantial power gain when the underlying variance magnitudes are not identical across different units.