Testing for error cross‐sectional independence using pairwise augmented regressions

This paper proposes two statistics for testing error cross‐sectional independence in a static linear heterogeneous panel data model by virtue of pairwise augmented regressions. The tests based on the two statistics are extensions to the cross‐sectional dependence test and the bias‐adjusted Lagrange multiplier test. Unlike the two existing tests that are justified under sequential limits, the newly developed tests can be justified under simultaneous limits without any additional restriction imposed on the cross‐sectional and time‐series dimensions. Moreover, it is proved that the new tests can even be justified under high dimension, low sample size limits, provided that a homo‐rank condition holds. Several simulation experiments are conducted to evaluate the performance of the newly introduced tests. The simulation results show that use of the tests can bring significant improvement, especially in cases of large cross‐sectional dimension and small time‐series dimension.