  This paper revisits the Lagrange multiplier type test for the null hypothesis
of no cross-sectional dependence in large panel data models. We propose a
unified test procedure and its power enhancement version, which show robustness
for a wide class of panel model contexts. Specifically, the two procedures are
applicable to both heterogeneous and fixed effects panel data models with the
presence of weakly exogenous as well as lagged dependent regressors, allowing
for a general form of nonnormal error distribution. With the tools from Random
Matrix Theory, the asymptotic validity of the test procedures is established
under the simultaneous limit scheme where the number of time periods and the
number of cross-sectional units go to infinity proportionally. The derived
theories are accompanied by detailed Monte Carlo experiments, which confirm the
robustness of the two tests and also suggest the validity of the power
enhancement technique.
