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This paper revisits the Lagrange multiplier type test for the null hypothesisof no cross-sectional dependence in large panel data models. We propose aunified test procedure and its power enhancement version, which show robustnessfor a wide class of panel model contexts. Specifically, the two procedures areapplicable to both heterogeneous and fixed effects panel data models with thepresence of weakly exogenous as well as lagged dependent regressors, allowingfor a general form of nonnormal error distribution. With the tools from RandomMatrix Theory, the asymptotic validity of the test procedures is establishedunder the simultaneous limit scheme where the number of time periods and thenumber of cross-sectional units go to infinity proportionally. The derivedtheories are accompanied by detailed Monte Carlo experiments, which confirm therobustness of the two tests and also suggest the validity of the powerenhancement technique.

Unified and robust Lagrange multiplier type tests for cross-sectional independence in large panel data models