A Bias-Adjusted LM Test of Error Cross Section Independence

This paper proposes bias-adjusted normal approximation versions of Lagrange multiplier (NLM) test of error cross section independence of Breusch and Pagan (1980) in the case of panel models with strictly exogenous regressors and normal errors. The exact mean and variance of the Lagrange multiplier (LM) test statistic are provided for the purpose of the bias-adjustments, and it is shown that the proposed tests have a standard normal distribution for the fixed time series dimension (T) as the cross section dimension (N) tends to infinity. Importantly, the proposed bias-adjusted NLM tests are consistent even when the Pesaran’s (2004) CD test is inconsistent. The finite sample evidence shows that the bias adjusted NLM tests successfully control the size, maintaining satisfactory power. However, it is also shown that the bias-adjusted NLM tests are not as robust as the CD test to non-normal errors and/or in the presence of weakly exogenous regressors.