A robust approach to heteroskedasticity, error serial correlation and slope heterogeneity in linear models with interactive effects for large panel data

In this paper, we propose a robust approach against heteroskedasticity, error serial correlation and slope heterogeneity in linear models with interactive effects for large panel data. First, consistency and asymptotic normality of the pooled iterated principal component (IPC) estimator for random coefficient and homogeneous slope models are established. Then, we prove the asymptotic validity of the associated Wald test for slope parameter restrictions based on the panel heteroskedasticity and autocorrelation consistent (PHAC) variance matrix estimator for both random coefficient and homogeneous slope models, which does not require the Newey-West type time-series parameter truncation. These results asymptotically justify the use of the same pooled IPC estimator and the PHAC standard error for both homogeneous-slope and heterogeneous-slope models. This robust approach can significantly reduce the model selection uncertainty for applied researchers. In addition, we propose a Lagrange Multiplier (LM) test for correlated random coefficients with covariates. This test has non-trivial power against correlated random coefficients, but not for random coefficients and homogeneous slopes. The LM test is important because the IPC estimator becomes inconsistent with correlated random coefficients. The finite sample evidence and an empirical application support the reliability and the usefulness of our robust approach.