Asymptotic collinearity in CCE estimation of interactive effects models

Researchers sometime fall into the dummy variable trap. A typical scenario in panel data is when wanting to estimate the effect of a regressor that is time invariant, such as sex or race, and accidentally including cross-section specific fixed effects. The problem here is that the fixed effects and the regressor are collinear, which causes the resulting pooled least squares estimator to break down. In interactive effects models such breakdowns can occur even if the regressors are not time invariant. The reason is that the interactive effects are flexible enough to generate a wide range of behaviours that are likely to be shared by the regressors. The current paper considers the challenging case when some of the regressors are asymptotically collinear with the interactive effects. The relevant asymptotic theory is developed and tested in small samples using both simulated and real data.