Panel Data Models With Interactive Fixed Effects

This paper considers large N and large T panel data models with unobservable multiple interactive effects. These models are useful for both micro and macro econometric modelings. In earnings studies, for example, workers ’ motivation, persistence, and diligence combined to influence the earnings in addition to the usual argument of innate ability. In macroeconomics, the interactive effects represent unobservable common shocks and their heterogeneous responses over cross sections. Since the interactive effects are allowed to be correlated with the regressors, they are treated as fixed effects parameters to be estimated along with the common slope coefficients. The model is estimated by the least squares method, which provides the interactive-effects counterpart of the within estimator. We first consider model identification, and then derive the rate of convergence and the limiting distribution of the interactive-effects estimator of the common slope coefficients. The estimator is shown to be √ NT consistent. This rate is valid even in the presence of correlations and heteroskedasticities in both dimensions, a striking contrast with fixed T framework in which serial correlation and heteroskedasticity imply unidentification. The asymptotic distribution is not necessarily centered at zero. Biased corrected estimators are derived. We also derive the constrained estimator and its limiting distribution, imposing additivity coupled with interactive effects. The problem of testing additive versus interactive effects is also studied. We also derive identification conditions for models with grand mean, time-invariant regressors, and common regressors. It is shown that there exists a set of necessary and sufficient identification conditions for those models. Given identification, the rate of convergence and limiting results continue to hold. Key words and phrases: incidental parameters, additive effects, interactive effects, factor