GENERALIZED LEAST SQUARES ESTIMATION OF PANEL WITH COMMON SHOCKS 1

This paper considers GLS estimation of linear panel models when the innovation and the regressors can both contain a factor struc-ture. A novel feature of this approach is that preliminary estimation of the latent factor structure is not necessary. Under a set of regular-ity conditions here provided, we establish consistency and asymptotic normality of the feasible GLS estimator as both the cross-section and time series dimensions diverge to infinity. In particular, dependence, both temporally and cross-sectionally, of the idiosyncratic innovation is permitted and in fact the latter can be eventually be correlated with the regressors, making the conventional OLS estimator invalid. Our results are presented separately for time regressions with unit-specific coefficients as well as for cross-section regressions with time-specific coefficients. As particular cases of our set up, we establish primitive conditions of our assumptions for Pesaran (2006) and Andrews (2005) regression models. A set of Monte Carlo experiments corroborate our results.