Moment-based estimation of linear panel data models with factor-augmented errors

I consider linear panel data models with unobserved factor structures when the number of time periods is small relative to the number of cross-sectional units. I examine two popular methods of estimation: the first eliminates the factors with a parameterized quasi-long-differencing (QLD) transformation. The other, referred to as common correlated effects (CCE), uses the cross-sectional averages of the independent and response variables to project out the space spanned by the factors. I show that the classical CCE assumptions imply unused moment conditions that can be exploited by the QLD transformation to derive new linear estimators, which weaken identifying assumptions and have desirable theoretical properties. I prove asymptotic normality of the linear QLD estimators under a heterogeneous slope model that allows for a tradeoff between identifying conditions. These estimators do not require the number of independent variables to be less than one minus the number of time periods, a strong restriction when the number of time periods is fixed in the asymptotic analysis. Finally, I investigate the effects of per-student expenditure on standardized test performance using data from the state of Michigan.