  We study estimation of factor models in a fixed-T panel data setting and
significantly relax the common correlated effects (CCE) assumptions pioneered
by Pesaran (2006) and used in dozens of papers since. In the simplest case, we
model the unobserved factors as functions of the cross-sectional averages of
the explanatory variables and show that this is implied by Pesaran's
assumptions when the number of factors does not exceed the number of
explanatory variables. Our approach allows discrete explanatory variables and
flexible functional forms in the covariates. Plus, it extends to a framework
that easily incorporates general functions of cross-sectional moments, in
addition to heterogeneous intercepts and time trends. Our proposed estimators
include Pesaran's pooled correlated common effects (CCEP) estimator as a
special case. We also show that in the presence of heterogeneous slopes our
estimator is consistent under assumptions much weaker than those previously
used. We derive the fixed-T asymptotic normality of a general estimator and
show how to adjust for estimation of the population moments in the factor
loading equation.
