  In many longitudinal settings, economic theory does not guide practitioners
on the type of restrictions that must be imposed to solve the rotational
indeterminacy of factor-augmented linear models. We study this problem and
offer several novel results on identification using internally generated
instruments. We propose a new class of estimators and establish large sample
results using recent developments on clustered samples and high-dimensional
models. We carry out simulation studies which show that the proposed approaches
improve the performance of existing methods on the estimation of unknown
factors. Lastly, we consider three empirical applications using administrative
data of students clustered in different subjects in elementary school, high
school and college.
