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In many longitudinal settings, economic theory does not guide practitionerson the type of restrictions that must be imposed to solve the rotationalindeterminacy of factor-augmented linear models. We study this problem andoffer several novel results on identification using internally generatedinstruments. We propose a new class of estimators and establish large sampleresults using recent developments on clustered samples and high-dimensionalmodels. We carry out simulation studies which show that the proposed approachesimprove the performance of existing methods on the estimation of unknownfactors. Lastly, we consider three empirical applications using administrativedata of students clustered in different subjects in elementary school, highschool and college.

Estimation of a Factor-Augmented Linear Model with Applications Using Student Achievement Data