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

TL;DR

This paper addresses the identification and estimation challenges in factor-augmented linear models, proposing new estimators and demonstrating their effectiveness through simulations and applications to student achievement data.

Contribution

It introduces novel identification methods using internally generated instruments and develops estimators suitable for high-dimensional, clustered data settings.

Findings

Proposed estimators outperform existing methods in simulations.

New identification strategies effectively resolve rotational indeterminacy.

Empirical applications demonstrate practical utility in educational data analysis.

Abstract

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.