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Factor and Factor Loading Augmented Estimators for Panel Regression With Possibly Nonstrong Factors

Author

Listed:
  • Jad Beyhum

    (KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven)

  • Éric Gautier

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

This article considers linear panel data models where the dependence of the regressors and the unobservables is modeled through a factor structure. The number of time periods and the sample size both go to infinity. Unlike in most existing methods for the estimation of this type of models, nonstrong factors are allowed and the number of factors can grow to infinity with the sample size. We study a class of two-step estimators of the regression coefficients. In the first step, factors and factor loadings are estimated. Then, the second step corresponds to the panel regression of the outcome on the regressors and the estimates of the factors and the factor loadings from the first step. The estimators enjoy double robustness. Different methods can be used in the first step while the second step is unique. We derive sufficient conditions on the first-step estimator and the data generating process under which the two-step estimator is asymptotically normal. Assumptions under which using an approach based on principal components analysis in the first step yields an asymptotically normal estimator are also given. The two-step procedure exhibits good finite sample properties in simulations. The approach is illustrated by an empirical application on fiscal policy.

Suggested Citation

  • Jad Beyhum & Éric Gautier, 2023. "Factor and Factor Loading Augmented Estimators for Panel Regression With Possibly Nonstrong Factors," Post-Print hal-04473333, HAL.
    • Handle: RePEc:hal:journl:hal-04473333
    DOI: 10.1080/07350015.2021.2011300
    as

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