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

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.

KEYWORDS:

• Factor models
• Flexible unobserved heterogeneity
• Interactive fixed effects
• Panel data
• Principal components analysis

Supplementary Materials

The supplementary material contains additional results discussed in the article and the MATLAB code used for the simulations.

Acknowledgments

The authors thank Domenico Giannone, Jihyun Kim, Pascal Lavergne, Thierry Magnac and Nour Meddahi, an associate editor and two referees of the Journal of Business & Economic Statistics for helpful comments and ideas.

Additional information

Funding

Financial support from the European Research Council (ERC grant POEMH 337665) and from the French National Research Agency (ANR) (grant ANR-17-EURE-0010) is gratefully acknowledged.