Factor and factor loading augmented estimators for panel regression

TL;DR

This paper introduces factor-augmented estimators for panel data models with potentially many and non-strong factors, providing asymptotic normality results and demonstrating good finite sample performance.

Contribution

It develops a two-step estimation method for panel regressions with factor structures, allowing for many and weak factors, and establishes conditions for asymptotic normality.

Findings

Two-step estimators are asymptotically normal under certain conditions.

Principal components analysis can be used effectively in the first step.

Finite sample simulations show good estimator performance.

Abstract

This paper considers linear panel data models where the dependence of the regressors and the unobservables is modelled through a factor structure. The asymptotic setting is such that the number of time periods and the sample size both go to infinity. Non-strong 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. 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.