Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects

TL;DR

This paper analyzes the properties of least squares estimators in panel data models with unknown interactive fixed effects, showing that correct inference is possible without precisely estimating the number of factors.

Contribution

It proves that the LS estimator's limiting distribution is unaffected by overestimating the number of factors, simplifying inference in panel models with unknown factors.

Findings

Limiting distribution of LS estimator is independent of overestimating factors.

Inference on regression coefficients does not require consistent estimation of the number of factors.

The results hold as both cross-sectional and time dimensions grow large.

Abstract

In this paper we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true number of factors in the data, we establish the limiting distribution of the LS estimator for the regression coefficients as the number of time periods and the number of cross-sectional units jointly go to infinity. The main result of the paper is that under certain assumptions the limiting distribution of the LS estimator is independent of the number of factors used in the estimation, as long as this number is not underestimated. The important practical implication of this result is that for inference on the regression coefficients one does not necessarily need to estimate the number of interactive fixed effects consistently.