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

2026-05-01

AI Summary

This study addresses the challenge of estimating and conducting inference in linear regression models with interactive fixed effects when the number of underlying factors is unknown. Under a high-dimensional asymptotic framework where both time and cross-sectional dimensions grow to infinity, the authors analyze the least squares estimator of the regression coefficients, assuming the selected number of factors is at least as large as the true number. They establish that, provided the factor dimension is not underestimated, the asymptotic distribution of the estimator is invariant to the chosen number of factors. This result enables valid statistical inference without requiring consistent estimation of the true factor count, thereby offering a robust theoretical foundation for practical applications.

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.

Problem

• linear regression
• panel data
• interactive fixed effects
• unknown number of factors
• inference

Innovation

• interactive fixed effects
• factor models
• linear panel regression
• least squares estimator
• asymptotic distribution