Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects
Hyungsik Roger Moon, Martin Weidner
TLDR
This paper shows the limiting distribution of the LS estimator in panel regression with unknown factors is independent of the estimated factor count if not underestimated.
Key contributions
- Analyzes the LS estimator in linear panel regression with unknown interactive fixed effects.
- Establishes the limiting distribution of the LS estimator for regression coefficients.
- Finds this distribution is independent of the number of factors used in estimation.
- Implies consistent estimation of the true factor number is not required for inference.
Why it matters
This research offers a crucial theoretical result for panel data analysis. It simplifies inference on regression coefficients by showing practitioners don't need to precisely estimate the number of interactive fixed effects, if not underestimated. This makes model application more robust and accessible.
Original 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.
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