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

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  • Hyungsik Roger Moon
  • Martin Weidner

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.

Suggested Citation

  • Hyungsik Roger Moon & Martin Weidner, 2026. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Papers 2605.00614, arXiv.org.
    • Handle: RePEc:arx:papers:2605.00614
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    References listed on IDEAS

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    1. Ahn, Seung Chan & Hoon Lee, Young & Schmidt, Peter, 2001. "GMM estimation of linear panel data models with time-varying individual effects," Journal of Econometrics, Elsevier, vol. 101(2), pages 219-255, April.
    2. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    3. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    4. Allen, Douglas W, 1992. "Marriage and Divorce: Comment," American Economic Review, American Economic Association, vol. 82(3), pages 679-685, June.
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