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

104 Pages Posted: 11 Jan 2015

See all articles by Hyungsik Roger Moon

Hyungsik Roger Moon

University of Southern California - Department of Economics; USC Dornsife Institute for New Economic Thinking

Martin Weidner

University College London - Department of Economics

Date Written: December 26, 2014

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 crosssectional 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.

Keywords: Panel data, interactive fixed effects, factor models, perturbation theory of linear operators, random matrix theory

JEL Classification: C23, C33

Suggested Citation

Moon, Hyungsik Roger and Weidner, Martin, Linear Regression for Panel with Unknown Number of Factors as Interactive Fixed Effects (December 26, 2014). USC-INET Research Paper No. 15-03, Available at SSRN: https://ssrn.com/abstract=2546114 or http://dx.doi.org/10.2139/ssrn.2546114

Hyungsik Roger Moon (Contact Author)

University of Southern California - Department of Economics ( email )

KAP 300
Los Angeles, CA 90089-0253
United States
213-740-2108 (Phone)
213-740-8543 (Fax)

USC Dornsife Institute for New Economic Thinking ( email )

3620 S. Vermont Avenue, KAP 364F
Los Angeles, CA 90089-0253
United States

Martin Weidner

University College London - Department of Economics ( email )

Gower Street
London WC1E 6BT, WC1E 6BT
United Kingdom

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