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

Abstract

In this paper we study the Gaussian quasi maximum likelihood estimator (QMLE) in a linear panel regression model with interactive fixed effects for asymptotics where both the number of time periods and the number of cross-sectional units go to infinity. Under appropriate assumptions we show that the limiting distribution of the QMLE for the regression coefficients is independent of the number of interactive fixed effects used in the estimation, as long as this number does not fall below the true number of interactive fixed effects present in the data. The important practical implication of this result is that for inference on the regression coefficients one does not need to estimate the number of interactive effects consistently, but can simply rely on any known upper bound of this number to calculate the QMLE.

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