Linear regression for panel with unknown number of factors as interactive fixed effects

In this paper we study the least sqares (LS) estimator 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 LS estimator 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 necessarily need to estimate the number of interactive effects consistently, but can rely on an upper bound of this number to calculate the LS estimator.