Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects
研究了面板线性回归模型中，当交互固定效应的因子数未知且估计时使用的因子数大于真实数时，最小二乘估计量的极限分布，发现该分布与使用的因子数无关，因此推断回归系数时无需一致估计因子数。
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.