Fixed effects demeaning in the presence of interactive effects in treatment effects regressions and elsewhere
证明，在时间期数T小而截面单元数N大时，对时间固定效应进行截面去均值能使交互效应模型的估计一致且渐近正态，这对OLS和更复杂的估计器都重要，并以平均治疗效应估计为例说明。
Summary The present paper shows that cross‐section demeaning with respect to time fixed effects is more useful than commonly appreciated, in that it enables consistent and asymptotically normal estimation of interactive effects models with heterogeneous slope coefficients when the number of time periods, T , is small and only the number of cross‐sectional units, N , is large. This is important when using OLS but also when using more sophisticated estimators of interactive effects models whose validity does not require demeaning, a point that to the best of our knowledge has not been made before in the literature. As an illustration, we consider the problem of estimating the average treatment effect in the presence of unobserved time‐varying heterogeneity. Gobillon and Magnac (2016) recently considered this problem. They employed a principal components‐based approach designed to deal with general unobserved heterogeneity, which does not require fixed effects demeaning. The approach does, however, require that T is large, which is typically not the case in practice, and the results reported here confirm that the performance can be extremely poor in small‐ T samples. The exception is when the approach is applied to data that have been demeaned with respect to fixed effects.