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.

中文翻译：

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固定效应在治疗效应回归和其他方面存在交互效应时贬低

本文表明，关于时间固定效应的横截面确定比普遍认可的更为有用，因为当时间段T较小时，它可以对具有不同斜率系数的交互效应模型进行一致且渐近的法线估计只有横截面单元的数量N，很大。这在使用OLS时也很重要，在使用交互作用模型的更复杂的估算器（其有效性不需要确定）时，这一点很重要，这一点据我们所知从未在文献中提及。作为说明，我们考虑在存在未观察到的时变异质性的情况下估计平均治疗效果的问题。Gobillon and Magnac（2016）最近考虑了这个问题。他们采用了一种基于主成分的方法，旨在应对一般性的未观察到的异质性，这种异质性不需要降低固定效应。但是，该方法确实要求T很大，实际上通常不是这种情况，并且这里报告的结果证实，在小T中，性能可能非常差。样品。例外情况是该方法应用于相对于固定效果已淡化的数据。