Spectral and post-spectral estimators for grouped panel data models
In this paper, we develop spectral and post-spectral estimators for grouped panel data models. Both estimators are consistent in the asymptotics where the number of units N and the number of time periods T simultaneously grow large. In addition, the post-spectral estimator is root-NT consistent and asymptotically normal with mean zero under the assumption of well-separated groups even if T is growing much slower than N. The post-spectral estimator has, therefore, theoretical properties that are similar to those of the grouped fixed-effect estimator developed by Bonhomme and Manresa (2015). In contrast to the grouped fixed-effect estimator, however, our post-spectral estimator is computationally straightforward.