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 observations $N$ 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 groped fixed-effect estimator, however, our post-spectral estimator is computationally straightforward.

Joint work with Elena Manresa (NYU)