Convergence rate of estimators of clustered panel models with misclassification

We study kmeans clustering estimation of panel data models with a latent group structure and $N$ units and $T$ time periods under long panel asymptotics. We show that the group-specific coefficients can be estimated at the parametric root $NT$ rate even if error variances diverge as $T\to \mathrm{\infty }$ and some units are asymptotically misclassified. This limit case approximates empirically relevant settings and is not covered by existing asymptotic results.