Convergence rate of estimators of clustered panel models with misclassification

TL;DR

This paper analyzes the convergence rate of kmeans clustering estimators in panel data models with latent groups, showing they can achieve parametric rates even with misclassification and diverging error variances.

Contribution

It provides new asymptotic results for clustered panel estimators under misclassification and diverging variances, extending existing theory.

Findings

Estimators converge at the parametric root NT rate.

Misclassification does not prevent consistent estimation.

Results apply to settings with diverging error variances.

Abstract

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 $T \to \infty$ and some units are asymptotically misclassified. This limit case approximates empirically relevant settings and is not covered by existing asymptotic results.