Panel data models with randomly generated groups

TL;DR

This paper introduces a Bayesian approach for modeling unobserved heterogeneity in dynamic panel data by estimating latent clusters, improving interpretability and inference accuracy over existing methods.

Contribution

It develops a novel mixture of finite mixtures framework with an efficient MCMC algorithm for dynamic panels, addressing clustering inconsistency issues and enabling full Bayesian inference.

Findings

The method accurately recovers latent clusters in simulations.

Posterior contraction rates are optimal in Wasserstein distance.

Application reveals hidden heterogeneity in income-democracy data.

Abstract

We develop a structural framework for modeling and inferring unobserved heterogeneity in dynamic panel-data models. Unlike methods treating clustering as a descriptive device, we model heterogeneity as arising from a latent clustering mechanism, where the number of clusters is unknown and estimated. Building on the mixture of finite mixtures (MFM) approach, our method avoids the clustering inconsistency issues of Dirichlet process mixtures and provides an interpretable representation of the population clustering structure. We extend the Telescoping Sampler of Fruhwirth-Schnatter et al. (2021) to dynamic panels with covariates, yielding an efficient MCMC algorithm that delivers full Bayesian inference and credible sets. We show that asymptotically the posterior distribution of the mixing measure contracts around the truth at parametric rates in Wasserstein distance, ensuring recovery of clustering and structural parameters. Simulations demonstrate strong finite-sample performance. Finally, an application to the income-democracy relationship reveals latent heterogeneity only when controlling for additional covariates.