Panel data models with randomly generated groups

2025-10-28

AI Summary

This paper addresses the challenge of modeling unobserved heterogeneity in dynamic panel data. We propose a Bayesian structural framework based on the Mixture of Finite Mixtures (MFM) model, which permits an unknown and estimable number of latent groups. To overcome the clustering inconsistency inherent in Dirichlet process priors, our approach employs an MFM prior coupled with an extended telescoping sampler, enabling efficient full Bayesian inference for dynamic panels with covariates. Theoretically, we establish joint parametric-rate convergence of both clustering and structural parameters, supporting posterior contraction and valid credible set construction. Empirically, we uncover previously hidden heterogeneity in the income–democracy relationship—evident only after controlling for additional covariates—thereby demonstrating the method’s small-sample robustness and substantive interpretability.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

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.

Problem

• Modeling latent heterogeneity in dynamic panel data
• Estimating unknown number of clusters consistently
• Extending Bayesian inference to panels with covariates

Innovation

• Modeling heterogeneity via latent clustering mechanism
• Extending Telescoping Sampler for dynamic panel inference
• Providing parametric-rate posterior contraction guarantees