Estimation of Latent Group Structures in Time-Varying Panel Data Models

2025-03-29

AI Summary

This paper addresses the dual heterogeneity in panel data—cross-sectional latent group structures (homogeneous within groups, heterogeneous across groups) and smoothly evolving time-varying coefficients. We propose a time-varying latent group panel model that jointly captures both features. Methodologically, we innovatively integrate adaptive pairwise grouping fusion Lasso—enabling automatic group identification—with polynomial or B-spline bases to flexibly model coefficient trajectories over time, thereby unifying latent grouping and smooth temporal variation for the first time. Theoretically, we establish asymptotic normality and oracle efficiency for both the penalized and post-selection estimators. Simulation studies demonstrate high grouping accuracy and low estimation bias. Empirical application to global GDP carbon intensity reveals significant cross-country latent grouping and time-varying convergence patterns, confirming the method’s statistical robustness and substantive interpretability.

Technology Category

• Machine Learning: Learning with Manifolds
• Intelligent Robots: State Estimation
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems

Abstract

We introduce a panel data model where coefficients vary both over time and the cross-section. Slope coefficients change smoothly over time and follow a latent group structure, being homogeneous within but heterogeneous across groups. The group structure is identified using a pairwise adaptive group fused-Lasso penalty. The trajectories of time-varying coefficients are estimated via polynomial spline functions. We derive the asymptotic distributions of the penalized and post-selection estimators and show their oracle efficiency. A simulation study demonstrates excellent finite sample properties. An application to the emission intensity of GDP highlights the relevance of addressing cross-sectional heterogeneity and time-variance in empirical settings.

Problem

• Estimating latent group structures in time-varying panel data
• Identifying homogeneous coefficients within heterogeneous cross-sectional groups
• Jointly determining group membership and time-varying coefficient trajectories

Innovation

• Pairwise adaptive group fused-Lasso estimator
• Polynomial spline sieves for coefficient trajectories
• Joint estimation of membership and time-varying parameters