Heterogeneous Grouping Structures in Panel Data

TL;DR

This paper explores heterogeneity in panel data with latent group structures, allowing for richer cross-sectional and within-group heterogeneity, and develops methods for consistent estimation and testing of group assumptions.

Contribution

It extends existing models by enabling the identification of complex heterogeneity patterns and provides estimation and testing procedures for unknown group structures.

Findings

Simulation results show good finite-sample performance.

Empirical analysis reveals multiple clusters in datasets.

Tests reject within group homogeneity hypothesis.

Abstract

In this paper we examine the existence of heterogeneity within a group, in panels with latent grouping structure. The assumption of within group homogeneity is prevalent in this literature, implying that the formation of groups alleviates cross-sectional heterogeneity, regardless of the prior knowledge of groups. While the latter hypothesis makes inference powerful, it can be often restrictive. We allow for models with richer heterogeneity that can be found both in the cross-section and within a group, without imposing the simple assumption that all groups must be heterogeneous. We further contribute to the method proposed by \cite{su2016identifying}, by showing that the model parameters can be consistently estimated and the groups, while unknown, can be identifiable in the presence of different types of heterogeneity. Within the same framework we consider the validity of assuming both cross-sectional and within group homogeneity, using testing procedures. Simulations demonstrate good finite-sample performance of the approach in both classification and estimation, while empirical applications across several datasets provide evidence of multiple clusters, as well as reject the hypothesis of within group homogeneity.