Inference methods for unit-specific coefficients in panel data models with latent group structure

2026-06-20

AI Summary

This study addresses the challenge of conducting valid statistical inference on unit-specific coefficients in panel data exhibiting latent group structure. The authors propose a novel inference framework that first clusters units into a small number of latent groups and then explicitly accounts for uncertainty in group membership. Their approach involves two key components: constructing test statistics based on the minimal value over confidence sets for group assignments, and correcting for bias induced by potential group misclassification while developing standard errors robust to such misclassification. Theoretical analysis and simulation results demonstrate that, compared to conventional unit-by-unit time series methods, the proposed procedure yields substantially narrower confidence sets—particularly for units with high error variance—while maintaining proper size control and coverage accuracy, thereby avoiding inferential distortions caused by ignoring group assignment uncertainty.

Abstract

This paper introduces statistical inference procedures for unit-specific coefficients in panel data models, where the coefficients exhibit a latent group structure. The proposed methods achieve efficiency gains by clustering units into a small number of groups, while explicitly accounting for the statistical uncertainty of group assignments. The core idea is to integrate standard inference procedures, such as the $t$-test and Wald tests, with confidence sets for group membership. Two methods are proposed: the first takes the minimum of the test statistics over the confidence set for group membership, and the second corrects for bias caused by possible group misassignment. The former can produce shorter but possibly disconnected sets, while the latter guarantees connected, interpretable intervals at some cost in length. We also develop standard errors that are adjusted for possible group misassignment and valid even with short time periods, which may be of independent interest. Monte Carlo simulations demonstrate that our approach yields narrower confidence sets for units with relatively large error variances than unit-by-unit time-series methods. In contrast, ignoring statistical uncertainty in the group membership estimation leads to distortions in size and coverage. We illustrate the method with an empirical example that estimates the effect of the minimum wage in each U.S. state.

Problem

• panel data
• latent group structure
• unit-specific coefficients
• statistical inference
• group uncertainty

Innovation

• latent group structure
• panel data
• statistical inference
• group uncertainty
• confidence sets