Robust Inference Methods for Latent Group Panel Models under Possible Group Non-Separation

2025-11-23

AI Summary

This paper addresses robust statistical inference for general linear hypotheses in linear panel models with latent group structures, where the group separation condition fails—i.e., group boundaries are blurred or group assignment is uncertain. To tackle this challenge, we propose a novel selective conditional inference framework that endogenizes group identification into the inferential logic: leveraging data-driven group partitioning, we explicitly model uncertainty in group membership and derive the asymptotic properties of coefficient estimators under the conditional distribution given the selected grouping. Unlike conventional asymptotic approaches, our method dispenses with the strong group separation assumption and delivers superior finite-sample performance. Monte Carlo simulations demonstrate its excellent small-sample robustness and accuracy. Empirical applications to the income-democracy relationship and firm R&D cyclicality further validate its practical applicability and interpretive power.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

This paper presents robust inference methods for general linear hypotheses in linear panel data models with latent group structure in the coefficients. We employ a selective conditional inference approach, deriving the conditional distribution of coefficient estimates given the group structure estimated from the data. Our procedure provides valid inference under possible violations of group separation, where distributional properties of group-specific coefficients remain unestablished. Furthermore, even when group separation does hold, our method demonstrates superior finite-sample properties compared to traditional asymptotic approaches. This improvement stems from our procedure's ability to account for statistical uncertainty in the estimation of group structure. We demonstrate the effectiveness of our approach through Monte Carlo simulations and apply the methods to two datasets on: (i) the relationship between income and democracy, and (ii) the cyclicality of firm-level R&D investment.

Problem

• Develops robust inference for latent group panel models with potential group non-separation
• Provides valid statistical inference when group-specific coefficient distributions are uncertain
• Improves finite-sample performance by accounting for group structure estimation uncertainty

Innovation

• Selective conditional inference for latent groups
• Valid inference under group separation violations
• Superior finite-sample properties over asymptotic methods