On Selection of Cross-Section Averages in Non-stationary Environments

2025-05-13

AI Summary

This paper identifies a systematic under-selection bias of information criteria (IC) in determining the number of cross-sectional averages (CAs) for nonstationary factor models, leading to severe underestimation of the true factor dimension—contradicting the prevailing consensus on IC’s robustness. Method: Through rigorous asymptotic theory and Monte Carlo simulations, we formally establish IC’s failure under mild nonstationarity and precisely characterize its breakdown boundary. Contribution/Results: We demonstrate that IC consistently over-prunes the CA set, undermining consistent factor space approximation. Building on this, we derive diagnostic boundary conditions and propose cautionary usage guidelines for IC in nonstationary settings. Our findings correct a long-standing misperception in the CA literature and provide both a theoretical benchmark and practical guidance for factor modeling and variable selection under nonstationarity.

Technology Category

• Reasoning under Uncertainty: Causality
• Game Theory and Economic Paradigms: Imperfect Information
• Machine Learning: Dimensionality Reduction/Feature Selection

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements

Abstract

Information criteria (IC) are important tools in the literature of factor models that allow one to estimate a typically unknown number of latent factors. Although first proposed for the Principal Components setting in the seminal work by Bai and Ng (2002), it has recently been shown that IC perform extremely well in Common Correlated Effects (CCE) and related setups with stationary factors. In particular, they can consistently select a sufficient set of cross-section averages (CAs) to approximate the factor space. Given that CAs can proxy nonstationary factors, it is tempting to believe that the consistency of IC continues to hold under such generality. This study is a cautionary tale for practitioners. We demonstrate formally and in simulations that IC has a severe underselection issue even under very mild forms of factor non-stationarity, which goes against the sentiment in the CAs literature.

Problem

• IC struggles with factor non-stationarity in CCE setups
• Underselection issue in cross-section averages under non-stationarity
• Challenges IC consistency in non-stationary factor environments

Innovation

• Information criteria for factor model selection
• Common Correlated Effects with stationary factors
• Underselection issue in non-stationary environments