Bias Correction in Factor-Augmented Regression Models with Weak Factors

2025-09-02

AI Summary

This paper addresses the asymptotic bias of factor-augmented regression (FAR) estimators under weak latent factors—where signal eigenvalues diverge at heterogeneous rates. Methodologically, it proposes a high-precision bias approximation and correction framework. Theoretically, it derives novel bias expressions under arbitrary rotation matrices and introduces a unique population-level rotation matrix $ H $ that depends solely on the signal subspace, thereby enhancing both theoretical accuracy and interpretability of the bias approximation. Computationally, it develops a split-panel jackknife procedure that achieves bias correction without requiring strong factor assumptions. Theoretically, the estimator is proven to eliminate first-order bias. Extensive simulations and empirical applications using real macroeconomic data demonstrate its robust finite-sample performance and consistent superiority over existing approaches.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Bias, Fairness & Privacy

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

In this paper, we study the asymptotic bias of the factor-augmented regression estimator and its reduction, which is augmented by the $r$ factors extracted from a large number of $N$ variables with $T$ observations. In particular, we consider general weak latent factor models with $r$ signal eigenvalues that may diverge at different rates, $N^{α_{k}}$, $0<α_{k}leq 1$, $k=1,dots,r$. In the existing literature, the bias has been derived using an approximation for the estimated factors with a specific data-dependent rotation matrix $hat{H}$ for the model with $α_{k}=1$ for all $k$, whereas we derive the bias for weak factor models. In addition, we derive the bias using the approximation with a different rotation matrix $hat{H}_q$, which generally has a smaller bias than with $hat{H}$. We also derive the bias using our preferred approximation with a purely signal-dependent rotation $H$, which is unique and can be regarded as the population version of $hat{H}$ and $hat{H}_q$. Since this bias is parametrically inestimable, we propose a split-panel jackknife bias correction, and theory shows that it successfully reduces the bias. The extensive finite-sample experiments suggest that the proposed bias correction works very well, and the empirical application illustrates its usefulness in practice.

Problem

• Addressing asymptotic bias in factor-augmented regression estimators
• Developing bias correction for weak factor models with divergent eigenvalues
• Proposing split-panel jackknife method to reduce parametrically inestimable bias

Innovation

• Proposes split-panel jackknife bias correction method
• Uses signal-dependent rotation matrix H approximation
• Derives bias for weak factor models with divergent eigenvalues