Econometric Seminar

Friday, 29 May 2026 at 13:30

Bias Correction in Factor-Augmented Regression Models with Weak Factors

Event details

We study the asymptotic bias of the factor-augmented regression estimator and its correction, augmented by r factors extracted from N variables over T observations. We consider general weak latent factor models with r signal eigenvalues that may diverge at different rates Nαk, 0<αk≤1, k=1,…,r. In the literature, the bias has been derived using an approximation based on a specific data-dependent rotation matrix Ĥ for models with αk=1 for all k. We instead derive the bias for general weak factor models without this restriction, and consider three rotation matrices: the data-dependent Ĥ and Ĥq, and their population counterpart H. We show that they induce distinct rotation-specific parameters, resulting in different asymptotic biases. This highlights the importance of explicitly specifying the rotation, as it determines the parameter being estimated and the associated asymptotic bias. Among these, the parameter associated with the population rotation matrix Ĥ is uniquely defined given signal components and particularly suitable for inference. Based on these results, we propose analytically bias-corrected estimators that do not require estimating αk, and establish their asymptotic normality centered at zero. Finite sample experiments show that the proposed bias-corrected estimators perform very well, and an empirical application illustrates its practical usefulness.

Organiser

University of Exeter Business School - Economics

Location

Syndicate Room B