A1181
Title: Bias correction in factor-augmented regression models with weak factors
Authors: Peiyun Jiang - Center for Data Science, Waseda University (Japan) [presenting]
Yoshimasa Uematsu - Hitotsubashi University (Japan)
Takashi Yamagata - University of York (United Kingdom)
Abstract: The asymptotic bias of the factor-augmented regression estimator and its correction, augmented by $r$ factors extracted from $N$ variables over $T$ observations, is studied for general weak latent factor models with $r$ signal eigenvalues that may diverge at different rates $N^{\alpha_{k}}$, $0<\alpha_{k}\leq 1$, $k=1,\dots,r$. In existing literature, the bias has been derived using an approximation with a specific data-dependent rotation matrix $\hat{\mathbf{H}}$ for models in which $\alpha_{k}=1$ for all $k$. The bias is derived here for general weak factor models, considering three rotation matrices: the data-dependent $\hat{\mathbf{H}}$ and $\hat{\mathbf{H}}_q$, and their population counterpart $\mathbf{H}$. Although these rotation matrices are asymptotically equivalent, they generally induce distinct rotation-specific parameters, resulting in different asymptotic biases. Based on these results, analytically bias-corrected estimators are proposed that do not require estimating $\alpha_k$, and their asymptotic normality centered at zero is established. The parameter associated with the population rotation matrix $\mathbf{H}$ is uniquely defined and therefore well suited for inference. Extensive finite-sample experiments suggest that the proposed analytical bias correction performs very well, and an empirical application illustrates its usefulness in practice.
