Characteristics-Based Factor Modeling via Reduced Rank Regression

Abstract

We provide a framework for extracting characteristics-based factors via Reduced
Rank Regression. This generalizes the Instrumented Principal Component Analysis by
Kelly et al. (2019), the Projected Principal Component Analysis in Fan et al. (2016b),
can accommodate cross-sectional and time-series dependencies, and recovers the closest
lower-dimensional approximation to GLS factors discussed in Kozak and Nagel (2023).
The asymptotic theory is derived and a bias in the IPCA inference is corrected. A sparse
design is introduced to interpret the factors. Our findings confirm that accounting for
cross-sectional dependence results in more efficient estimators leading to a better fit
and a higher spanning.

Keywords: Cross-sectional returns, Mean-Variance spanning, GLS, Industry-clustering, Factors, Principal components, Sparseness

JEL Classification: C23, G11, G12