Mining the Factor Zoo: Estimation of Latent Factor Models with Sufficient Proxies

TL;DR

This paper introduces a robust, flexible method for estimating latent factor models by combining domain knowledge and multivariate analysis, allowing the number of factors and proxies to grow, with improved convergence rates.

Contribution

It proposes a penalized reduced rank regression approach that integrates proxies and domain knowledge, accommodating diverging proxies and factors for more accurate latent factor estimation.

Findings

Faster convergence rates compared to benchmarks

Effective handling of heavy-tailed data

Validated through simulations and real data examples

Abstract

Latent factor model estimation typically relies on either using domain knowledge to manually pick several observed covariates as factor proxies, or purely conducting multivariate analysis such as principal component analysis. However, the former approach may suffer from the bias while the latter can not incorporate additional information. We propose to bridge these two approaches while allowing the number of factor proxies to diverge, and hence make the latent factor model estimation robust, flexible, and statistically more accurate. As a bonus, the number of factors is also allowed to grow. At the heart of our method is a penalized reduced rank regression to combine information. To further deal with heavy-tailed data, a computationally attractive penalized robust reduced rank regression method is proposed. We establish faster rates of convergence compared with the benchmark. Extensive simulations and real examples are used to illustrate the advantages.