Mining the Factor Zoo: Estimation of Latent Factor Models with Sufficient Proxies
This addresses the bias and information limitations in latent factor model estimation for statistical and econometric applications, representing an incremental improvement.
The paper tackles the problem of estimating latent factor models by bridging domain knowledge and multivariate analysis, allowing for diverging factor proxies and number of factors, resulting in robust, flexible, and statistically more accurate estimation with faster convergence rates compared to benchmarks.
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.