Yuan Ke, Princeton University
We study factor models when the latent factors can be explained partially by several observed covariates. In financial factor models for instance, the unknown factors can be reasonably well predicted by a few covariates, such as the Fama- French factors. To incorporate the explanatory power of these covariates, we propose a two-step estimation procedure: (i) regress the data onto the observables, and (ii) take the principal components of the fitted data to estimate the loadings and factors. With those covariates, the factors can be estimated accurately even if the cross- sectional dimension is mild. The proposed estimator is robust to possibly heavy- tailed distributions, which are encountered in many applications. Empirically, we apply the model to forecasting US bond risk premia, and find that the observed economic covariates contain strong explanatory powers of the factors. The gain of forecast is more substantial when these covariates are incorporated to estimate the common factors than directly used for forecasts.