Nº 19-65: Extracting Statistical Factors When Betas are Time-Varying

This paper deals with identification and inference on the unobservable conditional factor space and its dimension in large unbalanced panels of asset returns. The model specification is nonparametric regarding the way the loadings vary in time as functions of common shocks and individual characteristics. The number of active factors can also be time-varying as an effect of the changing macroeconomic environment. The method deploys Instrumental Variables (IV) which have full-rank covariation with the factor betas in the cross-section. It allows for a large dimension of the vector generating the conditioning information by machine learning techniques. In an empirical application, we infer the conditional factor space in the panel of monthly returns of individual stocks in the CRSP dataset between January 1971 and December 2017.