Identification of Time-varying Factor Models

The emergence of large data sets with long time spans has cast doubt on the assumption of constant loadings in conventional factor models. Being a potential solution, the time-varying factor model (TVFM) has attracted enormous interest in the literature. However, TVFM also suffers from the well-known problem of non-identifiability. This paper considers the situations under which both the factors and factor loadings can be estimated without rotations asymptotically. Asymptotic distributions of the proposed estimators are derived. Theoretical findings are supported by simulations. Finally, we evaluate the forecasting performance of the estimated factors subject to different identification restrictions using an extensive data set of the U.S. macroeconomic variables. Substantial differences are found among the choices of identification restrictions.