Efficient Estimation of Factor Models

This paper considers the factor model Xt = Ft + et. Assuming a nor- mal distribution for the idiosyncratic error et conditional on the factors fFtg, conditional maximum likelihood estimators of the factor and factor- loading spaces are derived. These estimators are called generalized prin- cipal component estimators (GPCEs) without the normality assumption. This paper derives the asymptotic distributions of the GPCEs of the fac- tor and factor-loading space. It is shown that variances of the GPCEs of the common components are smaller than those of the principal com- ponent estimators studied in Bai (2003). The approximate variance of the forecasting error using the GPCE-based factor estimates is derived and shown to be smaller than that based on the principal component es- timators. The feasible GPCE (FGPCE) of factor space is shown to be asymptotically equivalent to the GPCE. The GPCEs and FGPCEs are shown to be more efficient than the principal component estimators in finite samples.