Efficient Estimation of Nonstationary Factor Models

This paper studies the generalized principal component estimator (GPCE) of Choi (2007) for the factor model Xt = Ft + et where Ft is a unit-root process. First, this paper derives asymptotic distributions of the GPCEs of the factor and factor-loading spaces which show that the GPCE enjoys an e¡Ë - ciency gain over the conventional principal component estimator. Second, this paper extends the conventional static factor model to those with time polyno- mials, and studies the GPCE for the models. The GPCE continues to have an e¡Ë ciency gain over the conventional principal component estimator for the extended model. Third, this paper considers the forecasting regression that uses the GPCE-based estimates of nonstationary factors and shows that the GPCE yields more accurate forecasts than the conventional principal compo- nent estimator. Last, asymptotic equivalence of the GPCE and feasible GPCE (FGPCE) of the factor space is established.