Estimating the term structure with linear regressions: Getting to the roots of the problem

Linear estimators of the affine term structure model are inconsistent since they cannot reproduce the factors used in estimation. This is a serious handicap empirically, giving a worse fit than the conventional MLE estimator that ensures consistency. We show that a simple self-consistent estimator can be constructed using the eigenvalue decomposition of a regression estimator. The remaining parameters of the model follow analytically. The fit of this model is virtually indistinguishable from that of the MLE. We apply the method to estimate the model of the U.S. Treasury yields and a joint model of the U.S. and German yield curves.