A Shadow Rate or a Quadratic Policy Rule? The Best Way to Enforce the Zero Lower Bound in the United States

Abstract

We study whether it is better to enforce the zero lower bound (ZLB) in models of U.S. Treasury yields using a shadow rate model or a quadratic term structure model. We show that the models achieve a similar in-sample fit and perform comparably in matching conditional expectations of future yields. However, when the recent ZLB period is included in the sample, the models’ ability to match conditional expectations away from the ZLB deteriorates because the time-series dynamics of the pricing factors change. In addition, neither model provides a reasonable description of conditional volatilities when yields are away from the ZLB.