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.

Bond Risk Premiums at the Zero Lower Bound

“…This result supports the …ndings ofAndreasen and Meldrum (2018), who show that once the ZLB period is included in the estimation sample, the standard SRM cannot match the desired slope coe¢ cients in equation(2)conditional on yields being away from the ZLB. This is because the estimated factor dynamics change once the ZLB period is included in the estimation sample, and this distorts the time-series dynamics of yields when they are away from the ZLB.…”

“…Such a model would display even greater ‡exibility in …tting the cross section of bond yields than implied by the standard SRM and the two extensions we propose. However, previous studies have shown that the standard SRM with …xed parameters is able to …t the cross-section of bond yields closely, both when yields are away from and close to the ZLB (see, for example, Christensen and Rudebusch (2015) and Andreasen and Meldrum (2018)). Hence, any improvements to the cross-sectional …t in a more ‡exible SRM seems likely to be economically marginal and would increase the risk of over-…tting the data.…”

“…where b step1 1 denotes the step 1 estimate of 1 , N = P T t=1 n y;t , and 1 is the feasible domain of 1 . Andreasen and Christensen (2015) show that b step1 1 is consistent and asymptotically 5 The SR approach has been applied to SRMs previously by Andreasen and Meldrum (2018). Gaussian for n y;t !…”

“…One of the most widely used dynamic term structure models (DTSMs) in recent years is the shadow rate model (SRM) proposed by Black (1995) (see Kim and Singleton (2012), Christensen and Rudebusch (2015), Bauer and Rudebusch (2016), Wu and Xia (2016), Andreasen and Meldrum (2018), among others). The popularity of the SRM stems from the fact that it enforces the zero lower bound (ZLB) on nominal bond yields, while preserving a (near-)linear relationship between bond yields and the pricing factors away from the ZLB.…”

Modelling Yields at the Lower Bound Through Regime Shifts

“…A more empirical motivation for this assumption can also be directly obtained from recent U.S. data. Following up on the conclusion in Andreasen and Meldrum (2018), Table 1 reports autocorrelation coe¢ cients for the short rate and yields before and after the LB period. Since the fed funds rate hit the 0 0.25% range at the end of 2008, the cut-o¤ point is set to December 2008.…”