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

  • Martin M. Andreasen and Andrew Meldrum


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.


Corresponding author

*Andreasen (corresponding author),, Aarhus University CREATES and Danish Finance Institute; Meldrum,, Board of Governors of the Federal Reserve System.


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We give special thanks to Hendrik Bessembinder (the editor) and Jean-Sébastien Fontaine (the referee) for many helpful suggestions. We thank Jens Christensen, Michiel De Pooter, Hans Dewachter, Gregory R. Duffee, Tom Engsted, Peter Hördahl, Scott Joslin, Don Kim, Donna Lormand, Thomas Pedersen, Jean-Paul Renne, Glenn Rudebusch, Oreste Tristani, and Chris Young for helpful comments, as well as seminar participants at the 2015 SoFie Conference, the Federal Reserve Bank of San Francisco, the European Central Bank, and the Bank of England. Andreasen acknowledges financial support from the Danish e-Infrastructure Cooperation (DeIC) and financial support from CREATES (Center for Research in Econometric Analysis of Time Series; DNRF78) from the Danish National Research Foundation. Meldrum acknowledges the Bank of England, where he worked during the preparation of an early draft of this article (Bank of England Staff Working Paper No. 550, Sept. 2015). The analysis and conclusions are those of the authors and do not indicate concurrence by the Bank of England, the Board of Governors of the Federal Reserve System, or other members of the research staff of the Board.



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