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Estimating Shadow-Rate Term Structure Models with Near-Zero Yields


  • Christensen, Jens H. E.

    () (Federal Reserve Bank of San Francisco)

  • Rudebusch, Glenn D.

    () (Federal Reserve Bank of San Francisco)


Standard Gaussian term structure models have often been criticized for not ruling out negative nominal interest rates, but this flaw has been especially conspicuous with interest rates near zero in many countries. We provide a tractable means to estimate an alternative Gaussian shadow-rate dynamic term structure model that enforces the zero lower bound on bond yields. We illustrate this model by estimating one-, two-, and three-factor shadow-rate models on a sample of positive and near-zero Japanese bond yields. We find that the level of the shadow rate is sensitive to model fit and specification, including the number of factors employed.

Suggested Citation

  • Christensen, Jens H. E. & Rudebusch, Glenn D., 2013. "Estimating Shadow-Rate Term Structure Models with Near-Zero Yields," Working Paper Series 2013-07, Federal Reserve Bank of San Francisco.
  • Handle: RePEc:fip:fedfwp:2013-07
    DOI: 10.24148/wp2013-07

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    References listed on IDEAS

    1. Christensen, Jens H.E. & Diebold, Francis X. & Rudebusch, Glenn D., 2011. "The affine arbitrage-free class of Nelson-Siegel term structure models," Journal of Econometrics, Elsevier, vol. 164(1), pages 4-20, September.
    2. Jens H. E. Christensen & Glenn D. Rudebusch, 2012. "The Response of Interest Rates to US and UK Quantitative Easing," Economic Journal, Royal Economic Society, vol. 122(564), pages 385-414, November.
    3. Michael D. Bauer & Glenn D. Rudebusch & Jing Cynthia Wu, 2012. "Correcting Estimation Bias in Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 454-467, April.
    4. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2010. "Inflation Expectations and Risk Premiums in an Arbitrage-Free Model of Nominal and Real Bond Yields," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(s1), pages 143-178, September.
    5. Krippner, Leo, 2013. "Measuring the stance of monetary policy in zero lower bound environments," Economics Letters, Elsevier, vol. 118(1), pages 135-138.
    6. Viatcheslav Gorovoi & Vadim Linetsky, 2004. "Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 49-78.
    7. Leo Krippner, 2011. "Modifying Gaussian term structure models when interest rates are near the zero lower bound," CAMA Working Papers 2011-36, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
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    Cited by:

    1. Lemke, Wolfgang & Vladu, Andreea L., 2016. "Below the zero lower bound: A shadow-rate term structure model for the euro area," Discussion Papers 32/2016, Deutsche Bundesbank.
    2. Qianying Chen & Marco Lombardi & Alex Ross & Feng Zhu, 2017. "Global impact of US and euro area unconventional monetary policies: a comparison," BIS Working Papers 610, Bank for International Settlements.
    3. Blattner, Tobias & Joyce, Michael A. S., 2016. "Net debt supply shocks in the euro area and the implications for QE," Working Paper Series 1957, European Central Bank.
    4. Halberstadt, Arne & Krippner, Leo, 2016. "The effect of conventional and unconventional euro area monetary policy on macroeconomic variables," Discussion Papers 49/2016, Deutsche Bundesbank.
    5. Caggiano, Giovanni & Castelnuovo, Efrem & Pellegrino, Giovanni, 2017. "Estimating the real effects of uncertainty shocks at the Zero Lower Bound," European Economic Review, Elsevier, vol. 100(C), pages 257-272.
    6. Christensen, Jens H.E. & Lopez, Jose A. & Rudebusch, Glenn D., 2015. "A probability-based stress test of Federal Reserve assets and income," Journal of Monetary Economics, Elsevier, vol. 73(C), pages 26-43.
    7. Andreasen, Martin M & Meldrum, Andrew, 2015. "Dynamic term structure models: the best way to enforce the zero lower bound in the United States," Bank of England working papers 550, Bank of England.
    8. Leo Krippner & Michelle Lewis, 2018. "Real-time forecasting with macro-finance models in the presence of a zero lower bound," Reserve Bank of New Zealand Discussion Paper Series DP2018/04, Reserve Bank of New Zealand.
    9. Peter Feldhütter, 2016. "Can Affine Models Match the Moments in Bond Yields?," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 1-56, June.
    10. Christiaan Pattipeilohy & Christina Bräuning & Jan Willem van den End & Renske Maas, 2017. "Assessing the effective stance of monetary policy: A factor-based approach," DNB Working Papers 575, Netherlands Central Bank, Research Department.
    11. Martin M. Andreasen & Jens H.E. Christensen & Glenn D. Rudebusch, 1809. "Term Structure Analysis with Big Data," CREATES Research Papers 2017-31, Department of Economics and Business Economics, Aarhus University.
    12. Kuusela, Annika & Hännikäinen, Jari, 2017. "What do the shadow rates tell us about future inflation?," MPRA Paper 80542, University Library of Munich, Germany.
    13. Edda Claus & Iris Claus & Leo Krippner, 2016. "Monetary Policy Spillovers across the Pacific when Interest Rates Are at the Zero Lower Bound," Asian Economic Papers, MIT Press, vol. 15(3), pages 1-27, Fall.
    14. repec:bfr:rueban:2017:52 is not listed on IDEAS
    15. Andrea Carriero & Sarah Mouabbi & Elisabetta Vangelista, 2015. "UK Term Structure Decompositions at the Zero Lower Bound," Working Papers 755, Queen Mary University of London, School of Economics and Finance.
    16. Yoichi Ueno, 2017. "Term Structure Models with Negative Interest Rates," IMES Discussion Paper Series 17-E-01, Institute for Monetary and Economic Studies, Bank of Japan.
    17. Monfort, Alain & Pegoraro, Fulvio & Renne, Jean-Paul & Roussellet, Guillaume, 2017. "Staying at zero with affine processes: An application to term structure modelling," Journal of Econometrics, Elsevier, vol. 201(2), pages 348-366.
    18. Marco Jacopo Lombardi & Feng Zhu, 2014. "A shadow policy rate to calibrate US monetary policy at the zero lower bound," BIS Working Papers 452, Bank for International Settlements.
    19. Martin M. Andreasen & Jens H.E. Christensen & Simon Riddell, 1508. "The TIPS Liquidity Premium," CREATES Research Papers 2017-27, Department of Economics and Business Economics, Aarhus University.
    20. repec:eee:finlet:v:21:y:2017:i:c:p:100-106 is not listed on IDEAS
    21. Leo Krippner & Michael Callaghan, 2016. "Short-term risk premiums and policy rate expectations in the United States," Reserve Bank of New Zealand Analytical Notes series AN2016/07, Reserve Bank of New Zealand.

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