Hostname: page-component-65b85459fc-997vn Total loading time: 0 Render date: 2025-10-18T10:51:44.391Z Has data issue: false hasContentIssue false
  • English
  • Français

Are Shadow Rate Models of the Treasury Yield Curve Structurally Stable?

Published online by Cambridge University Press:  11 December 2023

Don H. Kim  and
Marcel A. Priebsch
Don H. Kim
Affiliation:
Division of Monetary Affairs, Board of Governors of the Federal Reserve System don.h.kim@frb.gov
Marcel A. Priebsch*
Affiliation:
Division of Monetary Affairs, Board of Governors of the Federal Reserve System
*
marcel.a.priebsch@frb.gov (corresponding author)
Get access Rights & Permissions [Opens in a new window]

Abstract

We examine the structural stability of Gaussian shadow rate term structure models in a sample of Treasury yields that includes the “effective lower bound” (ELB) period from 2008 to 2015. After highlighting the challenges of testing for structural breaks in a latent-factor model, we proceed to document various pieces of empirical evidence for a structural break. As one of several practical implications, the expected policy rate paths during ELB years are notably shallower in our model that accommodates a structural break compared with a model that imposes structurally stability.

Information

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 59 , Issue 7 , November 2024 , pp. 3500 - 3530
Creative Commons
This is a work of the US Government and is not subject to copyright protection within the United States. Published by Cambridge University Press on behalf of The University of Washington
Copyright
© Don H. Kim and Marcel A. Priebsch outside of the territories of the USA, 2023.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

This article has evolved from our earlier preliminary working paper entitled “Estimation of Multi-Factor Shadow Rate Term Structure Models.” The analysis and conclusions set forth in this article are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors of the Federal Reserve System. We thank an anonymous referee, Hendrik Bessembinder (the editor), Michiel De Pooter, Marco Giacoletti (a referee), Edith Liu, Andrew Meldrum, Hiroatsu Tanaka, Jonathan Wright, and seminar participants at the Federal Reserve Board for helpful comments.

References

Ahn, D.-H.; Dittmar, R. F.; and Gallant, A. R.. “Quadratic Term Structure Models: Theory and Evidence.” Review of Financial Studies, 15 (2002), 243–288.CrossRefGoogle Scholar
Andreasen, M. M.; Jørgensen, K.; and Meldrum, A.. Bond Risk Premiums at the Zero Lower Bound. Washington, DC: Board of Governors of the Federal Reserve System (2019).CrossRefGoogle Scholar
Andreasen, M. M., and Meldrum, A.. “A Shadow Rate or a Quadratic Policy Rule? The Best Way to Enforce the Zero Lower Bound in the United States.” Journal of Financial and Quantitative Analysis, 54 (2019), 2261–2292.CrossRefGoogle Scholar
Andrews, D. W. K. “Tests for Parameter Instability and Structural Change with Unknown Change Point.” Econometrica, 61 (1993), 821–856.10.2307/2951764CrossRefGoogle Scholar
Andrews, D. W. K., and Fair, R. C.. “Inference in Nonlinear Econometric Models with Structural Change.” Review of Economic Studies, 55 (1988), 615–639.10.2307/2297408CrossRefGoogle Scholar
Ang, A., and Piazzesi, M.. “A No-Arbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables.” Journal of Monetary Economics, 50 (2003), 745–787.10.1016/S0304-3932(03)00032-1CrossRefGoogle Scholar
Backus, D.; Foresi, S.; Mozumdar, A.; and Wu, L.. “Predictable Changes in Yields and Forward Rates.” Journal of Financial Economics, 59 (2001), 281–311.10.1016/S0304-405X(00)00088-XCrossRefGoogle Scholar
Bauer, M. D. “Restrictions on Risk Prices in Dynamic Term Structure Models.” Journal of Business & Economic Statistics, 36 (2018), 196–211.10.1080/07350015.2016.1164707CrossRefGoogle Scholar
Bauer, M. D., and Rudebusch, G. D.. “Monetary Policy Expectations at the Zero Lower Bound.” Journal of Money, Credit and Banking, 48 (2016), 1439–1465.10.1111/jmcb.12338CrossRefGoogle Scholar
Bauer, M. D., and Rudebusch, G. D.. “Interest Rates Under Falling Stars.” American Economic Review, 110 (2020), 1316–1354.10.1257/aer.20171822CrossRefGoogle Scholar
Bauer, M. D.; Rudebusch, G. D.; and Wu, J. C.. “Correcting Estimation Bias in Dynamic Term Structure Models.” Journal of Business & Economic Statistics, 30 (2012), 454–467.CrossRefGoogle Scholar
Bernanke, B. S. “The New Tools of Monetary Policy.” American Economic Review, 110 (2020), 943–983.CrossRefGoogle Scholar
Campbell, J. Y., and Shiller, R. J.. “Yield Spreads and Interest Rate Movements: A Bird’s Eye View.” Review of Economic Studies, 58 (1991), 495–514.10.2307/2298008CrossRefGoogle Scholar
Chow, G. C. “Tests of Equality Between Sets of Coefficients in Two Linear Regressions.” Econometrica, 28 (1960), 591–605.10.2307/1910133CrossRefGoogle Scholar
Christensen, J. H.; Diebold, F. X.; and Rudebusch, G. D.. “The Affine Arbitrage-Free Class of Nelson–Siegel Term Structure Models.” Journal of Econometrics, 164 (2011), 4–20.10.1016/j.jeconom.2011.02.011CrossRefGoogle Scholar
Christensen, J. H. E., and Rudebusch, G. D.. “Estimating Shadow-Rate Term Structure Models with Near-Zero Yields.” Journal of Financial Econometrics, 13 (2014), 226–259.10.1093/jjfinec/nbu010CrossRefGoogle Scholar
Chung, H.; Laforte, J.-P.; Reifschneider, D.; and Williams, J. C.. “Have We Underestimated the Likelihood and Severity of Zero Lower Bound Events?” Journal of Money, Credit and Banking, 44 (2012), 47–82.10.1111/j.1538-4616.2011.00478.xCrossRefGoogle Scholar
Dai, Q., and Singleton, K. J.. “Specification Analysis of Affine Term Structure Models.” Journal of Finance, 55 (2000), 1943–1978.10.1111/0022-1082.00278CrossRefGoogle Scholar
Dai, Q., and Singleton, K. J.. “Expectation Puzzles, Time-Varying Risk Premia, and Affine Models of the Term Structure.” Journal of Financial Economics, 63 (2002), 415–441.10.1016/S0304-405X(02)00067-3CrossRefGoogle Scholar
Duffee, G. R. “Term Premia and Interest Rate Forecasts in Affine Models.” Journal of Finance, 57 (2002), 405–443.10.1111/1540-6261.00426CrossRefGoogle Scholar
Duffee, G. R. “Information in (and not in) the Term Structure.” Review of Financial Studies, 24 (2011), 2895–2934.10.1093/rfs/hhr033CrossRefGoogle Scholar
Duffie, D., and Kan, R.. “A Yield-Factor Model of Interest Rates.” Mathematical Finance, 6 (1996), 379–406.10.1111/j.1467-9965.1996.tb00123.xCrossRefGoogle Scholar
Eggertsson, G. B., and Woodford, M.. “The Zero Bound on Interest Rates and Optimal Monetary Policy.” Brookings Papers on Economic Activity, 2003 (2003), 139–211.10.1353/eca.2003.0010CrossRefGoogle Scholar
Fama, E. F. “The Information in the Term Structure.” Journal of Financial Economics, 13 (1984), 509–528.10.1016/0304-405X(84)90013-8CrossRefGoogle Scholar
Ghysels, E., and Hall, A.. “A Test for Structural Stability of Euler Conditions Parameters Estimated Via the Generalized Method of Moments Estimator.” International Economic Review, 31 (1990), 355–364.10.2307/2526844CrossRefGoogle Scholar
Giacoletti, M.; Laursen, K. T.; and Singleton, K. J.. “Learning from Disagreement in the U.S. Treasury Bond Market.” Journal of Finance, 76 (2021), 395–441.10.1111/jofi.12971CrossRefGoogle Scholar
Gürkaynak, R. S.; Sack, B.; and Wright, J. H.. “The U.S. Treasury Yield Curve: 1961 to the Present.” Journal of Monetary Economics, 54 (2007), 2291–2304.CrossRefGoogle Scholar
Gust, C.; Herbst, E.; López-Salido, D.; and Smith, M. E.. “The Empirical Implications of the Interest-Rate Lower Bound.” American Economic Review, 107 (2017), 1971–2006.10.1257/aer.20121437CrossRefGoogle Scholar
Hansen, B. E. “Lagrange Multiplier Tests for Parameter Instability in Non-Linear Models.” Working Paper, University of Rochester (1990).Google Scholar
Hansen, B. E. “Tests for Parameter Instability in Regressions with I(1) Processes.” Journal of Business & Economic Statistics, 10 (1992), 321–335.Google Scholar
Hördahl, P., and Tristani, O.. “Modelling Yields at the Lower Bound Through Regime Shifts.” Working Paper, European Central Bank, Frankfurt (2019).10.2139/ssrn.3464245CrossRefGoogle Scholar
Hu, G. X.; Pan, J.; and Wang, J.. “Noise as Information for Illiquidity.” Journal of Finance, 68 (2013), 2341–2382.10.1111/jofi.12083CrossRefGoogle Scholar
Johannsen, B. K., and Mertens, E.. “A Time Series Model of Interest Rates with the Effective Lower Bound.” Working Paper, Board of Governors of the Federal Reserve System, Washington (2016).10.17016/feds.2016.033CrossRefGoogle Scholar
Joslin, S.; Priebsch, M.; and Singleton, K. J.. “Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks.” Journal of Finance, 69 (2014), 1197–1233.10.1111/jofi.12131CrossRefGoogle Scholar
Kim, D. H., and Orphanides, A.. “Term Structure Estimation with Survey Data on Interest Rate Forecasts.” Journal of Financial and Quantitative Analysis, 47 (2012), 241–272.10.1017/S0022109011000627CrossRefGoogle Scholar
Kim, D. H., and Singleton, K. J.. “Term Structure Models and the Zero Bound: An Empirical Investigation of Japanese Yields.” Journal of Econometrics, 170 (2012), 32–49.10.1016/j.jeconom.2011.12.005CrossRefGoogle Scholar
Kim, D. H., and Wright, J. H.. “An Arbitrage-Free Three-Factor Term Structure Model and the Recent Behavior of Long-Term Yields and Distant-Horizon Forward Rates.” Working Paper, Board of Governors of the Federal Reserve System, Washington (2005).10.2139/ssrn.813267CrossRefGoogle Scholar
King, T. B. “Expectation and Duration at the Effective Lower Bound.” Journal of Financial Economics, 134 (2019), 736–760.10.1016/j.jfineco.2019.05.009CrossRefGoogle Scholar
Krippner, L. “Measuring the Stance of Monetary Policy in Zero Lower Bound Environments.” Economics Letters, 118 (2013), 135–138.10.1016/j.econlet.2012.10.011CrossRefGoogle Scholar
Kuttner, K. N. “Outside the Box: Unconventional Monetary Policy in the Great Recession and Beyond.” Journal of Economic Perspectives, 32 (2018), 121–146.10.1257/jep.32.4.121CrossRefGoogle Scholar
Li, C.; Meldrum, A.; and Rodriguez, M.. “New Financial Market Measures of the Neutral Real Rate and Inflation Expectations.” Working Paper, Board of Governors of the Federal Reserve System, Washington (2017).Google Scholar
Liu, P.; Theodoridis, K.; Mumtaz, H.; and Zanetti, F.. “Changing Macroeconomic Dynamics at the Zero Lower Bound.” Journal of Business & Economic Statistics, 37 (2019), 391–404.10.1080/07350015.2017.1350186CrossRefGoogle Scholar
Nakata, T., and Tanaka, H.. “Equilibrium Yield Curves and the Interest Rate Lower Bound.” Working Paper, Board of Governors of the Federal Reserve System, Washington (2016).10.17016/feds.2016.085CrossRefGoogle Scholar
Nyblom, J. “Testing for the Constancy of Parameters over Time.” Journal of the American Statistical Association, 84 (1989), 223–230.10.1080/01621459.1989.10478759CrossRefGoogle Scholar
Priebsch, M. A. “Computing Arbitrage-Free Yields in Multi-Factor Gaussian Shadow-Rate Term Structure Models.” Quarterly Journal of Finance, 13 (2023), 2350013.CrossRefGoogle Scholar
Reifschneider, D., and Williams, J. C.. “Three Lessons for Monetary Policy in a Low-Inflation Era.” Journal of Money, Credit and Banking, 32 (2000), 936–966.10.2307/2601151CrossRefGoogle Scholar
Swanson, E. T., and Williams, J. C.. “Measuring the Effect of the Zero Lower Bound on Medium- and Longer-Term Interest Rates.” American Economic Review, 104 (2014), 3154–3185.10.1257/aer.104.10.3154CrossRefGoogle Scholar
Wan, E., and van der Merwe, R.. “The Unscented Kalman Filter.” In Kalman Filtering and Neural Networks, Haykin, S., ed. New York, NY: Wiley (2001), 221–280.10.1002/0471221546.ch7CrossRefGoogle Scholar
Wu, J. C., and Xia, F. D.. “Measuring the Macroeconomic Impact of Monetary Policy at the Zero Lower Bound.” Journal of Money, Credit and Banking, 48 (2016), 253–291.10.1111/jmcb.12300CrossRefGoogle Scholar
Supplementary material: File

Kim and Priebsch supplementary material

Kim and Priebsch supplementary material
Download Kim and Priebsch supplementary material(File)
File 552.1 KB