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Modifying Gaussian term structure models when interest rates are near the zero lower bound

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Abstract

With nominal interest rates near the zero lower bound (ZLB) in many major economies, it is theoretically untenable to apply Gaussian affine term structure models (GATSMs) while ignoring their inherent material probabilities of negative interest rates. I propose correcting that deficiency by adjusting the entire GATSM term structure with an explicit function of maturity that represents the optionality associated with the present and future availability of physical currency. The resulting ZLB-GATSM framework remains tractable, producing a simple closed-form analytic expression for forward rates and requiring only elementary univariate numerical integration (over time to maturity) to obtain interest rates and bond prices. I demonstrate the salient features of the ZLB- GATSM framework using a two-factor model. An illustrative estimation with U.S. term structure data indicates that the ZLB-GATSM "shadow short rate" provides a useful gauge of the stance of monetary policy; in particular becoming negative when the U.S. policy rate reached the ZLB in late 2008, and moving more negative with subsequent unconventional monetary policy easings.

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Paper provided by Reserve Bank of New Zealand in its series Reserve Bank of New Zealand Discussion Paper Series with number DP2012/02.

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Length: 49 p.
Date of creation: Mar 2012
Date of revision:
Handle: RePEc:nzb:nzbdps:2012/02

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  1. Langetieg, Terence C, 1980. " A Multivariate Model of the Term Structure," Journal of Finance, American Finance Association, American Finance Association, vol. 35(1), pages 71-97, March.
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  4. Leo Krippner, 2012. "A theoretical foundation for the Nelson and Siegel class of yield curve models," CAMA Working Papers, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University 2012-11, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  5. Leo Krippner, 2012. "A theoretical foundation for the Nelson and Siegel class of yield curve models," CAMA Working Papers, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University 2012-11, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
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  14. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, Econometric Society, vol. 60(1), pages 77-105, January.
  15. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 177-188, November.
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As found by EconAcademics.org, the blog aggregator for Economics research:
  1. How to measure the monetary stance when the interest rate is zero
    by Economic Logician in Economic Logic on 2012-10-31 14:49:00
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Cited by:
  1. Glenn Rudebusch & Michael Bauer, 2013. "The Shadow Rate, Taylor Rules, and Monetary Policy Lift-off," 2013 Meeting Papers, Society for Economic Dynamics 691, Society for Economic Dynamics.
  2. Leo Krippner, 2012. "Measuring the stance of monetary policy in zero lower bound environments," Reserve Bank of New Zealand Discussion Paper Series, Reserve Bank of New Zealand DP2012/04, Reserve Bank of New Zealand.
  3. Jens H.E. Christensen & Glenn D. Rudebusch, 2013. "Estimating shadow-rate term structure models with near-zero yields," Working Paper Series, Federal Reserve Bank of San Francisco 2013-07, Federal Reserve Bank of San Francisco.
  4. Christensen, Jens H.E. & Lopez, Jose A. & Rudebusch, Glenn D., 2013. "A probability-based stress test of Federal Reserve assets and income," Working Paper Series, Federal Reserve Bank of San Francisco 2013-38, Federal Reserve Bank of San Francisco.
  5. Leo Krippner, 2013. "Efficient Jacobian evaluations for estimating zero lower bound term structure models," CAMA Working Papers, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University 2013-77, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  6. Edda Claus & Iris Claus & Leo Krippner, 2014. "Asset markets and monetary policy shocks at the zero lower bound," CAMA Working Papers, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University 2014-42, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  7. Leo Krippner, 2012. "A model for interest rates near the zero lower bound: An overview and discussion," Reserve Bank of New Zealand Analytical Notes series, Reserve Bank of New Zealand AN2012/05, Reserve Bank of New Zealand.
  8. Leo Krippner, 2013. "A tractable framework for zero lower bound Gaussian term structure models," Reserve Bank of New Zealand Discussion Paper Series, Reserve Bank of New Zealand DP2013/02, Reserve Bank of New Zealand.
  9. Michael D. Bauer & Glenn D. Rudebusch, 2013. "Monetary policy expectations at the zero lower bound," Working Paper Series, Federal Reserve Bank of San Francisco 2013-18, Federal Reserve Bank of San Francisco.
  10. Leo Krippner, 2012. "A theoretical foundation for the Nelson and Siegel class of yield curve models," CAMA Working Papers, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University 2012-11, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  11. Leo Krippner, 2014. "Measuring the stance of monetary policy in conventional and unconventional environments," CAMA Working Papers, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University 2014-06, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  12. Jing Cynthia Wu & Fan Dora Xia, 2014. "Measuring the Macroeconomic Impact of Monetary Policy at the Zero Lower Bound," NBER Working Papers 20117, National Bureau of Economic Research, Inc.

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