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A three-factor econometric model of the U.S. term structure

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  • Frank F. Gong
  • Eli M. Remolona

Abstract

We estimate a three-factor model to fit both the time-series dynamics and cross-sectional shapes of the U.S. term structure. In the model, three unobserved factors drive a discrete-time stochastic discount process, with one factor reverting to a fixed mean and a second factor reverting to a third factor. To exploit the conditional density of yields, we estimate the model with a Kalman filter, a procedure that also allows us to use data for six maturities without making special assumptions about measurement errors. The estimated model reproduces the basic shapes of the average term structure, including the hump in the yield curve and the flat slope of the volatility curve. A likelihood ratio test favors the model over a nested two-factor model. Another likelihood ratio test, however, rejects the no-arbitrage restrictions the model imposes on the estimates. An analysis of the measurement errors suggests that the three factors still fail to capture enough of the comovement and persistence of yields.

Suggested Citation

  • Frank F. Gong & Eli M. Remolona, 1997. "A three-factor econometric model of the U.S. term structure," Staff Reports 19, Federal Reserve Bank of New York.
    • Handle: RePEc:fip:fednsr:19
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    Cited by:

    1. Tobias Adrian & Hao Wu, 2009. "The term structure of inflation expectations," Staff Reports 362, Federal Reserve Bank of New York.
    2. Nuno Cassola & Jorge Barros Luis, 2003. "A two-factor model of the German term structure of interest rates," Applied Financial Economics, Taylor & Francis Journals, vol. 13(11), pages 783-806.
    3. LuisM. Viceira & John Y. Campbell, 2001. "Who Should Buy Long-Term Bonds?," American Economic Review, American Economic Association, vol. 91(1), pages 99-127, March.
    4. Tkacz, Greg, 2004. "Inflation changes, yield spreads, and threshold effects," International Review of Economics & Finance, Elsevier, vol. 13(2), pages 187-199.
    5. Kozicki, Sharon & Tinsley, P. A., 2001. "Shifting endpoints in the term structure of interest rates," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 613-652, June.
    6. Michael J. Fleming & Eli M Remolona, 1999. "The term structure of announcement effects," BIS Working Papers 71, Bank for International Settlements.
    7. Cassola, N. & Luis, J.B., 2001. "A Two-Factor Model of the German Term Structure of Interest Rates," Papers 46, Quebec a Montreal - Recherche en gestion.
    8. Des Mc Manus & David Watt, 1999. "Estimating One-Factor Models of Short-Term Interest Rates," Staff Working Papers 99-18, Bank of Canada.
    9. Ben Fung & Scott Mitnick & Eli Remolona, 1999. "Uncovering Inflation Expectations and Risk Premiums From Internationally Integrated Financial Markets," Staff Working Papers 99-6, Bank of Canada.

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