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Estimating real and nominal term structures using Treasury yields, inflation, inflation forecasts, and inflation swap rates

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  • Joseph G. Haubrich
  • George Pennacchi
  • Peter Ritchken

Abstract

This paper develops and estimates an equilibrium model of the term structures of nominal and real interest rates. The term structures are driven by state variables that include the short term real interest rate, expected inflation, a factor that models the changing level to which inflation is expected to revert, as well as four volatility factors that follow GARCH processes. We derive analytical solutions for the prices of nominal bonds, inflation-indexed bonds that have an indexation lag, the term structure of expected inflation, and inflation swap rates. The model parameters are estimated using data on nominal Treasury yields, survey forecasts of inflation, and inflation swap rates. We find that allowing for GARCH effects is particularly important for real interest rate and expected inflation processes, but that long–horizon real and inflation risk premia are relatively stable. Comparing our model prices of inflation-indexed bonds to those of Treasury Inflation Protected Securities (TIPS) suggests that TIPS were underpriced prior to 2004 but subsequently were valued fairly. We find that unexpected increases in both short run and longer run inflation implied by our model have a negative impact on stock market returns.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Cleveland in its series Working Paper with number 0810.

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Date of creation: 2008
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Handle: RePEc:fip:fedcwp:0810

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Keywords: Interest rates ; Inflation (Finance) ; Asset pricing;

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References

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  1. Ang, Andrew & Bekaert, Geert & Wei, Min, 2007. "Do macro variables, asset markets, or surveys forecast inflation better?," Journal of Monetary Economics, Elsevier, Elsevier, vol. 54(4), pages 1163-1212, May.
  2. Jarrow, Robert & Yildirim, Yildiray, 2003. "Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 38(02), pages 337-358, June.
  3. Pierluigi Balduzzi & Sanjiv Ranjan Das & Silverio Foresi, 1997. "The Central Tendency: A Second Factor in Bond Yields," NBER Working Papers 6325, National Bureau of Economic Research, Inc.
  4. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, American Finance Association, vol. 55(5), pages 1943-1978, October.
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  6. Michael D. Bordo & Joseph G. Haubrich, 2004. "The yield curve, recessions, and the credibility of the monetary regime: long-run evidence, 1875-1997," Working Paper 0402, Federal Reserve Bank of Cleveland.
  7. John Y. Campbell & Adi Sunderam & Luis M. Viceira, 2009. "Inflation Bets or Deflation Hedges? The Changing Risks of Nominal Bonds," NBER Working Papers 14701, National Bureau of Economic Research, Inc.
  8. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
  9. Ang, Andrew & Bekaert, Geert, 2004. "The Term Structure of Real Rates and Expected Inflation," CEPR Discussion Papers, C.E.P.R. Discussion Papers 4518, C.E.P.R. Discussion Papers.
  10. Konstantijn Maes, 2004. "Modeling the Term Structure of Interest Rates: Where Do We Stand?," Working Paper Research, National Bank of Belgium 42, National Bank of Belgium.
  11. Benninga, Simon & Protopapadakis, Aris, 1983. "Real and Nominal Interest Rates under Uncertainty: The Fisher Theorem and the Term Structure," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 91(5), pages 856-67, October.
  12. V. Cvsa & P. Ritchken, 2001. "Pricing Claims Under GARCH-Level Dependent Interest Rate Processes," Management Science, INFORMS, INFORMS, vol. 47(12), pages 1693-1711, December.
  13. Refet S. Gürkaynak & Brian Sack & Jonathan H. Wright, 2008. "The TIPS yield curve and inflation compensation," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 2008-05, Board of Governors of the Federal Reserve System (U.S.).
  14. Haubrich, Joseph G & Ritter, Joseph A, 2000. "Dynamic Commitment and Incomplete Policy Rules," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 32(4), pages 766-84, November.
  15. Tobias Adrian & Hao Wu, 2009. "The term structure of inflation expectations," Staff Reports, Federal Reserve Bank of New York 362, Federal Reserve Bank of New York.
  16. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
  17. Buraschi, Andrea & Jiltsov, Alexei, 2005. "Inflation risk premia and the expectations hypothesis," Journal of Financial Economics, Elsevier, Elsevier, vol. 75(2), pages 429-490, February.
  18. Dean Croushore, 1993. "Introducing: the survey of professional forecasters," Business Review, Federal Reserve Bank of Philadelphia, Federal Reserve Bank of Philadelphia, issue Nov, pages 3-15.
  19. Brenner, Robin J. & Harjes, Richard H. & Kroner, Kenneth F., 1996. "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 31(01), pages 85-107, March.
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