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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. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
  2. Andrew Ang & Geert Bekaert & Min Wei, 2007. "The Term Structure of Real Rates and Expected Inflation," NBER Working Papers 12930, National Bureau of Economic Research, Inc.
  3. 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.
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  5. 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.
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  11. 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, vol. 31(01), pages 85-107, March.
  12. 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, vol. 91(5), pages 856-67, October.
  13. Tobias Adrian & Hao Wu, 2009. "The term structure of inflation expectations," Staff Reports 362, Federal Reserve Bank of New York.
  14. 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, vol. 38(02), pages 337-358, June.
  15. Konstantijn Maes, 2004. "Modeling the Term Structure of Interest Rates: Where Do We Stand?," Working Paper Research 42, National Bank of Belgium.
  16. Refet S. Gürkaynak & Brian Sack & Jonathan H. Wright, 2008. "The TIPS yield curve and inflation compensation," Finance and Economics Discussion Series 2008-05, Board of Governors of the Federal Reserve System (U.S.).
  17. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  18. Haubrich, Joseph G & Ritter, Joseph A, 2000. "Dynamic Commitment and Incomplete Policy Rules," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 32(4), pages 766-84, November.
  19. Buraschi, Andrea & Jiltsov, Alexei, 2005. "Inflation risk premia and the expectations hypothesis," Journal of Financial Economics, Elsevier, vol. 75(2), pages 429-490, February.
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Citations

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Cited by:
  1. Shiller, Robert J. & Campbell, John Y. & Viceira, Luis Manuel, 2009. "Understanding Inflation-Indexed Bond Markets," Scholarly Articles 10885503, Harvard University Department of Economics.
  2. Olivier Coibion & Yuriy Gorodnichenko, 2010. "Information Rigidity and the Expectations Formation Process: A Simple Framework and New Facts," Working Papers 102, Department of Economics, College of William and Mary.
  3. Marcello Pericoli, 2012. "Real term structure and inflation compensation in the euro area," Temi di discussione (Economic working papers) 841, Bank of Italy, Economic Research and International Relations Area.
  4. Olivier Coibion & Yuriy Gorodnichenko, 2012. "Information Rigidity and the Expectations Formation Process," IMF Working Papers 12/296, International Monetary Fund.
  5. Geert Bekaert & Xiaozheng Wang, 2010. "Inflation risk and the inflation risk premium," Economic Policy, CEPR & CES & MSH, vol. 25, pages 755-806, October.
  6. Nath, Golaka, 2012. "Estimating term structure changes using principal component analysis in Indian sovereign bond market," MPRA Paper 39229, University Library of Munich, Germany.
  7. John Campbell & Robert Shiller & Luis Viceira, 2009. "Understanding Inflation-Indexed Bond Markets," Yale School of Management Working Papers amz2587, Yale School of Management.
  8. Glenn D. Rudebusch, 2010. "Macro-finance models of interest rates and the economy," Working Paper Series 2010-01, Federal Reserve Bank of San Francisco.
  9. Hatcher, Michael, 2013. "The Inflation Risk Premium on Government Debt in an Overlapping Generations Model," SIRE Discussion Papers 2013-81, Scottish Institute for Research in Economics (SIRE).
  10. João Caldeira & Luiz Furlani, 2011. "Break-even inflation rate and the risk premium: an alternative approach to the VAR models in forecasting the CPI," Economics Bulletin, AccessEcon, vol. 31(2), pages 1379-1390.
  11. Michał Brzoza-Brzezina & Jacek Kotłowski, 2012. "Measuring the natural yield curve," National Bank of Poland Working Papers 108, National Bank of Poland, Economic Institute.
  12. Olivier Coibion & Yuriy Gorodnichenko, 2013. "Is The Phillips Curve Alive and Well After All? Inflation Expectations and the Missing Disinflation," NBER Working Papers 19598, National Bureau of Economic Research, Inc.
  13. Marcello Pericoli, 2012. "Expected inflation and inflation risk premium in the euro area and in the United States," Temi di discussione (Economic working papers) 842, Bank of Italy, Economic Research and International Relations Area.
  14. Marcello Pericoli, 2013. "Macroeconomic and monetary policy surprises and the term structure of interest rates," Temi di discussione (Economic working papers) 927, Bank of Italy, Economic Research and International Relations Area.
  15. Kajuth, Florian & Watzka, Sebastian, 2011. "Inflation expectations from index-linked bonds: Correcting for liquidity and inflation risk premia," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(3), pages 225-235, June.
  16. Grishchenko, Olesya V., 2011. "Asset pricing in the production economy subject to monetary shocks," Journal of Economics and Business, Elsevier, vol. 63(3), pages 187-216, May.

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