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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
Date of revision:
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. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
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  8. Andrew Ang & Geert Bekaert & Min Wei, 2005. "Do Macro Variables, Asset Markets or Surveys Forecast Inflation Better?," NBER Working Papers 11538, National Bureau of Economic Research, Inc.
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  12. Konstantijn Maes, 2004. "Modeling the Term Structure of Interest Rates: Where Do We Stand?," Working Paper Research 42, National Bank of Belgium.
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  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. 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.
  16. Buraschi, Andrea & Jiltsov, Alexei, 2005. "Inflation risk premia and the expectations hypothesis," Journal of Financial Economics, Elsevier, vol. 75(2), pages 429-490, February.
  17. 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.
  18. 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.
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Citations

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Cited by:
  1. 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.
  2. Glenn D. Rudebusch, 2010. "Macro-Finance Models Of Interest Rates And The Economy," Manchester School, University of Manchester, vol. 78(s1), pages 25-52, 09.
  3. Marcello Pericoli, 2014. "Real Term Structure and Inflation Compensation in the Euro Area," International Journal of Central Banking, International Journal of Central Banking, vol. 10(1), pages 1-42, March.
  4. John Campbell & Robert Shiller & Luis Viceira, 2009. "Understanding Inflation-Indexed Bond Markets," Yale School of Management Working Papers amz2587, Yale School of Management.
  5. 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.
  6. 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.
  7. Geert Bekaert & Xiaozheng Wang, 2010. "Inflation risk and the inflation risk premium," Economic Policy, CEPR & CES & MSH, vol. 25, pages 755-806, October.
  8. 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.
  9. Michał Brzoza-Brzezina & Jacek Kotłowski, 2012. "Measuring the natural yield curve," National Bank of Poland Working Papers 108, National Bank of Poland, Economic Institute.
  10. 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.
  11. 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.
  12. Nath, Golaka, 2012. "Estimating term structure changes using principal component analysis in Indian sovereign bond market," MPRA Paper 39229, University Library of Munich, Germany.

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