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The Inflation Premium implicit in the US Real and Nominal

  • J. Huston McCulloch

Monthly term structures are fit to US Treasury inflation-indexed securities using a QN (Quadratic-Natural) spline, developed in this paper, and also to conventional nominal securities of comparable maturities. The ratio of the real to nominal discount functions is an implicit forward CPI function. The difference between the nominal and real forward interest rate curves is an implicit marginal inflation premium. It is demonstrated that under consumption risk-neutrality per Stanley Fischer (1975), this inflation premium does not equal expected future inflation per Irving Fisher (1896,1930), but rather incorporates a weighted average of expectations about the future course of inflation, that tends to give greater weight to low inflation scenarios than to high. The method is applied to 29 dates since the introduction of the 30-year indexed bond in April 1998. Nominal interest rate volatility is 2-2.5 times greater (in terms of standard deviation) than real interest rate volatility, nominal rate shocks are highly correlated with shocks to the inflation premium, and real interest rate shocks are nearly orthogonal to inflation premium shocks. To date, there is no evidence against the log expectations hypothesis for real interest rates, nor against the Fisher hypothesis for the inflation premium. There is only weak evidence against the Fischer ypothesis. No evidence is found that the estimated forward rate beyond 30 years is nondecreasing over time, or even has lessened variance, despite the argument of Dybvig, Ingersoll and Ross (1996) that the asymptotic long-term forward rate and zero-coupon rate cannot fall without generating arbitrage opportunities. Monthly data updates will be posted at .

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2001 with number 210.

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Date of creation: 01 Apr 2001
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Handle: RePEc:sce:scecf1:210
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  1. Prasad V. Bidarkota & J. Huston McCulloch, . "Optimal Univariate Inflation Forecasting with Symmetric Stable Shocks," Computing in Economics and Finance 1997 116, Society for Computational Economics.
  2. Shiller, Robert J, 1979. "The Volatility of Long-Term Interest Rates and Expectations Models of the Term Structure," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1190-1219, December.
  3. Martin D. D. Evans, 1998. "Real Rates, Expected Inflation, and Inflation Risk Premia," Journal of Finance, American Finance Association, vol. 53(1), pages 187-218, 02.
  4. Duffie, Darrell, 1996. " Special Repo Rates," Journal of Finance, American Finance Association, vol. 51(2), pages 493-526, June.
  5. Jonathan E. Ingersoll Jr. & Philip H. Dybvig & Stephen A. Ross, 1998. "Long Forward and Zero-Coupon Rates Can Never Fall," Yale School of Management Working Papers ysm45, Yale School of Management.
  6. Daniel F. Waggoner, 1997. "Spline methods for extracting interest rate curves from coupon bond prices," FRB Atlanta Working Paper 97-10, Federal Reserve Bank of Atlanta.
  7. Francis Breedon & Jag Chadha, 1997. "The Information Content of the Inflation Term Structure," Bank of England working papers 75, Bank of England.
  8. McCulloch, J Huston, 1971. "Measuring the Term Structure of Interest Rates," The Journal of Business, University of Chicago Press, vol. 44(1), pages 19-31, January.
  9. Mark Fisher & Douglas Nychka & David Zervos, 1995. "Fitting the term structure of interest rates with smoothing splines," Finance and Economics Discussion Series 95-1, Board of Governors of the Federal Reserve System (U.S.).
  10. Fischer, Stanley, 1975. "The Demand for Index Bonds," Journal of Political Economy, University of Chicago Press, vol. 83(3), pages 509-34, June.
  11. Ingersoll, Jonathan E. & Skelton, Jeffrey & Weil, Roman L., 1978. "Duration Forty Years Later," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(04), pages 627-650, November.
  12. Mark Deacon & Andrew Derry, 1994. "Estimating the Term Structure of Interest Rates," Bank of England working papers 24, Bank of England.
  13. J. Huston McCulloch, 1977. "The Cumulative Unanticipated Change in Interest Rates: Evidence on the Misintermediation Hypothesis," NBER Working Papers 0222, National Bureau of Economic Research, Inc.
  14. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1981. "A Re-examination of Traditional Hypotheses about the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 36(4), pages 769-99, September.
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