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The Inflation Premium implicit in the US Real and Nominal

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  • J. Huston McCulloch

Abstract

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 http://www.econ.ohio-state.edu/jhm/ts/ts.html .

Suggested Citation

  • J. Huston McCulloch, 2001. "The Inflation Premium implicit in the US Real and Nominal," Computing in Economics and Finance 2001 210, Society for Computational Economics.
  • Handle: RePEc:sce:scecf1:210
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    References listed on IDEAS

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    1. 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, February.
    2. 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.
    3. Prasad V. Bidarkota & J. Huston McCulloch, 1998. "Optimal univariate inflation forecasting with symmetric stable shocks," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(6), pages 659-670.
    4. Duffie, Darrell, 1996. " Special Repo Rates," Journal of Finance, American Finance Association, vol. 51(2), pages 493-526, June.
    5. 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 769-799, September.
    6. Fischer, Stanley, 1975. "The Demand for Index Bonds," Journal of Political Economy, University of Chicago Press, vol. 83(3), pages 509-534, June.
    7. 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.
    8. 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.
    9. Francis Breedon & Jag Chadha, 1997. "The Information Content of the Inflation Term Structure," Bank of England working papers 75, Bank of England.
    10. 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.
    11. Mark Deacon & Andrew Derry, 1994. "Estimating the Term Structure of Interest Rates," Bank of England working papers 24, Bank of England.
    12. 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.).
    13. 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.
    14. Dybvig, Philip H & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1996. "Long Forward and Zero-Coupon Rates Can Never Fall," The Journal of Business, University of Chicago Press, vol. 69(1), pages 1-25, January.
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    Citations

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    Cited by:

    1. J. Huston McCulloch, 2000. "Long Forward and Zero-Coupon Rates Indeed Can Never Fall, but Are Indeterminate: A Comment on Dybvig, Ingersoll and Ross," Working Papers 00-12, Ohio State University, Department of Economics.
    2. Peter Hördahl & Oreste Tristani & David Vestin, 2006. "The term structure of inflation risk premia and macroeconomic dynamics," Computing in Economics and Finance 2006 203, Society for Computational Economics.
    3. Brian P. Sack, 2000. "Deriving inflation expectations from nominal and inflation-indexed Treasury yields," Finance and Economics Discussion Series 2000-33, Board of Governors of the Federal Reserve System (U.S.).
    4. Brian P. Sack & Robert Elsasser, 2002. "Treasury inflation-indexed debt: a review of the U.S. experience," Finance and Economics Discussion Series 2002-32, Board of Governors of the Federal Reserve System (U.S.).
    5. Peter Hördahl & Oreste Tristani, 2012. "Inflation Risk Premia In The Term Structure Of Interest Rates," Journal of the European Economic Association, European Economic Association, vol. 10(3), pages 634-657, May.
    6. Brian P. Sack & Robert Elsasser, 2004. "Treasury inflation-indexed debt: a review of the U.S. experience," Economic Policy Review, Federal Reserve Bank of New York, issue May, pages 47-63.
    7. Juan Angel Garcia & Adrian van Rixtel, 2007. "Inflation-linked bonds from a central bank perspective," Occasional Papers 0705, Banco de España;Occasional Papers Homepage.
    8. Santiago García Verdú, 2010. "Equilibrium yield curves under regime switching," Working Papers 2010-08, Banco de México.
    9. Leif Andersen, 2007. "Discount curve construction with tension splines," Review of Derivatives Research, Springer, vol. 10(3), pages 227-267, December.
    10. Balázs Romhányi, 2005. "A learning hypothesis of the term structure of interest rates," Macroeconomics 0503001, University Library of Munich, Germany.

    More about this item

    Keywords

    Term Structure of Interest Rates; Inflation-Linked Bonds; Real interest rates; splines; inflationary expectations;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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