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Macroeconomic Implications of Term Structures of Interest Rates under Stochastic Differential Utility with Non-Unitary EIS

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  • Hisasi Nakamura

    (Faculty of Economics, University of Tokyo)

  • Wataru Nozawa

    (Graduate School of Economics, University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

Abstract

This paper proposes a continuous-time term-structure model under stochastic differential utility with non-unitary elasticity of intertemporal substitution (EIS, henceforth) in a representative-agent endowment economy with mean-reverting expectations on real output growth and inflation. Using this model, we make clear structural relationships among a term structure of real and nominal interest rates, utility form and underlying economic factors (in particular, inflation expectation). Notably, we show that, if (1) the EIS is less than one, (2) the agent is comparatively more risk-averse relative to timeseparable utility, (3) short-term interest rates are pro-cyclical, and (4) the rate of expected inflation is negatively correlated with the rate of real output growth and its expected rate, then a nominal yield curve can have a low instantaneous riskless rate and an upward slope.

Suggested Citation

  • Hisasi Nakamura & Wataru Nozawa & Akihiko Takahashi, 2008. "Macroeconomic Implications of Term Structures of Interest Rates under Stochastic Differential Utility with Non-Unitary EIS," CIRJE F-Series CIRJE-F-603, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2008cf603
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Monika Piazzesi & Martin Schneider, 2007. "Equilibrium Yield Curves," NBER Chapters, in: NBER Macroeconomics Annual 2006, Volume 21, pages 389-472, National Bureau of Economic Research, Inc.
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    4. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
    5. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    6. Schroder, Mark & Skiadas, Costis, 1999. "Optimal Consumption and Portfolio Selection with Stochastic Differential Utility," Journal of Economic Theory, Elsevier, vol. 89(1), pages 68-126, November.
    7. Hansen, Lars Peter & Heaton, John & Lee, Junghoon & Roussanov, Nikolai, 2007. "Intertemporal Substitution and Risk Aversion," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 61, Elsevier.
    8. Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
    9. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
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    Cited by:

    1. Taiga Saito & Akihiko Takahashi, 2019. "A novel approach to asset pricing with choice of probability measures," CARF F-Series CARF-F-471, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2021.
    2. Taiga Saito & Akihiko Takahashi, 2021. "Supplementary file for "Sup-inf/inf-sup problem on choice of a probability measure by FBSDE approach (Forthcoming in IEEE Transactions on Automatic Control)"," CARF F-Series CARF-F-507, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Taiga Saito & Akihiko Takahashi, 2021. "Supplementary File for "Sup-Inf/Inf-Sup Problem on Choice of a Probability Measure by FBSDE Approach"," CIRJE F-Series CIRJE-F-1160, CIRJE, Faculty of Economics, University of Tokyo.
    4. Akihiko Takahashi & Toshihiro Yamada, 2012. "An Asymptotic Expansion for Forward-Backward SDEs: A Malliavin Calculus Approach," CARF F-Series CARF-F-296, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2013.
    5. Misumi, Takashi & 三隅, 隆司 & Nakamura, Hisashi & 中村, 恒 & Takaoka, Koichiro & 高岡, 浩一郎, 2014. "Moral-Hazard Premium," Working Paper Series G-1-7, Hitotsubashi University Center for Financial Research.
    6. Souta Nakatani & Kiyohiko G. Nishimura & Taiga Saito & Akihiko Takahashi, 2019. "Online Appendix for Interest Rate Model with Investor Attitude and Text Mining," CIRJE F-Series CIRJE-F-1136, CIRJE, Faculty of Economics, University of Tokyo.
    7. Souta Nakatani & Kiyohiko G. Nishimura & Taiga Saito & Akihiko Takahashi, 2019. "Online Appendix for Interest Rate Model with Investor Attitude and Text Mining," CARF F-Series CARF-F-470, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. Taiga Saito & Akihiko Takahashi, 2019. "A Novel Approach to Asset Pricing with Choice of Probability Measures," CIRJE F-Series CIRJE-F-1131, CIRJE, Faculty of Economics, University of Tokyo.
    9. Souta Nakatani & Kiyohiko G. Nishimura & Taiga Saito & Akihiko Takahashi, 2020. "Interest Rate Model with Investor Attitude and Text Mining (Published in IEEE Access)," CARF F-Series CARF-F-479, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    10. Souta Nakatani & Kiyohiko G. Nishimura & Taiga Saito & Akihiko Takahashi, 2020. "Interest Rate Model with Investor Attitude and Text Mining," CIRJE F-Series CIRJE-F-1152, CIRJE, Faculty of Economics, University of Tokyo.
    11. Akihiko Takahashi & Toshihiro Yamada, 2012. "An Asymptotic Expansion for Forward-Backward SDEs; A Malliavin Calculus Aproach," CIRJE F-Series CIRJE-F-865, CIRJE, Faculty of Economics, University of Tokyo.

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