A Consumption-Based Model of the Term Structure of Interest Rates

TLDR: This paper proposed a consumption-based model that can account for many features of the nominal term structure of interest rates, such as a time-varying price of risk generated by external habit.

Abstract: This paper proposes a consumption-based model that can account for many features of the nominal term structure of interest rates. The driving force behind the model is a time-varying price of risk generated by external habit. Nominal bonds depend on past consumption growth through habit and on expected inflation. When calibrated data on consumption, inflation, and the average level of bond yields, the model produces realistic volatility of bond yields and can explain key aspects of the expectations puzzle documented by Campbell and Shiller (1991) and Fama and Bliss (1987). When Actual consumption and inflation data are fed into the model, the model is shown to account for many of the short and long-run fluctuations in the short-term interest rate and the yield spread. At the same time, the model captures the high equity premium and excess stock market volatility.

Figures

Table 4: Moments of Bond Yields

Table 3: Statistics for the Aggregate Market

Figure 9: Adjusted long-Rate Regressions. Lines with plus signs represent coefficients β from the regression

Figure 3: The Price-Dividend Ratio as a Function of Surplus Consumption St. The price-dividend ratio is the ratio of aggregate wealth to aggregate consumption (divided by four to annualize).

Table 2: Utility Parameters

Figure 2: Past Consumption Growth and Interest Rate. This figure plots the history of average past (inflation-adjusted) consumption growth ∑40 j=0 φ j∆ct−j and the continuously compounded rate of return on the 90-day Treasury bill, adjusted for inflation. The parameter φ = 0.95. Variables are de-meaned and standardized.

Full text

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The Rodney L. White Center for Financial Research
A Consumption-Based Model of the
Term Structure of Interest Rates
Jessica A. Wachter
27-04

A Consumption-Based Model of the Term Structure
of Interest Rates
∗
Jessica A. Wachter
†
University of Pennsylvania and NBER
July 9, 2004
∗
I thank Andrew Ang, Ravi Bansal, Michael Brandt, Geert Bekaert, John Campbell, John Cochrane,
Francisco Gomes, Vassil Konstantinov, Martin Lettau, Anthony Lynch, David Marshall, Lasse Pederson,
Andre Perold, Ken Singleton, Christopher Telmer, Jeremy Stein, Matt Richardson, Stephen Ross, Robert
Whitelaw, Yihong Xia, seminar participants at the 2004 Western Finance Association meeting in Vancouver,
the 2003 Society of Economic Dynamics meeting in Paris, and the 2001 NBER Asset Pricing meeting in
Los Angeles, the the NYU Macro lunch, the New York Federal Reserve, Washington University, and the
Wharton School. I thank Lehman Brothers for financial support.
†
Address: The Wharton School, University of Pennsylvania, 3620 Locust Walk, Philadelphia, PA 19104;
Tel: (215) 898-7634; Email: jwachter@wharton.upenn.edu; http://finance.wharton.upenn.edu/˜ jwachter/

A Consumption-Based Model of the Term Structure
of Interest Rates
Abstract
This paper proposes a consumption-based model that can account for many features of the
nominal term structure of interest rates. The driving force behind the model is a time-varying
price of risk generated by external habit. Nominal bonds depend on past consumption growth
through habit and on expected inflation. When calibrated to data on consumption, inflation, and
the average level of bond yields, the model produces realistic volatility of bond yields and can
explain key aspects of the expectations puzzle documented by Campbell and Shiller (1991) and
Fama and Bliss (1987). When actual consumption and inflation data are fed into the model, the
model is shown to account for many of the short and long-run fluctuations in the short-term interest
rate and the yield spread. At the same time, the model captures the high equity premium and
excess stock market volatility.

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This paper proposes a consumption-based model that can account for many features of the nominal term structure of interest rates.