The Long-Term Discount Rate∗

We develop an expression for the long-term discount rate in an economy in which a representative consumer has access to both a risk-free and a risky production technology. Even when the risk-free sector is very small, and with probability one becomes a negligible fraction of the economy in the long run, interest rates are determined differently than in a single-sector economy. As in a single-risky-sector economy, the short rate depends on risk aversion; however, the long rate depends on consumption growth and volatility (i.e., the production possibilities of the economy), but not on the representative investor’s risk aversion. Rather than always being flat, the yield curve is usually upward sloping but may be downward sloping. In the latter case, the slope predicts a future increase in consumption growth rates and lower future short-term interest rates. ∗A previous version of this paper was circulated under the title “The Term Structure in an Exchange Economy with Two Trees.” We thank Jonathan Berk, Bob Goldstein, Dwight Jaffee, Hayne Leland, Dmitry Livdan, Ian Martin, Nancy Wallace, James Wilcox, and seminar participants at the May 2008 BerkeleyStanford seminar and at Uppsala University, June 2008, for helpful comments. †Haas School of Business, U.C. Berkeley, [email protected]. ‡Haas School of Business, U.C. Berkeley, [email protected]. §Haas School of Business, U.C. Berkeley, [email protected].