The consumption-based determinants of the term structure of discount rates

Abstract

The rate of return of a zero-coupon bond with maturity T is determined by our expectations about the mean (+), variance (-) and skewness (+) of the growth of aggregate consumption between 0 and T. The shape of the yield curve is thus determined by how these moments vary with T. We first examine growth processes in which a higher past economic growth yields a first-degree dominant shift in the distribution of the future economic growth, as assumed for example by Vasicek (J. Financ. Econ. 5, 177–188, 1977). We show that when the growth process exhibits such a positive serial dependence, then the yield curve is decreasing if the representative agent is prudent ($u^{\prime \prime \prime } > 0$), because of the increased risk that it yields for the distant future. A similar definition is proposed for the concept of second-degree stochastic dependence, as observed for example in the Cox–Ingersoll–Ross model, with the opposite comparative static property holding under temperance ($u^{\prime \prime \prime \prime } < 0$), because the change in downside risk (or skweness) that it generates. Finally, using these theoretical results, we propose two arguments in favor of using a smaller rate to discount cash-flows with very large maturities, as those associated to global warming or nuclear waste management.