The Consumption-Based Determinants of the Term Structure of Discount Rates

The efficient 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 (1977). We show that when the growth process exhibits such a positive serial correlation, then the yield curve is decreasing if the representative agent is prudent (u'''> 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 correlation, as observed for example in the Cox-Ingersoll-Ross model, with the opposite comparative static property holding under temperance (u''''< 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, such as those associated to global warming or nuclear waste management.