Sustainability in a Risky World. John Y. Campbell & Ian Martin. NBER Working Paper 28899, June 2021. DOI 10.3386/w28899
Abstract: We view sustainability as a requirement that welfare should not be expected to decline over time. We impose this requirement as a prior constraint on the consumption-savings-investment problem, and study its implications for saving, risky investment, and the social discount rate. The constraint does not distort portfolio choice, but it imposes an upper bound on the sustainable time preference rate and on the sustainable consumption-wealth ratio, which we show must lie between the riskless rate and the expected return on optimally invested wealth.
6 Conclusion
In this paper we have argued, in the spirit of Koopmans (1960, 1967), that the implication of an
ethical criterion—sustainability—for social discounting and consumption decisions depends on the
production technology available to society. Specifically, in a risky world with a binding sustainability
20constraint, the sustainable social rate of time preference and consumption-wealth ratio, which equal
one another, are not equal to either the riskless interest rate or the risky return on invested wealth,
but lie in between these two. In the special case where invested wealth has only Brownian risk and
no jump risk, the sustainable social rate of time preference is the equal-weighted average of the
riskless interest rate and the risky return.
We have made this point in the context of an extremely simple model with iid returns in which the
parameters governing the distribution of returns are known. We have therefore ignored parameter
uncertainty, a phenomenon emphasized by Weitzman (2001). We have also ignored the possibility
that returns may not be iid, because expected returns or risks change over time. Models with non-iid
returns in general imply time-varying consumption growth and a term structure of discount rates.
When consumption growth is persistent, this term structure is generally downward-sloping for safe
investments and upward-sloping for risky ones as in the long-run risk model of Bansal and Yaron
(2004). Gollier (2002) emphasizes the potential importance of a downward-sloping term structure
of discount rates for social discounting. Our iid model has discount rates that are invariant to the
horizon of an investment.
Although we have emphasized the sustainable social rate of time preference in this paper, we
conclude by noting that this is not the same as the appropriate social discount rate that should
be applied to an investment project. That discount rate depends on the project’s risk. For a
riskless project, the appropriate discount rate is the riskless interest rate, which is lower than the
sustainable social rate of time preference in a risky world; and for a project that has the same
risk as society’s invested wealth, the appropriate discount rate is the expected risky return, which
is higher than the sustainable social rate of time preference. Some previous discussions of social
discounting have obscured these distinctions by ignoring the risk that society faces. Our analysis is
deliberately simple in order to achieve clarity about these issues.