We view sustainability as a requirement that welfare should not be expected to decline over time; it depends on the production technology available to society

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.