The first mistake: My model assumed that utility is logarithmic with income. Empirical research suggests that utility may be sub-logarithmic with income, which my model does not allow for. Accounting for this would make giving now look relatively better. (I do not think it is clearly true that utility is sub-logarithmic with income, but it could be, and it would be better to account for the possibility.)
The second mistake: My model compared the present-day discount rate with the present-day investment rate, but this is not the correct comparison. To see why, consider the possibility that the discount rate currently exceeds the investment rate, but that the discount rate is dropping (because good giving opportunities are drying up), and at some future time
t, the investment rate will surpass and then permanently exceed the discount rate.
In this scenario, you will do more good by donating all your money today than by waiting until time
t to donate. But if you continue investing for long enough after time
t, the discounted present value of your donation will eventually surpass the value of donating today. Therefore, in this scenario you should give later, no matter how high the present-day discount rate may be.
Trammell discusses this scenario, including why the investment rate will eventually exceed the discount rate, in his paper. The paper is a draft, but as of this writing, the relevant discussion occurs in section 5.1. He discusses the argument at a high level in RPTP Is a Strong Reason to Consider Giving Later on the Effective Altruism Forum (and probably explains it better than I did).
The third mistake: My model ignored risk. We can only directly compare the investment rate
r with the growth rate
g using a simple inequality (namely,
r > g) if
g are perfectly correlated. If
g move in lock step, our utility function over future spending can be simplified to directly compare
g. But my model introduced modifications that could disrupt the correlation. It added discounts to global poverty interventions that don’t directly depend on the consumption level
g, and it introduced factors such as valuation into the investment rate of return. These additional factors violate the assumption that the investment rate and discount rate have perfect correlation.
To account for risk, we cannot simply add up all the terms on each side. Instead, we need to do the hard(er) work of calculating the discounted expected utility of giving later relative to the utility of giving now.
Fixing these problems requires making substantial modifications to my model. Trammell’s paper covers the subject much more effectively than my essay did, so rather than updating my model, I will defer to his.
It is worth emphasizing that Trammell’s paper is still a draft—it contains some missing sections and may substantially change before publication—but I believe his general approach works much better than the one in my essay.