How realistic is a logarithmic relationship between utility and consumption? And how sensitive is this analysis to that assumption? Intuitively, I would value the £1000 that took me from £1000 annual consumption to £2000 annual consumption far more than I would value the £20,000 that took me from £20,000 to £40,000, which I think means that the actual relationship between my consumption and my utility is a long way from being logarithmic?
As you pointed out in another comment, this analysis makes sense for direct cash transfers, but is not obviously relevant for health interventions, which are considered more effective than cash transfers by Givewell. The pattern you pointed to between 2015 and 2018 is over a very short space of time. Over a longer time scale, shouldn’t we expect global health to continue to improve dramatically, as it has over the last few decades? If it does, maybe we should expect the gap in effectiveness between health charities and cash transfers to become smaller over time.
Redoing the math with a general isoelastic utility function, for η>1 you get an optimal point at which to donate, with that point depending on the parameters of the model (income and investment growth rates, the rate of diminishing returns, etc.). This optimal donation time is also dependent on the size of the population you can donate too, so to get a more accurate model you would need to incorporate that (as well as a bunch of currently-unaccounted-for factors like the changing effectiveness of non-cash charities).
This is an interesting analysis!
The two parts that seem most unrealistic to me:
How realistic is a logarithmic relationship between utility and consumption? And how sensitive is this analysis to that assumption? Intuitively, I would value the £1000 that took me from £1000 annual consumption to £2000 annual consumption far more than I would value the £20,000 that took me from £20,000 to £40,000, which I think means that the actual relationship between my consumption and my utility is a long way from being logarithmic?
As you pointed out in another comment, this analysis makes sense for direct cash transfers, but is not obviously relevant for health interventions, which are considered more effective than cash transfers by Givewell. The pattern you pointed to between 2015 and 2018 is over a very short space of time. Over a longer time scale, shouldn’t we expect global health to continue to improve dramatically, as it has over the last few decades? If it does, maybe we should expect the gap in effectiveness between health charities and cash transfers to become smaller over time.
good points!
with respect to the utility function I originally chose log because it’s what Open Philanthropy uses. However I now see that GiveWell sometimes uses an isoelastic utility function with η=1.59, which is faster diminishing returns than log-utility (η=1).
Redoing the math with a general isoelastic utility function, for η>1 you get an optimal point at which to donate, with that point depending on the parameters of the model (income and investment growth rates, the rate of diminishing returns, etc.). This optimal donation time is also dependent on the size of the population you can donate too, so to get a more accurate model you would need to incorporate that (as well as a bunch of currently-unaccounted-for factors like the changing effectiveness of non-cash charities).