Great post, thank you for writing it. I particularly appreciate the sketch of your causal model summarizing the evidence for the relationships between growth, liberal democracy, human capital, peace, and x-risk; I think you deconfused me quite a bit w.r.t “the world getting better” with that.
But even if GDP percentage growth slows, wellbeing growth can still speed up, for two reasons:
The dollar GDP/capita growth rate goes up. Even if we adjust for inflation, Americans had ~$600 more every year in the 60s, but now have ~$900 more per year in the 2010s.[65]
At first blush this seemed wrong, since I tend to assume log utility to simplify modeling. Your footnote linking to Basil Halperin’s essay does note that this assumption is in fact an assumption, and that if utility is in fact “less curved” than log we can still have wellbeing growth speedup with GDP % growth slowdown (this was probably obvious to you but isn’t clarified in the text):
But Halperin’s essay doesn’t actually explore whether this “less curved than log” assumption is true. Do you happen to know of empirical evidence for it?
Isoelastic vs Logarithmic increases in consumption
GiveWell measures GiveDirectly’s cost-effectiveness by doublings of consumption per year. For instance, Increasing an individual’s consumption from $285.92 to $571.84 for a year would be considered 1 unit of utility.
However, there is a bit of ambiguity here. What happens when you double someone’s consumption twice? For instance, $285.92 to $1,143.68 a year? So, if increasing consumption by 100% has a utility of 1, how much utility does this have? A natural answer might be that doubling twice creates two units of utility. This answer is what the GiveWell CEA currently assumes. This assumption is implicit by representing utility as logarithmic increases in consumption.
However, how much people prefer the first double of consumption over the second is an empirical question. And empirically, people get more utility from the first doubling of consumption than the second. Doubling twice creates 1.66 units rather than 2. An isoelastic utility function can represent this difference in preferences.
Isoelastic utility functions allow you to specify how much one would prefer the first double to the second with the η parameter. When η=1, the recipient values the first double the same as the second and is what the current CEA assumes. When η>1, recipients prefer the first doubling in consumption as worth more than the second. Empirically, η≈1.5. GiveWell recognises this and uses η=1.59 in their calculation of the discount rate:
Increases in consumption over time meaning marginal increases in consumption in the future are less valuable. We chose a rate of 1.7% based on an expectation that economic consumption would grow at 3% each year, and the function through which consumption translates to welfare is isoelastic with eta=1.59. (Note that this discount rate should be applied to increases in ln(consumption), rather than increases in absolute consumption; see calculations here)
I’ve created a desmos calculator to explore this concept. From the calculator, you can change the value of η and see how isoelastic utility compares to logarithmic utility.
GiveDirectly transfers don’t usually double someone’s consumption for a year but increase it by a lower factor. So an isoelastic utility would find that recipients would gain more utility than logarithmic utility implies.
Changing η from 1 to 1.59 increases GiveDirectly’s cost-effectiveness by 11%. Reducing the cost of doubling someone’s consumption for a year from $466.34 to $415.87.
To be clear, I don’t know anything else about this topic; I was just surprised/skeptical to see the wellbeing growth speedup point.
Edited to add: I was trivially wrong, sorry, I misread Sam’s post. Quoting the relevant section from the passage above:
When η>1, recipients prefer the first doubling in consumption as worth more than the second. Empirically, η≈1.5. GiveWell recognises this and uses η=1.59 in their calculation of the discount rate
My ambition here was perhaps simpler than you might assumed: my point here was just to highlight an even weaker version of Basil’s finding that I thought was worth highlighting: even if GDP percentage growth slows down a smaller growth rate can still mean more $ every year in absolute terms.
Sorry I also don’t know much more about this and don’t have the cognitive capacity right now to think this through for utility increases and maybe this breaks down at certain ηs.
Maybe it doesn’t make sense to think of just ‘one true average η’, like 1.5 for OECD countries, but rather specific ηs for different comparisons and doublings.
Appreciate the pointer to that post! That’s basically the sort of thing I’m looking for (more reading material for ‘gears’). And thanks again for writing the main post.
Great post, thank you for writing it. I particularly appreciate the sketch of your causal model summarizing the evidence for the relationships between growth, liberal democracy, human capital, peace, and x-risk; I think you deconfused me quite a bit w.r.t “the world getting better” with that.
At first blush this seemed wrong, since I tend to assume log utility to simplify modeling. Your footnote linking to Basil Halperin’s essay does note that this assumption is in fact an assumption, and that if utility is in fact “less curved” than log we can still have wellbeing growth speedup with GDP % growth slowdown (this was probably obvious to you but isn’t clarified in the text):
But Halperin’s essay doesn’t actually explore whether this “less curved than log” assumption is true. Do you happen to know of empirical evidence for it?
The only reference I’ve come across provides evidence against it – it’s this section in Sam Nolan’s Quantifying Uncertainty in GiveWell’s GiveDirectly Cost-Effectiveness Analysis. Quote:
To be clear, I don’t know anything else about this topic; I was just surprised/skeptical to see the wellbeing growth speedup point.
Edited to add: I was trivially wrong, sorry, I misread Sam’s post. Quoting the relevant section from the passage above:
So this is evidence for your point, not against.
Thanks! Excellent comment.
My ambition here was perhaps simpler than you might assumed: my point here was just to highlight an even weaker version of Basil’s finding that I thought was worth highlighting: even if GDP percentage growth slows down a smaller growth rate can still mean more $ every year in absolute terms.
Sorry I also don’t know much more about this and don’t have the cognitive capacity right now to think this through for utility increases and maybe this breaks down at certain ηs.
Maybe it doesn’t make sense to think of just ‘one true average η’, like 1.5 for OECD countries, but rather specific ηs for different comparisons and doublings.
There was a related post on this recently—would love for someone to get to the bottom of it.
Appreciate the pointer to that post! That’s basically the sort of thing I’m looking for (more reading material for ‘gears’). And thanks again for writing the main post.