We all know that an extra dollar is worth more to you the poorer you are. That's why it can be good to donate money to an organisation like GiveDirectly even when a few cents in the dollar get used up in transaction costs. But how much more is it worth? Economists have a good quantitative model of what is going on, which can enable us to make rough comparisons about whether, say, people on $1,000 per year would get more value from an extra $100 than people on $2,000 per year would get from $200. This can help us work out how much additional cost we should bear to get money to the very poorest people.

It can also be useful for improving our thinking about the relative values of different financial flows such as remittances and aid. It is easy to find out the sizes of these in dollars, but what about the size in terms of value to the individuals? If the individuals in one case are substantially richer, then this can really change things.

I've written an article explaining how all of this works up on centerforeffectivealtruism.org. Have a read and let me know what you think.

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I read and comment on this post, as well as Toby Ord’s full essay on my podcast HERE 'found in the struce'

Also added some hypothes.is comments within Toby' s CEA essay

Also, note you can leave voicemails if you use the Anchor app to listen to my podcast ... and I can add these so others can here and comment on them, I think.

I've put up another version of this on the EA Forum podcast without any commentary here

I like this article and I agree with the argument in principle, but I'd like to see a bit more information presented about how the elasticity parameter is estimated.

In other words, what data has been used to compute this parameter? Experiments where people make choices among different lotteries? Implicit choices where people make tradeoffs involving risk? Stated preferences over comparisons of societal distributions of wealth?

I think it is mainly from individuals' explicit preferences over hypothetical gambles for income streams. e.g. if you are indifferent between a sure salary of $50,000 PA and a 50-50 gamble between a salary of $25,000 or one of $100,000, then that fits logarithmic utility (eta = 1). Note that while people's intuitions about such cases are far from perfect (e.g. they will have status quo bias) this methodology is actually very similar to that of QALYs/DALYs. But I imagine all methods you mention are used. Also other methods such as happiness surveys give results in the same ballpark. If asking about ideal societal distribution, then that is actually a somewhat different question as there could be additional moral reasons in favour of equality or priority to the worst off on top of diminishing marginal utility effects. Eta is typically intended to set aside such issues, though there are other tests to measure those.

Thank you Toby. The 'preference over gambles' as a way of measuring diminishing marginal utility will depend strongly on the expected utility maximization assumption; in practice, it could be vulnerable to reference-point effects I believe. (Also the logarithmic utility function is obviously an imposed parametric assumption, but a good start.)

Still, these approaches seem reasonable, especially insofar as broadly similar results come from varying contexts.

Something that will complicate the effects is that money given to people may increase not only consumption today but also consumption tomorrow through investment. This could be investments in physical capital (e.g. iron roof, livestocks) or human capital (e.g. health and education). Most of the time when people are given money, some will be consumed and some saved/invested (and consumption itself could have investment effects too, if better nutrition improves ability to work/learn), e.g. see Give Directly recipients.

This is relevant if we think that, for instance, poor people in Kenyan villages have more profitable investment opportunities than poor people in the US, for the cash they receive -- which is probably the case, e.g. there are many more opportunities to start small businesses in Kenyan villages (or higher returns to improving nutrition because they start at such a low level, though I remember "Poor Economics" says there's not much of evidence for a nutrition-based poverty trap, so probably not). In that case the benefits of giving cash to poor Kenyans (relative to giving to poor Americans) is further amplified. In fact in GiveWell's cost-effectiveness calculation for Give Directly, future increase in consumption is responsible for a substantial fraction of the effect (even with discounting) if we assume some persistence in investment returns (even if it's not compounded).

Do you happen to know what the most cost effective American charity is and how it compares to GiveDirectly? I think that information could be useful when making the case that it's better to focus on developing countries.

GiveWell's "Your Dollar Goes Further Overseas" is, I think, the best attempt at answering that question and making that case.

That page is good, but it would be better if they could give an apples-to-apples comparison. There must be domestic US charities that aim to save lives domestically, from which a 'cost per life saved' estimate could be drawn. ... Or a developing country charity that provides a similar service as the US charities mentioned (education, neo-natal care, etc), from which many more people could be serverd for the same $.

I think the best comparison to the Against Malaria Foundation would be the Nurse Family Partnership (NFP), which also primarily benefits young children (albeit through a different intervention). Olds et al. (2014) reports the results of an RCT examining the effect of NFP on child mortality and maternal mortality,[1] and GiveWell has an (old) estimate of the cost per child served for the Nurse Family Partnership.[2] You could potentially use these two sources to arrive at a rough estimate of the cost per death averted for NFP.

[1] https://jamanetwork.com/journals/jamapediatrics/fullarticle/1886653

[2] http://www.givewell.org/united-states/charities/nfp

Tengs, et. al. (1994) quotes some cost-effectiveness estimates for a bunch of developed world interventions. The best seems to be anti-smoking campaigns.

Xu, et. al. (2015) finds a US CDC-led antismoking campaign to cost $393 per life year and $268 per QALY. Ratcliffe, Cairns, & Platt (1997) find a Scottish anti-smoking campaign to save a life year for £304-£656 (roughly $742-$1603 in 2016 USD). Stevens, Thorogood, and Kayikki (2002) found a London anti-smoking campaign to cost £33-£391 per life year ($66-$786 in 2016 US dollars).

Apples-to-apples, we could look at anti-smoking campaigns in the developing world, with Savedoff and Alwang (2015), writing for the Center for Global Development, quoting it as $3 - $70 per DALY averted.

Taking these numbers literally, it looks like developing world anti-smoking campaigns are ~20x more cost-effective than developed world anti-smoking campaigns. Other interventions are likely to be even more tilted in favor of the developing world, because they treat important problems that just aren't problems here anymore. Malaria is still a huge problem in Africa, but was eradicated in the US by 1960.

I think that's the best direct comparison I have right now.

Proposing small correction to this article: footnote 9 states “it isn’t more important to help someone living on $200 per year (at official exchange rates) in a place where PPP [purchasing power parity] is high than someone on the same amount where PPP is low”. 

This isn’t right; purchasing power doesn’t matter if the elasticity parameter , but it does matter if  (so in particular, the estimates in the article for  are only correct for comparing contexts with equal purchasing power). We have expanded on this in "Correction to “The Value of Money Going to Different Groups”.

I like the way you introduced the calculus, it was artful. I think going one step further would be useful, I.e. Looking at the income distributions of recipients of different interventions and charities.

I like the article. The first table makes it viscerally available that the VOI for better estimating eta (or for finding a better model for utility as a function of consumption on the margins) could be high, if you're relatively more interested in global poverty-focused EA than in other causes within EA.

I'm not aware of any better figures you could have used for GWWC/TLYCS/REG's leverage, and I'm not sure if many of us take estimates of leverage for meta-organizations literally, even relative to how literally we take normal EA cost-effectiveness estimates. I agree that combining the leverage estimates with the consumption multipliers in order to estimate impact would be the correct thing to do if you managed to get accurate estimates of both that weren't dependent or interdependent on each other, though!

To the extent that GWWC/TLYCS/REG count donations that they have received themselves as having a certain leverage because of the donations "caused"/influenced by GWWC/TLYCS/REG, everyone who has had their donations "caused"/influenced by GWWC/TLYCS/REG (at least according to GWWC/TLYCS/REG) should count their donations as having proportionally less than 1.0x leverage. (Alternatively, GWWC/TLYCS/REG could claim to have less leverage, and thereby allow those who they claim to have influenced to claim that they've caused a greater fraction of the impact that their own donations have caused). This prevents double-counting of impact, and gives us a more accurate estimate of how much good donations to various organizations cause, which in turn lets us figure out how we can do the most good.

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