Allocating Global Aid to Maximize Utility

by Aaron Gertler2 min read15th Feb 20213 comments

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Impact assessmentGlobal health and development
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Note from the crossposter: I've bolded a few sections for emphasis.


The idea of the declining marginal utility of income and its potential use in allocation decisions is both historied and widely accepted in economics. In short, the idea is that each additional dollar of income makes you happier, but the first dollar increases your happiness more than the second dollar, more again than the third dollar and a *lot* more than the billionth dollar. Jeff Bezos probably wouldn’t jump up and down with delight if someone handed him $1,000, the reaction might be a bit more positive from someone living on $2 a day. In a paper released today I ask what declining marginal utility means for aid and its allocation.

The idea dates back to at least JS Mill and engaged economists including Samuelson and Fisher.  A comparatively recent use of declining marginal utility in international economics and global allocation issues was The Stern Review on Climate. Stern argues that empirical estimates based on savings behavior suggest utility is a function of the natural log of consumption. That implies that a doubling of income has the same impact on utility whether it is a doubling from living on $1.90 a day to $3.80 a day or from living on $3.80 a day to $7.60 a day. There are a bunch of reasons to think that’s a reasonable approximation, including that it matches savings behaviors and with what is suggested by actually asking people how happy they are and comparing it with their income.

So, imagine we followed the Stern Review approach as an aid allocation mechanism—if we decided that we wanted the maximum utility gain out of the ODA we were given, and money would have its biggest effect where people were poorest. What would that imply for aid flows?

Without any concern about “absorptive capacity” or differing aid effectiveness because of policies, the utility maximizing aid strategy would be to “kink the tail” of global income distribution, using aid to raise the poorest countries up to the incomes of richer countries. The figure below suggests what this process would generate in terms of allocation in the first years, assuming net ODA receipts of a little over $100 billion (a little above the 2018 figure for net receipts), and compared to current ODA net receipts. Aid is concentrated in the world’s 19 poorest countries in this scenario. (In reality they receive about 26 percent of all ODA).

Cumulative aid allocated assuming declining utility of income ($bn)

In the paper I show that even if you allow for concerns that too much aid can’t be spent well, you still end up providing more money to the poorest countries than current aid allocations. Certainly, governments aren’t trying to maximize global utility in all of their spending—they are a considerable distance from doing that even domestically. But perhaps, at least in the fraction of a percentage of GDP donors provide in foreign assistance, global utility maximization should at least be the primary goal. And if it is, that suggests a laser focus on the poorest countries.

It also suggests something about the returns you should be looking for if you still want to spend money in a richer developing country. For each doubling of average incomes in a recipient country, the expected returns from aid projects should be twice as high. The richest developing countries at the top end of the middle income category (Brazil, China) are about sixteen times richer than the world’s poorest countries (Central African Republic, Madagascar), so you should be looking for about sixteen times the return you’d expect in the poorest countries. Of course, if you want to spend the aid money at home, you should expect the return to be even higher. A reason to minimize domestic spend as much as possible.

Aid Returns and Country Incomes

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Somewhat related:

The Limitations of Decentralized World Redistribution: An Optimal Taxation Approach

A centralized scheme of world redistribution that maximizes a border-neutral social welfare function, subject to the disincentive effects it would create, generates a drastic reduction in world consumption inequality, dropping the Gini coefficient from 0.69 to 0.25. In contrast, an optimal decentralized (i.e., with no cross-country transfers) redistribution has a miniscule effect on world income inequality. Thus, the traditional public finance concern about the excess burden of redistribution cannot explain why there is so little world redistribution.

Actual foreign aid is vastly lower than the transfers under the simulated world income tax, suggesting that voluntary world transfers—subject to a free-rider problem—produces an outcome that is consistent with rich countries such as the United States either placing a much lower value on the welfare of foreigners, or else expecting that a very significant fraction of cross-border transfers is wasted. The product of the welfare weight and one minus the share of transfers that are wasted constitutes the implicit weight that the United States assigns to foreigners. We calculate that value to be as low as 1/2000 of the value put on the welfare of an American, suggesting that U.S. policy is consistent with social preferences that place essentially no value on the welfare of the citizens of the poorest countries, or that implicitly assumes that essentially all transfers are wasted.

Hello! I'd like to apologise that I'm not well-versed in economics, and I'm not a utilitarian, so I'm not sure I followed this very well, but I'd be interested to know a bit more about what's being presented in this article. 

If I understood it correctly, this argues that different nations yield different 'utility returns' (i.e. quantified representations of positive impact?) based on the average income of people in those countries- assuming that the aid projects are targeting people in near identical socioeconomic conditions within those countries. If this is the argument, how could this be evidenced in data? It seems tricky to me to understand whether you are getting greater 'returns' from a family who are able to pay off a protection racket and avoid violence for an indeterminate period of time, a single homeless person who can get a bed for a week, or a struggling small ethnic minority businessperson who can afford to pay rent on the next month of their store, across national differences. In short, how do you translate real circumstances into utility?  

I know that this might be a big question and I appreciate that it might not be possible to condense down to a comment, but if you'd be willing to explain your perspective on this I would appreciate it a lot.

Another thing I was wondering is if you'd say that 'returns' correlate to or are the same thing as 'effectiveness'? 

Thank you

I don't have a background in development economics, either, and posted this mostly because I thought people with an interest in that topic might enjoy it.

I do have some thoughts on your question, though. You are correct in pointing out that people's real circumstances vary widely, and that someone wealthier might get more "returns" on money than someone poorer because of other differences in their lives. (As an extreme example, you could argue that hunter-gatherers living outside of any economic system are some of the poorest people in the world but would have no use for money.)

However, I think the author of this article would argue that these differences tend to be subsumed by the vast numbers of people in the areas being discussed, and that there are good reasons to believe that, in general, the marginal utility of extra money is much higher for people with lower incomes. From the full paper:

To interpret and expand on this (in a way I'm not sure the author would endorse): People around the world spend a lot of their money on the same kinds of things (food, housing, healthcare). These "product categories" all seem to have clear patterns in marginal utility. For example, imagine the difference between a $500 and $1000 apartment in Edinburgh, and then the difference between $1000 and $1500. Or the difference between $1 and $3 vs. $3 and $5 worth of food in a Kinshasa market.

Of course, people don't always have access to the types of goods they'd need to derive the most benefit from their funds. And sometimes, a relatively small amount of money (for one's country) could be lifesaving -- for example, you sometimes see stories about people dying in the United States because they couldn't afford an inexpensive medication.

But it's very difficult to find lifesaving opportunities in richer countries at scale. It's much more complex to find indebted people who are about to be attacked by mobsters than it is to find children who need vaccinations.

That's all I have time for in a response now, but I hope it added a bit of useful context. As with many questions relevant to EA, one could write a long book on this topic without running out of new things to say and arguments to make, but I think that most of the details are relatively minor compared to the basic argument that money goes further for the average poorer person than the average richer person.