What is the return on giving?

by paulfchristiano

Suppose I have $1 to spend and I want to use it to make the world as rich as possible.  How far can my dollar go? Can I use $1 to to make the world $2 richer? $50 richer? $1000 richer? It’s hard to know what to even expect a priori, and people seem to have widely varying estimates. Let’s call this figure the return on giving. This seems like an important number, and I’ve seen lots of implicit speculation. I think it would be great to have much more explicit discussion, though it seems worthwhile to first clarify what exactly we are talking about.

Definition

It is appropriate to talk about an absolute return rather than a rate of return. This is a one-time multiplier that we earn when we transfer money from our pockets to the public’s. After the money is transferred it’s in the rest of the world’s hands. At this point I expect it grows at roughly the same pace as the world economy at large.

In general, a philanthropic opportunity might not directly transfer money from the philanthropist to the public. For example, the money I give could first end up in the public school system, before eventually spreading out to the world at large. Each of these steps might have its own multiplier—for example, I might use $1 to make the local public school system $2 richer, and the school system being $2 richer might cause the world at large to become $5 richer. Or alternatively an investment might make the world somewhat richer and also make me somewhat richer, and I’ll use the money to go make another investment, etc. I’m interested in the multiplier for the whole process—how much your money has increased by the time it has completely diffused throughout the world.

I am most interested in the returns to giving over a very long time. To normalize, I suggest dividing by the total size of the world economy. How many percent richer can you make the world in 200 years, by donating 1% of gross world product today? I expect this number to roughly stabilize after many years, and I’m interested in the long-run behavior.

I am interested in marginal opportunities. There may be great giving opportunities that are already taken, and I don’t really care how efficient they are. Conversely, there may only be a few of the best giving opportunities, and for now I don’t care too much about that either. If there are only $10M of optimal donations left then that is an interesting and important (and surprising) fact. But at any given time I mostly care about how good the next dollar is.

I am interested in effects in expectation. The world economy is big and an individual philanthropist’s effect on it is small; I don’t much care about whether someone makes the world $1B richer with certainty or $2B richer with probability 1/2.

In principle some opportunities might only be accessible for big donors. $1B might go more than a thousand times farther than $1M. But if we are really only interested in expectations, then we can always just take a 1000:1 bet and turn our $1M into a 1/1000 chance of $1B. This guarantees that there are no increasing returns to money. (If you don’t believe you can find a 1000:1 bet, I appeal to the optional stopping theorem and common sense. Simple strategies probably work quite easily until you get up to billions of dollars, and I would guess that you can manage a small profit in exchange for taking on so much risk.)

I don’t exactly want to measure impacts on gross world product. If I create a new laptop ex nihilo and give it to someone, that won’t increase GDP much, but it will manifestly make the world richer. I’m going to assume that I perturb the world little enough that I don’t significantly affect prices, so that I can measure wealth by people’s total willingness to pay for everything they’ve received. Basically, this is a thought experiment and I don’t actually have to measure the resulting changes in welfare, so I can just imagine away many of the usual problems that beset GDP measurement. There are still tricky questions to be answered and it’s not clear this is exactly the right thing to measure (see here for a discussion of some relevant considerations). The most important constraint is that I want to measure a notion of instantaneous wealth which actually contributes in the intuitive way to long-term wealth.

In many cases estimates for the return on giving doesn’t seem too sensitive to these measurement issues, and so I feel relatively comfortable even with a very crude estimate. I think the most ambiguous case is probably creating a new consumable for which people are willing to pay a lot of money; it is pretty plausible that such contributions don’t contribute much to long-term prosperity, but for now I don’t want to deal with that issue. The other big problem (which I also don’t want to deal with) is the value of the labor force and the dynamics of population growth. These effects might mean that making the world 1% richer today makes the world much less than 1% richer down the line, though depending on the significance of per capita wealth the result could be either a larger or smaller effect on long-term outcomes. I think this is an important issue and I’ll come back to it in the future. For now, I’m going to ignore it.

With all of those caveats in place, let’s call the expected marginal impact on real wealth over the long run, normalized as a percentage of total wealth, the return to givingNow we can ask: what is it?

Estimation

My current intuition is that good traditional philanthropic opportunities have a return of around 10 and the best available opportunities probably have returns of 100-1000, with most of the heavy hitters being research projects that contribute to long term tech progress and possibly political advocacy. But these numbers have very little quantitative justification, and I wouldn’t be surprised if they changed substantially as I learn more (especially given the a priori improbability of such a large wedge between the optimum and the status quo).

Some back of the envelope calculations (warning: these may be cringe-inducing):

  1. GiveWell estimates you can save a very poor child’s life for around $2300 (though given historical trends we might expect that number to inch down over time). Even in the poorest areas (where lives can be most cheaply saved) average annual incomes still tend to be around $400 / year. It is not clear how much value is consumed for food and housing etc., but it seems reasonable to suppose that the economic value created is commensurate with income. Life expectancies for kids who are saved is around 40 years, though after growth discounting the net present value is only 20-30 years of income. Multiplying gives you a return of about 4, though that could easily be an underestimate by a factor of 2 or more if well-integrated capital in the developing world is more useful than capital elsewhere (the developing world is growing faster than the world on average, so this is quite plausible). Moreover, the estimate is only good to within an order of magnitude. For illustration, note that GiveWell’s original estimates for VillageReach’s effectiveness were more like 40, and so other estimates that haven’t yet been so well investigated should probably be expected to fall significantly as well. Also, note that AMF (GiveWell’s current top charity) is a relatively cost-effective way of saving lives, but might also have important impacts on productivity.
  2. Empirical estimates put the rate of social return to R&D at 30-100%, meaning that doing $1 of R&D one year earlier creates an extra $0.30-$1.00 of value. If one could take such estimates at face value, the net present value (discounted by growth) of extra R&D work would be something like 6-30 times their cost. But both the empirical work and the analytical methodology seem shaky and error-prone; moreover, there is a marginal vs. average issue here, which surely reduces the benefit but I’m not sure by how much. I would guess the truth is within an order of magnitude. (There is also the question of how you can purchase extra corporate R&D; evidence suggests that $1 of tax breaks or matching grants tends to stimulate about $1 of R&D, so it might not be too hard, but it’s another source of uncertainty. I’ll revisit these issues at more length soon.)
  3. This study suggests that the growth-discounted total consumption increases from a $1 cash transfer to a poor family in Mexico are about $3-4. Again, this could be several times too low if growth in the developing world was more economically valuable than growth in the developed world (which seems likely) or if domestic production is associated with positive externalities (which seems less likely).
  4. More frivolously: Facebook is worth about $60B, and people spend about 60B hours on Facebook per year. We might suppose generously that an investor who owns 5% of Facebook early in its life (1) increases the probability of Facebook existing by 5% and (2) earns market returns on their investment in (ex ante) expectation. If the half-life of Facebook’s current traffic is 10 years, and if time on Facebook is worth [-$20, $20] more than the activity it substitutes for, the social return to investment is around [-200, 200]. It seems like a few dollars is probably a better estimate for the social value given the existence of close substitutes, and combined with realistic assumptions about investment and counterfactuals it seems like these numbers are basically comparable with the estimates above (when your error bars span 2 orders of magnitude, this isn’t a surprising outcome.) Of course, if the investor actually recoups their investment in expectation, then the money can be reused which would bring up the estimate significantly. At the same time there is a marginal vs. average issue here which will drag down the impact and could even plausibly bring it to 0 (I don’t want to get into this here, because I don’t care enough about the example).
  5. If you invested in a bundle of publicly traded firms across developed nations and held onto it from 1900 to 2011, you would end up with roughly 6 times as much money (as a share of world production) as you started with. If you could have held on to money longer you would have done better, but under normal conditions 111 years is probably stretching it. After 111 years you would have the opportunity to donate the proceeds and in total you would get 6 times whatever returns the ultimate charitable opportunity had. You’ll probably get lower returns than you would have without waiting 111 years; you have less direct control over the money, and good opportunities for giving might have dried up. And I don’t expect this to work as well over the next 6 doublings of the world economy.

I hope to make some more serious estimates in the future, and to have a better sense of what exactly we should be trying to estimate if our eventual aim is to pin down the long-term social impact. I think that aggregate economic impact isn’t quite right, but it’s probably not a bad proxy.

I don’t think that contributing to global prosperity is likely to be the best philanthropic cause. But I do think it’s a plausible candidate, and one which many people care about. I think the considerations that come up here are interesting more generally. And I think that even for donors who don’t care about more speculative interventions, taking a slightly more quantitative look at ordinary philanthropy is probably a very good change.

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