As organisations receive more funding, the value of extra funding changes. This is relevant for donation decisions. People have used various concepts to discuss this feature:
- Room for more funding
- Funding gaps
- Diminishing (marginal) returns
In this pair of posts I discuss what people might mean by these different terms:
- Defining returns functions and funding gaps sharpens up the definitions of these terms.
- Selecting the appropriate model for marginal returns analyses the strengths and weaknesses of different models
The second post is co-authored with Owen Cotton-Barratt. He provided many of the ideas in the posts.
Max, thanks for the post!
For someone like GiveWell that spends a lot of time investigating charities, they may have enough information about the charity's budget to tell when there is (something similar to) a discrete jump in the derivative of the returns function. E.g. the way they talk about "capacity-relevant funding" and "execution funding" in the post you linked to ("incentive funding" is for a completely different purpose that has no direct relationship with returns).
Also, to fix ideas it helps to think what we represent by the funding axis on the impact against funding graph, i.e. returns function. Is the function specifying the relationship between total impact, and total funding the charity expects to receive for a time period (i.e. next year), or we are looking within a time period and plotting what the charity does as (unexpected) new money comes in? In the latter case, diminishing returns seems most likely. In the former case, increasing returns is possible (but diminishing returns is as well).
Ben Todd has written about increasing returns in small organizations here. I wrote here that "Whether returns are increasing or decreasing in additional funding depends on how the funding is received. Expecting a large chunk of funding (either in the form of receiving such amounts at once, or even expecting a total large amount received in small chunks if there is no lumpy investment or borrowing constraint) could enable an organization to do more risk taking, while getting unanticipated small amounts of funding at a time -- even if the total adds up to more -- will probably just lead the organization to use the marginal dollar to “fund the activity with the lowest (estimated) cost-effectiveness”. ... The scenario Ben Todd has in mind probably applies more when a large funder is considering how much to give to an organization. This may be another argument to enter donor lottery or donate through the EA fund: giving a large and certain amount of donations to a small organization enables them to plan ahead for more risky but growth enhancing strategies, hence could be more valuable than uncoordinated small amounts even if the latter add up to the same total (because the latter may be less certain). ... This mechanism is articulated in “5.2 The funding uncertainty problem” on this page about the EA fund.” (There are probably some analogous economic model of firm investment under liquidity constraint and uncertainty, but I don't have one on the top of my head.)
In practice it may not be a big deal: even if the charity receives random small amounts of money during the year, it is probably at least as good as receiving the total amount all at once at the beginning of next year when they do the next round of planning. But for small organisations where earlier growth is much better, it could be much more preferable to have small amounts of donations be coordinated and committed at the same time to help with more ambitious planning and growth. (Of course we are assuming the charity is borrowing constrained; otherwise if earlier growth is much better they'd borrow to achieve it and repay with later donation. Also, if the market is efficient and earlier growth is really much better, then some donors should capture the opportunity ... but of course market may not be!)
In response to your first paragraph, I think it's true that GiveWell will have more information about any changes in the returns function. For the reasons given the in the second post, I think it's unlikely that GiveWell charities do have inflection points in their returns functions. I'm not sure from GiveWell's writing whether they think that there are inflection points or not (In particular, I don't think they take a clear stance on this in the linked post).
I think your second paragraph is answered by footnote 1 of the first post. I don't fully understan... (read more)