Under what circumstances is it potentially cost-effective to move money within low-impact causes?
This is preliminary and most likely somehow wrong. I’d love for someone to have a look at my math and tell me if (how?) I’m on the absolute wrong track here.
Start from the assumption that there is some amount of charitable funding that is resolutely non-cause-neutral. It is dedicated to some cause area Y and cannot be budged. I’ll assume for these purposes that DALYs saved per dollar is distributed log-normally within Cause Y:
I want to know how impactful it might, in general terms, be to shift money from the median funding opportunity in Cause Y to the 90th percentile opportunity. So I want the difference between the value of spending a dollar at those two points on the impact distribution.
The log-normal distribution has the following quantile function:
So the value to be gained by moving from p = 0.5 to p = 0.9 is given by
This simplifies down to
Not a pretty formula, but it’s easy enough to see two things which were pretty intuitive before this exercise. First, you can squeeze out more DALYs from moving money in causes where the mean DALYs per dollar across all funding opportunities is higher, and, for a given average, moving money is higher-value where there’s more variation across funding opportunities (roughly, since variance is proportional to but not precisely given by sigma). Pretty obvious so far.
Okay, what about making this money-moving exercise cost-competitive with a direct investment in an effective cause, with a benchmark of $100/DALY? For that, and for a given investment amount $x, and a value c such that an expenditure of $c causes the money in cause Y to shift from the median opportunity to the 90th-percentile one, we’d need to satisfy the following condition:
Moving things around a bit...
Which, given reasonable assumptions about the values of c and x, holds true trivially for larger means and variances across cause Y. The catch, of course, is that means and variances of DALYs per dollar in a cause area are practically never large, let alone in a low-impact cause area. Still, the implication is that (a) if you can exert inexpensive enough leverage over the funding flows within some cause Y and/or (b) if funding opportunities within cause Y are sufficiently variable, cost-effectiveness is at least theoretically possible.
So just taking an example: Our benchmark is $100 per DALY, or 0.01 DALYs per dollar, so let’s just suppose we have a low-impact Cause Y that is between three and six orders of magnitude less effective than that, with a 95% CI of [0.00000001,0.00001], or one for which you can preserve a DALY for between $100,000 and $100 million, depending on the opportunity. That gives mu = −14.97 and sigma = 1.76. Plugging those numbers into the above, we get approximately...
...suggesting, I think, that if you can get roughly 4000:1 leverage when it comes to spending money to move money, it can be cost-effective to influence funding patterns within this low-impact cause area.
There are obviously a lot of caveats here (does a true 90th percentile opportunity exist for any Cause Y?), but this is where my thinking is at right now, which is why this is in my shortform and not anywhere else.
Interesting. You might get more comments as a top-level post.
I guess a more useful way to think about this for prospective funders is to move things about again. Given that you can exert c/x leverage over funds within Cause Y, then you’re justified in spending c to do so provided you can find some Cause Y such that the distribution of DALYs per dollar meets the condition...
...which makes for a potentially nice rule of thumb. When assessing some Cause Y, you need only (“only”) identify a plausibly best or close-to-best opportunity, as well as the median one, and work from there.
Obviously this condition holds for any distribution and any set of quintiles, but the worked example above only indicates to me that it’s a plausible condition for the log-normal.