Change "roof" to "food". Giving money only to people who don't have enough food to eat isn't a perverse incentive: there's little point in going hungry to get money; any money you get will be spent on food before anything else.
Not that easy. Roof was picked up probably because it's obvious and unambiguous - you literally only have to take one look at a house to know whether or not it's eligible. "Food" is not a well-defined metric, and whatever particular proxy for "food" you'd use, it seems to me that that proxy is much easier to manipulate than roof material.
As for perverse incentives, GP is right that as the news spread, people may save the money they have instead of investing it in a roof in a hope of getting additional money from GiveDirectly in the near future. That's, unfortunately, human behaviour 101. So in time, they'll have to change the criteria they use for distributing grants, and the article hints that they're thinking about it already.
Uh, that's not what I meant, though I guess my comment wasn't clear enough.
I'm not saying they should change the criteria to food security/malnutrition/etc. I'm saying that,
1) suppose the criteria was food-related; people wouldn't likely game the system by voluntarily not getting food because, well, eating is pretty high on people's list of desires.
(there are food-related metrics like "reported food consumption" and "malnutrition" that are used to assess the performance of GiveDirectly and charity/aid/welfare programs in general. They are well-defined, even if subject to manipulation. In any case, I understand that the roof criteria is more practical at the enrolment phase)
2) analogously, people aren't likely gaming the system by keeping non-metal roofs, as having good shelter is also very high on most people's list. In fact, one of the most common ways recipients spend the grant money is getting an iron roof.
Also, it's not like having a non-metal roof automatically entitles you to a grant, as this is isn't a nation-wide government program.
GiveDirectly is considering changing requirements not because they think they're including too many (relatively) high-income families with non-metal roofs, but because they might be excluding some people who live in metal-roof houses but are still poor.
If we grant your condition of the grant being small relative to the value of the roof, the following scenario might play out.
Suppose GD will give 10 if you have not upgraded your roof.
Suppose a roof costs 100 and benefits you 150.
Suppose fertilizer costs 100 and benefits you 145.
In the absence of any potential GD grant then buying a new roof is both socially optimal and the thing the farmer is incentivized to do.
But with the potential for a GD grant then buying a new roof is still the socially optimal choice, but the farmer is no longer incentivized to do it. Thus, a farmer might forgo buying a new roof in the hopes of securing a cash reward, which is inefficient.
As economists I know they know this, thanks to the Lucas Critique ;) But I didn't see what was being done about it.