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Saw a new paper on the lead-crime hypothesis, and it is pretty much the perfect randomised intervention. Notes to follow. https://www.aeaweb.org/articles?id=10.1257/app.20160056
In this paper they explicitly measured he blood lead levels of children, and then took a group of hose with the highest lead exposure and intervened to lower the blood lead level of some of those with the highest lead levels.
If lead in the blood stream causally causes crime then you would expect that crime rates should be correlated with measured lead except for the intervention group who should have lower crime than their high lead comparators.
That is just to say, that if lead causes crime and you remove the lead, then crime rates in those individuals should be lower. And that is exactly what they find.
Here is the key chart:
You can see both that measured lead levels (BLL) does show a smooth relationship with a variety of anti social behaviours, and also that the intervention to lower lead levels massively lowers those behaviours relative to the control group.
You can see both that measured lead levels (BLL) does show a smooth relationship with a variety of anti social behaviours, and also that the intervention to lower lead levels massively lowers those behaviours relative to the control group.
This is the holy grail for causality. It conclusively proves that the lead crime effect is causal and not just a proxy for other factors. It also shows its large size. Interventions to lower lead halve the rates of anti social behaviour.
Bonus footnote: It must be getting dull citing all the evidence so they just decided to put it all in a massive footnote rather than clutter the text.
