This New Zealand study [1] attempted to look at the crime-lead relation in a place where it wasn't confounded by childhood socioeconomic status, and "failed to support a dose-response association between BLL (blood lead level) and consequential criminal offending".
I'm not trying to say the theory is wrong; just that correlations are really tricky to study, it's hard to control for all confounding variables, and it's hard to know for certain when a correlation is due to causation.
The harm by lead occurs in the first 3 years of life. High blood lead in early childhood is not detected later in childhood [0]. The New Zealand study uses blood tests performed ten years too late. This flaw makes the study almost useless.
Additionally, only 30 of the children in the study had low blood lead, <5 ug/dL. This is because the blood was collected in the 1980s and New Zealand only banned leaded gasoline in 1996. Look at Figure 1 in [1], and notice that at 5ug/dL, the damage is already done.
[0] Caito, S., & Aschner, M. (2017). Developmental Neurotoxicity of Lead. Neurotoxicity of Metals, 3–12. doi:10.1007/978-3-319-60189-2_1
[1] Nevin, R. (2000). How Lead Exposure Relates to Temporal Changes in IQ, Violent Crime, and Unwed Pregnancy. Environmental Research, 83(1), 1–22. doi:10.1006/enrs.1999.4045
That does sound like a flaw, although the paper by Jessica Wolpaw Reyes I often see mentioned that argues lead causes crimes isn't based on measuring lead levels in individuals at all, but on the total lead released by cars during the time studied. That sounds even less robust.
I'm not sure if the paper you linked measures the correlation between blood lead levels in the first 3 years and crime rates because it's behind a paywall.
I wasn't aware of sci-hub, but it seems awesome. Thanks!
The paper you linked by Nevin seems to be doing the same thing as the paper by Reyes. They didn't test the lead levels in individuals studied, but looked at the total lead released by vehicles at the time.
I'm not trying to say the theory is wrong; just that correlations are really tricky to study, it's hard to control for all confounding variables, and it's hard to know for certain when a correlation is due to causation.
[1] https://jamanetwork.com/journals/jamapediatrics/fullarticle/...