Different states introduced and subsequently banned leaded gasoline on different schedules, so this was a 'natural' experiment, unless you can think of some other causative factor that precisely explains the timing of the rise and fall of crime.
I don't understand this content-free 'correlation does not equal causation' argument.
Sure, in the absence of other evidence and a mechanism of action, we should have healthy skepticism, but it's known how lead affects brain development, particularly how it screws up development of the frontal cortex, lowering both intelligence and social inhibition.
Did they also account for changes in how crime rates are reported over time?
One would have to account for hundreds of different variables before you could ever conclusively prove a connection between lead and crime.
The Bureau of Justice Statistics conducts a yearly survey asking people about the crimes they were a victim of in the past year regardless if the crimes were reported. The Bureau of Justice survey shows a much more dramatic reduction in crime than if you just look at reported crimes.
http://www.pewresearch.org/fact-tank/2018/01/30/5-facts-abou...
>Using the FBI numbers, the violent crime rate fell 48% between 1993 and 2016. Using the BJS data, the rate fell 74% during that span.