Well, a good first step would be to analyse possible causes of Z and show they are not matching it. Quoting Feynman:
For example, if you're doing an experiment, you should report everything that you think might make it invalid — not only what you think is right about it; other causes that could possibly explain your results; and things you thought of that you've eliminated by some other experiment, and how they worked — to make sure the other fellow can tell they have been eliminated.
I did not see such explanation done in this case - it looks like everything described talks about what matches the hypothesis, and no effort is done to look for alternative explanations and refute them.
>>>> Thus your hidden Z would have to move in sync not only with X and Y, but also with their widely varying rates in different states.
Use of gasoline is highly correlated with use of cars, which again is highly correlated with income, population density, business activity, etc. Any of which can be also associated with crime. I.e. if both effects are caused, say, by population density (I do not say it is, I just take it as an example), then gasoline use would raise and crime would raise when population density raises (say, because some economic factors attract people, like it happens now in North Dakota due to shale gas boom) and both would fall when some factors cause population to move away - as it happening in Detroit, for example. There might be also other factors.
>>> In fact, use of leaded gasoline varied widely among states, and this gave Reyes the opening she needed. If childhood lead exposure really did produce criminal behavior in adults, you'd expect that in states where consumption of leaded gasoline declined slowly, crime would decline slowly too. Conversely, in states where it declined quickly, crime would decline quickly. And that's exactly what she found.
And this is exactly what she would find if both were strongly related to some third cause Z, but completely causally independent from each other. The fact that the MJ author takes it as evidence confirming the causation means they do not understand how causation needs to be proven. It is not evidence for causation, since it equally applies to both when causation exists and when it does not.
Yes, this means causation is hard to prove. It is.
I don't see you addressing what I find to be the most important point, though I realize now that I didn't emphasize it enough. If we know that leaded gas was phased out at different rates because legislators mandated different schedules in different states (I say "if" — I don't know if that's true), then any hidden cause Z would have had to produce not only X (decline of lead at a certain rate) and Y (decline of crime at a similar rate) but also the legislation which caused X in the first place. Many plausible Z's become absurd if that is the case. To use your example, population density might conceivably determine both gas consumption and crime, but surely not the behavior of state legislatures implementing federal mandates. I find it hard to imagine history getting closer to a controlled experiment than that.
Does that mean that causation is proved? Of course not. But it does mean that the evidence here is stronger than garden-variety correlation.
For example, if you're doing an experiment, you should report everything that you think might make it invalid — not only what you think is right about it; other causes that could possibly explain your results; and things you thought of that you've eliminated by some other experiment, and how they worked — to make sure the other fellow can tell they have been eliminated.
I did not see such explanation done in this case - it looks like everything described talks about what matches the hypothesis, and no effort is done to look for alternative explanations and refute them.
>>>> Thus your hidden Z would have to move in sync not only with X and Y, but also with their widely varying rates in different states.
Use of gasoline is highly correlated with use of cars, which again is highly correlated with income, population density, business activity, etc. Any of which can be also associated with crime. I.e. if both effects are caused, say, by population density (I do not say it is, I just take it as an example), then gasoline use would raise and crime would raise when population density raises (say, because some economic factors attract people, like it happens now in North Dakota due to shale gas boom) and both would fall when some factors cause population to move away - as it happening in Detroit, for example. There might be also other factors.
>>> In fact, use of leaded gasoline varied widely among states, and this gave Reyes the opening she needed. If childhood lead exposure really did produce criminal behavior in adults, you'd expect that in states where consumption of leaded gasoline declined slowly, crime would decline slowly too. Conversely, in states where it declined quickly, crime would decline quickly. And that's exactly what she found.
And this is exactly what she would find if both were strongly related to some third cause Z, but completely causally independent from each other. The fact that the MJ author takes it as evidence confirming the causation means they do not understand how causation needs to be proven. It is not evidence for causation, since it equally applies to both when causation exists and when it does not.
Yes, this means causation is hard to prove. It is.