Also, the parallelism in curves for lead and time-shifted crime seem too good to be true, since the lead hypothesis assumes that the effects of lead exposure are greatest in childhood. But 23 years after the first lower-lead cohort, only a small fraction of the crime-prone cohort should be lead-free; there are still all those lead-laden young adults who have many years of crime ahead of them. Only gradually should the crime-prone demographic sector be increasingly populated by lead-free kids. The time-shifted curve for crime should be an attenuated, smeared version of the curve for lead, not a perfect copy of it. Also, the effects of age on crime are not sharply peaked, with a spike around the 23rd birthday, and a sharp falloff—it’s a very gentle bulge spread out over the 15-30 age range. So you would not expect such a perfect time-shifted overlap as you might, for example, for first-grade reading performance, where the measurement is so restricted in time.
Am I misreading this, or is this suggesting that the fact that the time-shifted correlation is unusually strong should be taken as evidence -against- the correlation?
What Pinker is saying is that P(data | lead causes crime) is not as high as you’d think, because if lead really does cause crime, we should not expect the crime curve to be a time-shifted version of the lead curve. It’s probably still true that P(data | lead causes crime) > P(data), so that you should update in the direction of lead causes crime, but this update should probably be smaller than you thought before reading that paragraph.
Has anyone figured out what crime curve you would expect based on the lead curve (presumably a version that is shifted & smeared out based on the age distribution of criminals), and checked how well it fits the actual crime data? It’s not obvious to me, from looking at the pictures that I’ve seen with the shifted curves, that adding the smearing would make the fit worse. For instance, the graph I linked earlier shows that the recent drop in crime is more gradual than the drop in lead that happened 20-30 years ago, which seems to fit the more rigorous “time-shifted and smeared out” prediction better than it fits the simplistic time-shifted curve approach that Nevin used.
Am I misreading this, or is this suggesting that the fact that the time-shifted correlation is unusually strong should be taken as evidence -against- the correlation?
Suppose you’re Bayesian, and you’re calculating
P(lead causes crime | data) = P(data | lead causes crime) * P(lead causes crime) / P(data).
What Pinker is saying is that P(data | lead causes crime) is not as high as you’d think, because if lead really does cause crime, we should not expect the crime curve to be a time-shifted version of the lead curve. It’s probably still true that P(data | lead causes crime) > P(data), so that you should update in the direction of lead causes crime, but this update should probably be smaller than you thought before reading that paragraph.
Has anyone figured out what crime curve you would expect based on the lead curve (presumably a version that is shifted & smeared out based on the age distribution of criminals), and checked how well it fits the actual crime data? It’s not obvious to me, from looking at the pictures that I’ve seen with the shifted curves, that adding the smearing would make the fit worse. For instance, the graph I linked earlier shows that the recent drop in crime is more gradual than the drop in lead that happened 20-30 years ago, which seems to fit the more rigorous “time-shifted and smeared out” prediction better than it fits the simplistic time-shifted curve approach that Nevin used.