Thread by @delmoi

Interesting study looking 545 cities that installed lead pipes vs. iron water pipes in the 19th century (mostly between 1870 and 1896) and crime rates between 1921 and 1936 cloudfront.escholarship.org/dist/prd/conte…

Nowadays poor people are exposed to more lead, but back then no one no one knew using it for pipes was a bad idea, and the main difference was how close a lead refinery was, which determined cost.

Interestingly there is also a huge impact of acidity on homicide rates in cities with lead pipes - essentially due to the fact that more acidic water will pick up more of the lead in the pipes:

It seems the average number of homicides per 100k in the data is about 9.3, and in cities with acidic water and lead pipes there would have been about 13 or so about 39% more then baseline (based on the graphs) above.

interesting, they didn't have any direct information on the amount of lead used in "Some Lead" cities, just a binary yes/no. But since the probability of using lead at all was dependent on proximity to lead refiners, they used that as an "instrumental" variable

I guess the assumption is, if the probability of using lead pipes overall is dependent on whether or not lead pipes are used, then likely the probability of each individual pipe being lead or not would similarly be clustered so.

When they did the regression analysis using the synthetic variable they it showed homicide rates were nearly 2.5 times as high in cities with estimated lead pipe usage (clipped from two sections of the paper)

here's the table, you can see the 'raw' coefficient for the binary (some lead/no lead) option, raw probability for distance to refinery, and the synthetic pipe probability.

You can see the raw increase in homicide rates is e^0.219 -1 = 24.48% for the binary "some lead/no lead" option, that's with a really low error rate.

In columns 1 and 2 you can see that there's actually e^0.099 -1 = 10.4% increase in homicide rate per 100 miles from a refinery.

They also include "non-refinery" cities which are more then 10 miles out from a refinery - the idea is to isolate pipe-based lead from pollution from refineries. If those cities are excluded distance effect is just 10.3% / 100mi instead of 10.4%

(Also remember this is exponential so essentially 'compounding interest' - every 100mi closer to a refinery you get probability should go up another 10 (so 34% at 300 miles, 64% at 500 miles, etc)

The last one is the synthetic estimator value which is kind of speculation - assumes the reason for the distance effect is that cities closer to lead refiners used a greater percentage of lead pipes.

They estimate that 100% lead cities would have e^0.953 -1 = 159.5% more murder

Again, if I'm reading that right.

The way they compute the coefficient for acidity is a little weird, they compute do the regression for both the pH (-7) and the log of the pH (-ln(7))

So, for a Ph of 4, between grapefruit juice and coffee, you get

e^((ln(4)-ln(7))*(-0.594)) - 1 = 39.4% with the logarithmic estimator
e^((4-7)*(-0.094)) - 1 = 32.5% with the 'linear' one

Weird. Looking at the old reference they used from 1952 I do see some places had 'raw' water around 5, 6 ph - the treated water was usually basic, but presumably they might not have been doing that in the 1800s. Doesn't really correspond to the 4 more per 100k number above.

I feel like that part of the paper could have used some more work. Oh well.

Like, try to look up how much lead gets released from a pipe depending on acidity, if you're using an exponential curve on lead exposure then you should check to see what the relation is between pH and lead levels in water, rather then just trying ln(ph)

One interesting follow up study you could do would be to look at, among the cities with lead pipes and acidic water, when did they start water treatment? Was there a commensurate drop in crime 20 years later?