Does crime explain the exceptional US incarceration rate?

Open Philan­thropy mo­ti­vates their crim­i­nal jus­tice grants with sen­tences like this: “The United States in­car­cer­ates its res­i­dents at a higher rate than any other ma­jor coun­try. ”

This sounds bad, but con­ser­va­tives ar­gue that this is be­cause of our uniquely high crime rate. I didn’t see any straight­for­ward re­search look­ing at in­car­cer­a­tion and crime rates across coun­tries, so I did some sim­ple anal­y­sis be­low.

One-line sum­mary: the US’s in­car­cer­a­tion rate is still sur­pris­ingly high ac­count­ing for its homi­cide rate.

Up­date on 8/​16/​2020: Cross­post­ing from here:

We don’t have an in­car­cer­a­tion prob­lem—we have a crime prob­lem…The crit­ics of ‘mass in­car­cer­a­tion’ love to com­pare Amer­i­can in­car­cer­a­tion rates un­fa­vor­ably with Euro­pean ones. Crime is in­evitably left out of the anal­y­sis.

That’s from Heather MacDon­ald.

It’s true that the US in­car­cer­a­tion rate is rarely pre­sented next to crime rates. For in­stance, a fa­mous statis­tic is that the US has around 20 per­cent of the world’s pris­on­ers, but we typ­i­cally don’t hear peo­ple fol­low that with our crime vic­tim­iza­tion num­bers.

So to what ex­tent is this all a crime prob­lem? A sim­ple way to test this idea is to see, at the coun­try level, how our in­car­cer­a­tion rate scales with our crime rate com­pared to other coun­tries.

I couldn’t find these plots from some ba­sic googling so I tried do­ing it my­self. The in­car­cer­a­tion data is from Wikipe­dia and the homi­cide data is from the World Bank, in both cases us­ing the most re­cent data available. I be­lieve data tends to be bet­ter for homi­cide rates; this is meant to be a proxy for crime broadly.

Here’s the in­car­cer­a­tion rate against the homi­cide rate for all coun­tries that were in both datasets:

In­car­cer­a­tion rate vs. homi­cide rate for all coun­tries from both datasets.

The green line shows the fit­ted val­ues from re­gress­ing the in­car­cer­a­tion rate on the homi­cide rate. The re­gres­sion sug­gests that the in­car­cer­a­tion rate in­creases by 7.1 (stan­dard er­ror = 1.9) when the homi­cide rate in­creases by 1, and the R-squared is 0.10.

So in­car­cer­a­tion definitely in­creases with crime, but based on the R-squared and a vi­sual as­sess­ment of the points, this isn’t a very tight fit.

And yes, the US in an enor­mous out­lier. Below I re­strict to places with 3-7 homi­cides for ev­ery 100k peo­ple so that it’s eas­ier to see the coun­tries that are similar to the US.

In­car­cer­a­tion rate vs. homi­cide rate for coun­tries similar to the US in homi­cide rate.

What about com­pared to the US’s “peer” coun­tries? I went through and hap­haz­ardly coded a list of richer na­tions and re­stricted to those. The US is quite an out­lier in both ways. Our homi­cide and in­car­cer­a­tion rates are around 5 times higher than that clump at the bot­tom. The trend line seems ba­si­cally mean­ingless here, but we’re way above it.

In­car­cer­a­tion rate vs. homi­cide rate for “first world” countries

So: MacDon­ald’s ar­gu­ment sup­poses that the ap­pro­pri­ate level of in­car­cer­a­tion de­pends on the level of crime. But that first cross-coun­try pic­ture sug­gests that we can’t jus­tify the US’s cur­rent in­car­cer­a­tion rates based on how they gen­er­ally scale with homi­cide rates in other coun­tries.

Does this mean that our in­car­cer­a­tion prob­lem is not a crime prob­lem? One re­sponse is that we should just ig­nore the trendline al­to­gether be­cause the re­la­tion­ship I found was too weak to be use­ful—other fac­tors are more im­por­tant. But then it seems it’s on the in­car­cer­a­tion defen­ders to point to the crime mea­sures that do mat­ter and make the US seem nor­mal.

Re­lated to this is that so far we’ve ba­si­cally taken the homi­cide rate as ex­oge­nous, but of course there’s re­verse causal­ity. Hav­ing a large chunk of the pop­u­la­tion in prison will af­fect the mur­der rate. What we re­ally want on the x-axis might be some mea­sure of the homi­cides we would get if no one were in prison. Maybe this la­tent mea­sure would put the US more to the right and closer to the trendline—it de­pends on how effec­tive the each coun­try is at catch­ing mur­der­ous peo­ple, which seems hard to know.

Another way out for them is that maybe all the coun­tries with similar homi­cide rates should im­prison peo­ple as much as the US, but their in­sti­tu­tions don’t func­tion well enough.

Here’s a sim­ple way this could be. First, it seems gener­i­cally true that in­car­cer­a­tion should in­crease un­til the marginal costs equal the marginal benefits—peo­ple just de­bate these quan­tities. Next, just sup­pose that US courts are es­pe­cially good at con­vict­ing the guilty party, but in the other coun­tries with similar homi­cide rates (which tend to be poorer) the courts are way less likely to have the right defen­dant. This kind of in­effec­tive­ness in the crim­i­nal jus­tice sys­tem would lower the marginal benefits of in­car­cer­at­ing some­one with­out af­fect­ing the marginal costs (it’s still one per­son hav­ing to suffer through prison). In this case, poorer coun­tries with the same homi­cide rate should have much lower in­car­cer­a­tion rates but would op­ti­mally in­crease them if their in­sti­tu­tions were as good as in the US.

All the data and code used for this is available here.


After writ­ing this I found this ar­ti­cle with a similar graph from Ta­pio Lappi-Sep­pälä that shows that, us­ing vic­tim­iza­tion rates on the x-axis, the US is once again a huge out­lier.

I’m sure plenty of aca­demic pa­pers ex­ist that do this bet­ter and in more de­tail, I’ll up­date this post as I find out about them.