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:

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.

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.

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.

Notes:

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.