“WE DON’T have a sentencing problem; we have a crime problem”, Jeff Sessions told sheriffs in Oklahoma in a recent speech. Arguing that jail sentence times and prison populations had been declining while there had been a “national surge in violent crime” the attorney-general concluded: “If we want to bring down our prison population then we should bring down crime.” His statements are hard to reconcile with the academic literature on the effects of incarceration.

David Roodman, an economist working for the Open Philanthropy Project, has recently carried out an exhaustive review, replication and analysis of papers and articles on the impact of locking people up in America. The five word summary of his work might be: America has a sentencing problem.

It is unarguable that prison populations and crime rates have moved in opposite directions over the past two decades. The latest FBI data suggests property crime continued to decline in 2015 and that while the violent crime rate increased 3% in 2015 over 2014 levels that still left it 41% lower than it was in 1996. And an analysis through 2017 by the Brennan Center for Justice suggests the overall crime rate this year will be the second lowest since 1990. While that trend doesn’t exactly match Mr. Sessions’s rhetoric about surging crime levels, the decline does coincide with a rising prison population: the number of incarcerated (including people in both prisons and jails) was 1.1m in 1990, peaked at 2.3m in 2008 and was still around 2.2 million in 2015.

But Mr Roodman’s work suggests that rising incarceration rates aren’t behind the drop in crime. He looked at thirty ‘high-credibility’ studies that exploit randomised or natural experiments related to changing prison populations. And he re-ran and extended the regression analyses for eight of those studies, suggesting four needed “major re-interpretation” as a result. He concludes that “the best estimate of the impact of additional incarceration on crime in the United States today is zero”—there is at least as much evidence suggesting that decarceration reduces crime as increases it.

Behind that conclusion are three main findings. First, the deterrence impact of long sentences is very small. Studies of the three strikes law in California and mandatory minimum sentencing laws across the states suggest increasing sentences by 10% cuts crime by 1% and Mr Roodman’s re-analysis “calls even those mild estimates into question”. Second, tougher sentencing does reduce crime while prisoners are behind bars: Mr Roodman’s tentative conclusion from a California early release programme is that a year’s reduction in incarceration was associated with 6.7 more property crimes.

But third: the impact of reduced crime while perpetrators are behind bars is matched by increased criminal activity after they are released. Mr Roodman cites a study by Donald Green and Daniel Winik Criminology, a journal that looked at drug crime defendants in Washington DC, some of whom came before lenient judges and others before comparatively harsh judges. Each group of defendants was equally likely to be re-arrested within four years –those in jail longer caught up with their brothers in crime who had been let out earlier.

If incarceration doesn’t help, what lies behind the dropping crime rate? A Brennan Center for Justice study in 2015 suggested that while no one factor could explain more than a part of the decline, demographic change; lower levels of lead exposure from paint and pipes; growing income and improved policing may all have played a role.

If the social benefit of incarceration in terms of reduced crime is limited to non-existent, the social costs are very high. Mr Roodman estimates the benefit of decarceration is $92,000 per person-year of averted confinement, largely thanks to taxpayer savings ($26,000 a year) and the money value of gained liberty (estimated at $50,000 a year –about the same value put on avoiding amputation of both legs). Given that America has gone from a jail population of 357,000 in 1970 to 2.2m in 2015 that adds up to a social cost of increased incarceration over that period of around $170bn a year.

Sadly Oklahoma, where Mr. Sessions gave his speech, bears more than its share of that cost. While the Bureau of Justice Statistics reports that the national imprisonment rate has declined from 0.52% of the population in 2010 to 0.47% in 2015, the state’s prison population keeps on growing—from 0.69% of the population in 2010 to 0.73% in 2015.