There are 2.3 million Americans in prison or jail. The U.S. has 5 percent of the world’s population but 25 percent of its prisoners. One in three black men can expect to spend time in prison. There are 2.7 million minors with an incarcerated parent. The imprisonment rate has grown by more than 400 percent since 1970.

It’s supposed to help the country reduce crime in two ways: incapacitation — it’s hard to be a habitual offender while in prison — or deterrence — people scared of prison may do their best to not end up there.

But recent research suggests that incarceration has lost its potency. A reportreleased this week from the Brennan Center for Justice at the New York University School of Law finds that increased incarceration has had a very limited effect on crime over the past two and a half decades.

At incarceration’s current elevated levels, the effect of more incarceration on crime is not statistically different than zero. It’s no longer working.

In 1970, there were just shy of 200,000 Americans in prison. Today there are more than 1.5 million — 496 prisoners for every 100,000 people. That’s more than in any developed country. According to the International Centre for Prison Studies, the imprisonment rate in Russia is 467. In the U.K., it’s 148. In France, 102. In Germany, it’s 76. In Japan, 50.

It’s because of these elevated levels that we’re likely to see diminishing returns. If we assume — fairly! — that the criminal justice system tends to incarcerate the worst offenders first, it becomes clear why. Once the worst offenders are in prison, each additional prisoner will yield less benefit in the form of reduced crime. Increased incarceration — and its incapacitation effect — loses its bite. And at its world-historic level, it’s not surprising that it would’ve lost nearly all of it.

And diminishing returns are what we saw. Crime rates dropped as incarceration rates rose, for a time, but incarceration’s effect on crime weakened as more people were imprisoned. An increase in incarceration was responsible for something like 5 percent of the decrease in crime in the 1990s, when its levels were lower, but has played no meaningful role since. If I were speaking to a fellow economist, I’d say the incarceration elasticity of crime is not distinguishable from zero. At a cocktail party, I’d say that crime no longer responds to changes in incarceration.

Evidence of incarceration’s diminishing returns can be found outside of big data sets and regression models, too. It can also be found via a natural experiment. A report from the Brookings Institution’s Hamilton Project compared the prisoner releases from California’s realignment with similar releases in Italy, following clemency legislation passed by the Italian Parliament. California saw no discernable change in crime. Italy saw a spike in crime. The reason? California’s incarceration rate was high, and Italy’s was low. Italy hadn’t yet experienced dramatically diminishing returns.