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On Tuesday, Amazon announced that it would be raising the minimum wage of all its workers—including temps—to $15 an hour. And it also urged the federal government to do the same.The move was variously hailed as a PR masterstroke, a ploy to fend off its employees’ unionization efforts, and a political win for Bernie Sanders. But one thing it definitely accomplished: It has raised the stakes on the debate over raising the minimum wage, with supporters and critics listing what they see as the benefits or threats of a national $15 wage.In a new working paper published in the National Bureau of Economic Research (NBER), a pair of economists add some new evidence in support of the argument for boosting paychecks—it could keep people out of prison, and thus help trim the enormous social costs associated with incarceration.In the paper, Amanda Y. Agan of Rutgers University and Michael D. Makowsky of Clemson University analyzed the effect of 200 state and federal minimum wage increases on 6 million people released from prison between 2000 and 2014. What they found was striking: Raising the minimum wage by $0.50 reduced the chance that a person would end up incarcerated within a year by 2.8 percent.The impact on recidivism might look surprising, but it makes sense if you think about it. What’s the first thing a person might need after being released from prison? A place to live and a job—two basic needs that can be particularly difficult to come by for ex-offenders. Lack of work experience and institutional barriers form significant barriers to successful reentry; around two-thirds of people released from prison end up back there within three years. Without housing and jobs, formerly incarcerated people may become homeless or seek illegal work to make ends meet, kicking off a self-perpetuating cycle between the street and the prison.Before they tested it, researchers thought that the effect of raising the minimum wage could go either way for former inmates. Higher wages might mean a better standard of living, and potentially, a lower incentive to engage in criminality. On the other, raising the minimum wage—as critics often point out—risks depressing the number of jobs available, because employers may not be able to afford the higher labor costs. “Given employers’ particular distaste for hiring individuals with criminal records and the potential for labor-labor substitution … released prisoners are likely to be particularly vulnerable to any potential unemployment effects of the minimum wage, even if higher minimum wages do not cause aggregate decreases in employment,” the authors explain.In other words, it’s conceivable that a wage hike could lead to a decrease in available jobs and a negative impact on workers with criminal records, who’re already pinched for options—raising the probability that they’ll end up back in jail.While this study doesn’t tease out the extent of these two opposed potential effects of minimum wage hikes, it does find that a raised standard of living, which tends to lowers recidivism, is stronger overall. They write in the paper:This observed reduction, within our theoretical framework, implies that, on net, there are more individuals for whom their wages of crime are higher than their uncontrolled market wage—the higher minimum wage draws them into the legal labor market, a phenomenon determined on the supply side of the labor market.In the study, the researchers also tested the impact of state Earned Income Tax Credit (EITC)—a tax refund for low-income workers that varies in amount depending on the size of the family. They found some evidence that EITC also reduces recidivism within the first three years, but only among women. This makes sense because the subsidy generally tends to be more generous for single mothers, who are more likely to be in custody of their children.After running the numbers, the researchers estimate that a 5 percent increase in state EITC (which may result in a $159 more per year) leads to the same decline in recidivism as a $0.50 increase in minimum wage for a full-time working woman (which may yield $1,000 more in annual income).The study comes with a few big caveats. The first is a data limitation: Because one person may have been to prison in multiple states, it’s possible that some of the individuals categorized as first-time offenders in the data were actually not. Second, in the time period observed, the highest minimum wage was $9.50—far lower than the $15 rate that Amazon has joined many advocates and local governments in pushing for. That more dramatic wage hike might lead to a different result, especially in poorer cities.Finally, the researchers don’t have insights on how family or social networks figure into these results. It’s possible that the reduction in recidivism is a side effect of benefits that are accruing to the entire household, or to the community itself. Because their partner is making more, an ex-offender may be able to go back to school and get new skills, for example.The authors conclude that their results “raise the possibility of significant second-order welfare benefits of broad wage policies.” If wages help keep formerly incarcerated workers from criminal activity, that’s a public good that might be worth a few extra bucks an hour.