For a while there, Detroit’s income tax might as well have been optional.

About 400,000 people—residents and anyone working inside the city limits—are required to file a tax return to Detroit. Almost half of them weren’t doing so. Perhaps that explains, in part, why the city filed for bankruptcy four years ago.

Detroit “sent out thousands of letters to people,” said Debra Pospiech, the city’s deputy treasurer for tax. “People just threw them out.”

Getting people to pay taxes is a problem everywhere, of course, but Detroit had a particularly hard time going after scofflaws because budget cuts decimated its ability to enforce the law. Even the people who paid up created logistical havoc for beleaguered city bureaucrats. In Detroit, the only way to file taxes was on paper. An irritation for taxpayers turned into a nightmare for city workers, who spent hours typing data into computer systems.

Detroit’s tax trouble became the basis of an economic experiment last year. The city decided to send out more than 7,000 mailings to deadbeat tax filers, people whose 2014 tax returns were already a year late. The city suspected each delinquent owed at least $350. Taxpayers were randomly selected to receive one of six different letters, each with a different message in a black box on the mailing.

One message appealed to residents’ civic pride, as the city tried to bounce back from its bankruptcy: “Detroit’s rising is at hand. The collection of taxes is essential to our success.”

Another simply made clear that the city’s tax collectors had detailed information on the deadbeats: “Our records indicate you had a federal income of $X for tax year 2014.” Detroit residents owe 2.4 percent of their incomes to the city, after a $600 exemption. Nonresidents who work in Detroit pay a rate of 1.2 percent.

And one message made a bold declaration: “Failure to file a tax return is a misdemeanor punishable by a fine of $500 and 90 days in jail.”

It turned out that the threat worked best. More than 10 percent of taxpayers responded to the letter mentioning a fine and jail time, more than three times the response rate of a basic control letter.

Ben Meiselman, a graduate student at the University of Michigan’s economics department, took a desk in the city tax office to run the experiment. He wrote the messages included in the mailings to reflect behavioral economics research. “I find that a single sentence, strategically placed in mailings to attract attention, can have an economically meaningful impact on tax filing behavior,” Meiselman wrote in a working paper that will eventually become a chapter in his doctoral dissertation.

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