The implication is that the housing experiment reveals the effect of moving from a bad neighborhood, for those least affected by the bad neighborhood.

In order to test his theory, Mr. Chyn would need to compare the results of a voluntary housing lottery with an experiment that essentially forces all families to enter the lottery.

Fortunately for Mr. Chyn, the demolition of many public housing projects in Chicago in the late 1990s effectively provides precisely this experiment. From 1995 to 1998, the Chicago Housing Authority demolished many high-rise public housing buildings, including the projects you might recognize from the 1970s sitcom “Good Times.”

These demolitions were effectively a lottery, because they led to the dislocation of some families — those whose buildings were demolished — but not those whose buildings were left standing. Thus those families that left did so for essentially random reasons. And just as in the Moving to Opportunity lottery, those families that “won” the lottery — that is, those families whose building was set for demolition — were offered a housing voucher to help them pay the rent if they moved out of the projects. Those families whose buildings remained standing were effectively a control group, as they continued to live in public housing, undisturbed.

Importantly, this real-world natural experiment differs from the Moving to Opportunity experiment, because all families could be pushed to move, not just those who volunteered for a government relocation program.

Mr. Chyn finds that these demolitions had very large — and very positive — effects on the children who were forced to move out of the projects. The children forced out of public housing went on to have annual earnings that were 16 percent higher than those who remained, and they were 9 percent more likely to be employed. Over all, being kicked out of public housing might add about $45,000 to each child’s lifetime earnings. The effects may be even larger for those who moved while they were young.