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The debate about the Phillips curve and the amount of “slack” in the U.S. labor market has to do with the prospects of long-term unemployed workers. In the wake of the Great Recession of 2007-2009, the share of unemployed workers who were unemployed for 27 weeks or longer hit historical highs. In fact, the share is higher now than it was at its previous peak in June 1983. The question is whether the long-term unemployed are locked out of the labor market or if they can return to work in the short term.

Princeton economist Alan Krueger has argued that the long-term unemployed really shouldn’t be counted as part of labor market slack as they don’t influence wage growth. Stephen Williamson, Vice President at the Federal Reserve of St. Louis, presents historical data that show the long-term unemployed being more likely to drop out of the labor force. A National Bureau of Economic Research working paper released this week, however, presents evidence that we might be able to get long-term unemployed workers back into employment more readily than many have assumed.

With the high levels of long-term unemployment staying elevated as the labor market recovered from the Great Recession, many economists and commenters worried that these workers would be unable to find work again. Their story was that employers would discriminate against long-term unemployed workers and instead hire workers who had been unemployed for a shorter time or already had a job. Several papers backed up this concern, including one by economist Rand Ghayad, now of the Brattle Group. By sending out fake resumes to prospective employers—in which he varied how long these job seekers had been out of work, how frequently they switched jobs, and how much industry experience they had—Ghayad tried to figure out how much discrimination the long-term unemployed faced. His answer: quite a bit. Other research found similar results.

But the new working paper released this week finds some contradictory evidence. The paper, by economists Henry Farber of Princeton University, Dan Silverman of Arizona State University, and Till von Wachter of the University of California, Los Angeles, also uses a resume field experiment. In order to make sure they were looking just at the effects of unemployment length, the economists sent out resumes from women with college degrees looking for office administrative jobs. Unlike the earlier research, the economists find no connection at all between the likelihood a resume gets a call back from an employer and the length of unemployment on the resume. Other recent research also finds little relationship between the two, so Farber, Silverman, and von Wachter aren’t on an island by themselves.

What could explain the discrepancy between this new paper and the older research? The three authors compare their data and analysis to one of the earlier papers to see what factors could be driving the different results. While they don’t find a smoking gun, their analysis points to a difference in the ages of the fictitious workers whose resumes they sent out. The earlier research tended to have more resumes of younger workers while Faber, Silverman, and von Wachter focus on workers between their mid-30s and mid-50s. It could be that employers are more likely to brush aside concerns about long spells of unemployment if the worker has a longer resume. Or it could be, as the authors note, that their result only holds up for the specific group their experiment looks at.

This paper is part of a larger debate that certainly won’t get settled anytime soon. But these results should give us pause in thinking that employer discrimination against the long-term unemployed is a pervasive phenomenon across the labor market. And if there’s less discrimination, that means these workers are more likely to be able to get a job. In other words, this paper might give some of them new hope.