The long-term unemployed “are an unlucky subset of the unemployed.” They tend to be a little older, a little more educated, a little less white – but really they’re not that different from the broader pool of people who have lost jobs in recent years. Except for one thing: There is a good chance they’ll never work again.

These are the sobering conclusions of a new paper by three Princeton University economists including Alan B. Krueger, the former chairman of President Obama’s Council of Economic Advisors. The paper, presented Thursday at the Brookings Panel on Economic Activity, is part of a growing body of research showing that the prospects of people who lose jobs deteriorate rapidly unless they find new jobs quickly.

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This has important, but opposite, implications for monetary and fiscal policymakers. It suggests the Federal Reserve has limited power to reduce long-term unemployment without tolerating higher inflation, which Professor Kreuger and his colleagues argue is affected primarily by the level of short-term unemployment. At the same time, it suggests that legislators acting with greater force and urgency could help people whose hopes are slipping away.

“Overcoming the obstacles that prevent many of the long-term unemployed from finding gainful employment, even in good times,” they wrote, “will likely require a concerted effort by policy makers, social organizations, communities and families, in addition to appropriate monetary policy.”

The idea that the long-term unemployed are on the margins of the labor market, exerting little pressure on wages or prices, is relatively new. On Wednesday I asked Janet L. Yellen, the Fed chairwoman, what she thought of papers that have reached the same conclusions as Mr. Krueger’s group.

“I think it would be tremendously premature to adopt any notion that says that that is an accurate read on either how inflation is determined or what constitutes slack in the labor market,” she responded. “I wouldn’t endorse — I certainly don’t think our committee would endorse the judgment of the research that you cited.”

The basic argument made by the new paper, and others like it, is that the long-standing relationship between movements in inflation and unemployment, which appeared to break down during the Great Recession and its aftermath, can be restored by writing off long-term unemployment. The Phillips curve, a description of this relationship, predicted a decline of one percentage point per year between 2009 and 2013. The actual average was just 0.2 percentage points.

Adjust for – which is to say, ignore – long-term unemployment and voila! The difference almost completely vanishes.

People are only counted among the long-term unemployed if they say they are still looking for jobs. As time passes, people tend to give up, and those who do are no longer counted as members of the labor force. So why do the people who persist in trying become less successful with time?

“Either because, on the supply side, they grow discouraged and search for a job less intensively or because, on the demand side, employers discriminate against the long-term unemployed, based on the (rational or irrational) expectation that there is a productivity-related reason that accounts for their long jobless spell,” the new paper says. It adds that the two explanations are complementary, “as statistical discrimination against the long-term unemployed could lead to discouragement, and skill erosion that accompanies long-term unemployment could induce employers to discriminate against the long-term unemployed.”

But there is no necessity to this explanation, and the paper itself contains some countervailing findings. It notes that the long-term unemployed tend to be older and more highly educated, suggesting their labor is relatively more expensive, and their prospects may improve with the economy.

The paper also presents striking evidence that few people are finding jobs in new industries. Professor Krueger and his colleagues draw the conclusion that government may be able to help. The authors write, “These results suggest that assisting unemployed workers to transition to expanding sectors of the economy, such as health care, professional and business services, and management, is a major challenge.” But if long-term unemployment is more common in industries recovering more slowly, because would-be workers are trapped in those industries, this too suggests that the problem may be economic rather than personal.

There is a way to resolve the question. Fiscal and monetary policy makers could try to help, and we could all see what happens.

Instead, the debate seems increasingly likely to remain purely academic, and the long-term unemployed permanently lost.