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As of December 28, 1.3 million out-of-work Americans will no longer receive emergency federal unemployment benefits. Economists fear the program's expiry could impact growth, and that this latest dose of austerity will actually spark a dip in the national unemployment rate – but for all the wrong reasons.

In 2008, the United States government introduced emergency benefits for those who had been looking for work for over 6 months, as a temporary safety net for throngs of Americans rendered newly jobless by the Great Recession. The program was extended 11 times since then, but Congress failed to extend it as part of the budget deal reached in November.

It's a particularly dismal time for the government to cut off insurance checks to the unemployed. The labour force participation rate, or percentage of the adult population actively looking for work, is at a 37 year low. Economists have raised concerns that much of the decline in the unemployment rate since the recession is the result of discouraged workers giving up on finding a job altogether. A growing number of observers fear that, with benefits having finally ended, the long-term unemployed will now drop out of the labour force entirely.

U.S. Unemployment vs Labour Participation Rate

SOURCE: Anna Nicolaou/Bureau of Labor Statistics

Measuring the cost of ending the emergency benefits is more of an art than a science. According to the U.S. Department of Labor, extending the insurance program will save the federal government about $25-billion (U.S.).

But Mark Zandi, an economist at Moody's Analytics, expects that every dollar of unemployment benefits generates $1.55 in economic activity, and under this model, failing to renew the benefits would cut activity by $39-billion in 2014. The Congressional Budget Office estimated that an extension would lift real GDP by 0.2 per cent in 2014, and that letting benefits expire could cost 300,000 jobs.

North Carolina serves as an interesting case study in how this could pan out. In July, the state decided to end long-term unemployment benefits payments, even though the federal government was still offering them.

Michael Feroli, chief economist at JPMorgan, used North Carolina as a proxy for what might happen to unemployment rates nationwide. Mr. Feroli says when benefits end, a "participation effect" takes place: People stop classifying themselves as "actively seeking work," since being officially unemployed will no longer summon any checks in the mail. Because the unemployment rate is the number of unemployed divided by the size of the labour force, this shrinking group would create a decline in the overall unemployment rate.

Since July, North Carolina's labour force participation rate fell 0.7 per cent (compared to 0.4 per cent nationally), and its unemployment rate dramatically dropped 1.5 per cent, while the U.S. rate is down 0.4 per cent.

Even if the benefit cuts deliver a small blow to the economy next year, the prospect seems to be a pebble thrown into a waterfall of optimism surrounding the U.S. economy. Economists across the board are brightening their forecasts for growth next year, encouraged by an acceleration in jobs and manufacturing figures in the second half of 2013.

But it's hard to reconcile this glossy picture with such troubling metrics below the surface: A shrinking labour force, and persistently high levels of the long-term unemployed.

If growth continues to accelerate in the coming quarters, there should be a bounce back in the labour participation rate, or at least a pause in its decline. But if the participation rate remains sticky, it will indicate that the issue is a structural, chronic one. And while extending unemployment benefits alone won't solve the problem, if it proves intractable, the American work force will need all the help it can get.