The study is based on a simple idea: population aging is already long underway and has been playing out with varying degrees of intensity across different regions of the country.

By looking at variations in state population aging, authors Nicole Maestas at Harvard Medical School, and Kathleen Mullen and David Powell at policy research group RAND Corporation, are able to estimate how a graying workforce affects output, participation rates and productivity.

What's surprising is the composition of the slowdown. Just one-third is driven by slowing workforce expansion and the rest by a drop in productivity gains.

Related: Obstacles to flexible retirement lie with employers

The productivity slump isn't reserved to older workers: it takes place across age groups, the researchers find.

The authors suggest a few theories about why that's the case. It could simply be that younger and older workers complement one another.

Or the most productive older workers might be leaving the workforce, while less-productive old timers stay on the job. "How much of it is that relatively productive workers are the ones who are choosing to retire? It's very hard to say," Maestas said in an interview.

Regardless of what's behind it, the discovery that the aging workforce could be weighing on productivity comes in contrast to other guesses and is important.

As Federal Reserve officials meet in Washington this week, tepid growth in ouput-per-hour is likely to be one of the economic questions they're pondering.

It's not clear why productivity growth has dropped off, and the change has real-world implications: it's one factor that caused Fed officials to lower their projections for where interest rates will settle in the longer-run, based on meeting minutes from their June meeting.

Another notable feature of the new findings: they're really pessimistic. If growth over the next 20 years otherwise held near its average for the 1960-2010 period — about 1.9 percent — adjusting for the demographic shift would lower per-capita GDP gains to 0.7 percent this decade and 1.3 percent next, based on the estimates.

Other research on the topic has suggested that population aging will have a smaller drag on output growth — for instance, a 2012 National Research Council report found that aging could knock 0.3 to 0.6 percentage point off of growth over the next two decades as the workforce structure changes, which it characterized as a "modest" macroeconomic consequence. The difference arises because the council didn't factor in productivity as a major way aging could drag on growth, Maestas said.

"The real challenge next is to take a closer look at productivity and whether there are ways to redesign the way we work, and take a look at policy that can inadvertently encourage retirement by productive workers,'' she said.

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