Trend growth could slow gradually to around 6.5 percent by 2030, or it could break much more sharply to a pace under 1 percent if forces undermining economic activity combine in a "worst-case scenario," according to the study, which was published online on Monday. Over the past decade, China's economy grew on average around 10 percent a year.

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"The GDP growth rate is the sum of the growth in employment and the growth in output per employee. China faces challenges in both of these categories," wrote author Jane Haltmaier, a senior adviser in the Fed's Division of International Finance.

Buoyant Chinese growth helped support the global economy after recessions in the United States and Europe, and a significant slowdown in China could dent output, employment and corporate profits around the world.

The study concluded that some slowing was inevitable, although boosting Chinese education to get more kids through high school could provide an offset.

"Most people would probably agree that the Chinese economy cannot maintain the extremely rapid growth rates it has seen over the past three decades indefinitely. The question is thus not whether the Chinese economy will slow (but) by when and by how much," Haltmaier wrote.

Growth in China's working age population has slowed and is expected to turn negative before 2020, according to United Nations' projections. Like other nations, China is getting older. The percentage of the population aged over 60 is expected to reach nearly 25 percent by 2030, from 12 percent in 2010.

DIMINISHING RETURNS

With 80 percent of the working age population already employed, there is limited room for employment growth to contribute strongly to economic activity in the future.

As a result, the bulk of any further increase in Chinese output will have to come from greater productivity, something that faces an uphill battle.

Although China has enjoyed a productivity boom due to massive investment, that could be hard to sustain as rising living standards drive up domestic demand for consumer goods, diverting resources away from capital investment into spending.

Also, as the capital stock in the economy grows, an increasing amount of investment needs to be allocated to replacing aging plant and machinery, leaving less overall for net new investment.

In addition, slower employment growth could reduce the returns on capital, reducing the incentive to invest.

The scope for millions of more Chinese workers to move from less productive primary sectors in the economy like agriculture, to much more productive factory jobs is also likely to shrink over time.

"The share of the secondary sector is now about half of GDP, much higher than in most other countries. This suggests that further movement out of the primary sector in China is more likely to be into the tertiary sector, where the productivity dividend is lower," the study says.

In her "baseline" forecast, which showed growth slowing to just over 6 percent by 2030, Haltmaier assumed the employment-population ratio stayed at current levels, investment stayed high, workers kept moving out of primary industries, and investment shifted from primary and secondary industries into the service, or tertiary sector.

She also sketched out four alternative scenarios: slower growth in employment; lower investment; reduced incentives to invest; and a decline in the share of high-productivity manufacturing.

In all cases, Chinese output slowed by more than in the baseline forecast. But the real damage was done when all four factors began to bite together. In that worst-case scenario, growth halves to 5 percent by 2020 and declines to under 1 percent by 2030.

"Investment falls as a share of GDP and becomes less productive, employment growth is slower ... and output shifts from the manufacturing to the services sector as the economy matures," Haltmaier wrote. "It should be noted that these are all in fact very reasonable assumptions."

(Reporting by Alister Bull; Editing by Leslie Adler)