U.S. will still have double China's per capita income by 2061

China's income per person will grow by two to three times the U.S. pace over the next half century. But that pace will still leave income levels in China at half those of the U.S. Image: Thinkstock.

The United States will still have more than double China's per capita income by 2061 even as Chinese income levels are tipped for more rapid growth.

A study by the Federal Reserve Bank of Minneapolis found China's income per person will grow by two to three times the U.S. pace over the next half century. But that pace will still leave income levels in China at half those of the U.S., underscoring the gap between the world's two biggest economies.

China's annual per capita gross domestic product surged almost 500 percent from 1980 to $7,700 in 2010.

The Fed said it undertook the study to get a handle on potential ramifications for the U.S. in the event of an economic shock in China.

"Perhaps the paramount U.S. policy concern is that, all else equal, higher standards of living in China mean a larger Chinese share of the global economy, suggesting that shocks originating there will more strongly buffet the U.S. economy," according to the paper.

The study's findings come as China undergoes a painful transformation of its economy.

The government wants to shift the nation away from reliance on debt-fueled investment and an export-led model to an economy where consumer spending and the services sector make up a larger share.

As that shift happens, growth is slowing. China's GDP in 2014 expanded at the slowest pace since 1990.

The Fed study drew on a mix of academic theory and economic data and used the experience of South Korea and Japan, two economies which experienced rapid growth before slowing to levels similar to the U.S.