[I]n the year since the monetary fund first said it would bestow that status on the renminbi, the Chinese currency has become less attractive. Despite Mr. Trump's contention -- which, like his assertions about Japan, harks back to another era -- many economists say they believe the renminbi is overvalued, not undervalued.

Tony Gao, a senior at the University of Southern California, helped found a start-up called Easy Transfer three years ago. The company helps Chinese parents with children going to American schools exchange their renminbi for dollars. But business growth is down this year, he said, because many affluent Chinese have already changed their renminbi for dollars.

"A lot of them already have acknowledged this depreciation," Mr. Gao said, adding that he was thinking of switching his renminbi to dollars, too. "Now I'm actually on the edge." [...]

There are other forces at work. China has taken steps over the past few years to relax its hold on the renminbi. That makes it easier for banks and merchants abroad to save the renminbi or to use it in transactions. Manufacturing has also declined as a major growth driver in the country's economy, as the government pushes to build its growing consumer and high-tech sectors.

Since August of last year, when Beijing surprised global markets with a one-time devaluation of its currency, investors have been broadly seeking to unload their renminbi in favor of dollars.

In Hong Kong, the biggest offshore center for renminbi banking, deposits of the Chinese currency peaked in December 2014 and have since fallen by a third.

For five years since 2010, the renminbi had made small but progressive gains as a global payment currency, as measured by transactions processed on the Swift global payment system. But that usage crested in August 2015 at 2.8 percent of transactions, and it has declined steadily since then, to 1.9 percent in August.

China has spent hundreds of billions of dollars from its foreign reserves over the past year to support the value of the renminbi and to prevent it from weakening more drastically. A sharp fall could lead even more people to find ways to convert their renminbi into other currencies, resulting in an exodus of money from the country. More broadly, it could undermine Beijing's case that the renminbi is worth holding.