The threat is likely to materialize in the new administration, given that a large number of Democrats also favor labeling China a currency manipulator.

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Yet many economists who study China say that, at least regarding currency, the charges of cheating don't stick — anymore.

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“When I heard Mr. Trump talking about China, I had this uncomfortable feeling that he was more than 10 years out of date,” said Pieter Bottelier, an economist who has studied China’s economic development for decades. “The idea that China has manipulated its currency by keeping it artificially undervalued is totally untrue today. … In fact, the situation is the exact opposite from what Mr. Trump seems to be claiming.”

In the 1990s and early 2000s, China held down the value of its currency, called the yuan or renminbi, to the detriment of U.S. exporters, who found that their goods could not compete with China’s low prices abroad. For almost two decades, currency manipulation gave Chinese exporters an edge that helped the country morph into an economic powerhouse.

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Today, that era in China’s economy appears to be over, at least for now. Between 2005 and 2015, China allowed the yuan to gradually gain value, and over that decade, the currency appreciated by about a third. Until the middle of 2014, one could have argued that China was still intervening in foreign-exchange markets to keep the value of its currency low.

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But over the past year and half, the country’s economic situation has transformed, economists say. As China’s growth slows, its people have tried to send more capital out of the country to find more lucrative and safer investments around the world. That has put downward pressure on China’s currency, and policymakers have switched to propping it up, rather than holding it down, economists say.

When evaluated against the U.S. dollar, China's currency appears to be depreciating in recent months. But that is because the U.S. dollar has been gaining in strength. When measured against other currencies, such as the euro, the yuan looks more stable.

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In a report in October, the U.S. treasury said that China did not fulfill the three criteria currently necessary to be labeled a currency manipulator (which are having a large trade surplus with the United States, engaging in persistent and one-sided intervention in foreign-exchange markets, and having a material current account surplus). In fact, China met only one of the criteria (the trade surplus), while Japan, Korea, Germany, Taiwan and Switzerland each met two.

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The Treasury report concluded that China was actually intervening in foreign-exchange markets “to prevent a rapid RMB depreciation that would have negative consequences for the Chinese and global economies.” Between August 2015 and August 2016, China sold more than $570 billion in foreign currency to prop up the value of the yuan, the Treasury report said — a trend that is visible in the chart below.

“The reality is that, if anything, China is doing the U.S. a favor by keeping its currency from falling as fast as markets seem to want it to fall,” said Eswar Prasad, a senior fellow at the Brookings Institution and the author of the recent book “Gaining Currency: The Rise of the Renminbi.”

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The currency-manipulation charge stems from a real concern over the Chinese economy: that America's trade deficit with China continues to grow. But in its report, the Treasury Department concluded that the solution to China's massive trade surplus with the U.S. is not in China's currency, but in encouraging Beijing to rebalance its economy toward consuming more and producing less. China experts have championed these changes for years.

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Nothing would stop a Trump administration from changing Treasury rules and labeling China a currency manipulator anyway. That would trigger a formal process in which the U.S. government could limit Chinese investment in the United States or introduce tariffs and trade barriers against China.

Such a move — accurate or not — could provoke retaliation from Beijing that could hurt U.S. companies and workers.

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Prasad says China is unlikely to bend to U.S. pressure, in part because it is in the midst of a political transition in which the government will probably want to appear strong to a domestic audience. In addition, the U.S. market today is not as central to China's economy as it once was: It accounts for about 17-18 percent of China’s exports, down from about one-quarter years ago. If pressured, China could respond by restricting access to the Chinese market for some of America’s biggest firms, such as Apple, Walmart or Boeing, as well as America's farmers.

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“Taking action against China’s currency or trade practices could very quickly escalate into a tit-for-tat battle that turns into an all-out trade war. The hope on both sides is that reason will prevail, but the political context in both countries makes this a particularly dangerous time when words and actions could have much greater consequences,” Prasad says.

To be sure, there are plenty of aspects of the Chinese economy that a Trump administration could criticize on stronger ground. China entered the World Trade Organization in 2001 promising to grant companies around the world freer access to its markets. And in many sectors, such as financial services, technology and the media, China has broken those promises.