If we define currency manipulation in a broad sense by viewing the word "manipulate" in a neutral sense, then all central banks are guilty of manipulating currency because that is what monetary policy entails. You honestly think that something like quantitative easing isn't a form of manipulating currency? Let's go with the more economic definition of currency manipulation, which is a fiscal or monetary authority purchasing large amounts of foreign currency to positively affect the value of its domestic currency. With currency manipulation, a country uses its monetary policy to make its exports comparatively cheaper, which in this case, fuels China's export-growth model.
It's hard to take the "currency manipulator" claim seriously because it's not as if China is the only one doing it. Not only are there other nations doing it, but there are worse offenders than China (Gagnon, 2012). If we're going to be intellectually honest in our vehemence against currency manipulation, we should target all countries, not just China. Even if China isn't the only one, let's buy into the counterargument that it should still be stopped, and given that China's economy is growing immensely, we should particularly target China. Is China's currency manipulation so egregious that the United States government should take action?
Even if China is a currency manipulator, it cannot keep it up forever, and all the while, it's doing itself a disservice, in part because a devalued yuan is actually subsidizing the American importer, not the Chinese exporter. Plus, we get a greater value from Chinese imports than our exports we send to them (International Trade Commission, p. xv, Table ES.4). As the Richmond Federal Reserve Bank points out, there will be a point that neither having a managed floating exchange rate referenced to a currency basket, relying on the export-growth model, nor buying up mass amounts of foreign currency reserves will work in perpetuity. China's interventionist plans will eventually run out of steam, and when they do, their currency will have to strengthen. As a matter of fact, we already have seen that happen. If China were truly manipulating its currency, we would see the yuan either remain at the same exchange rate or weaken. What we have seen in the past few years is that the yuan has actually strengthened as the trade deficit has widened.
Even if you're one to argue that Chinese currency manipulation was an issue back in the early 2000's, currency manipulation is not a major issue anymore. Chinese monetary policy does not have nearly as big of an impact on American GDP growth or unemployment rate (see chart below for relationship between trade deficit and employment) as American domestic policy does. Even if you "revalued" the yuan, it's not going to "bring back American jobs," whatever that might mean. It's easier to blame a foreign entity for problems caused by American tax policy and regulations, including more trade protectionism that exacerbates the issue. Especially if we want to have constructive economic relations with China, we need to blame China less and focus on ways to encourage entrepreneurship and a higher savings rate. That way, China can shoot its foot all it wants while America enjoys its comparative advantage in the global marketplace.
2-18-2017 Addendum: Since Trump is looking to denounce China as a currency manipulator at some point, here's a piece from the American Enterprise Institute showing that since I initially wrote this blog entry in 2014, China is still not a currency manipulator.