The New York Times had an article on the status of Trump's trade war with China. While the piece pointed out Trump's claim that his trade war is responsible for China's economic problems, it didn't point out that this is almost certainly not true.

In spite of Trump's tariffs, China's exports to the United States were up by more than $30 billion in the first ten months of 2018 compared to 2017. While their exports may have grown even faster without the tariffs, it doesn't make sense that slower than expected growth in exports to the United States could be too big a hit to the Chinese economy.

It is also worth noting that China's exports to the United States are actually not that large a share of its economy. If we just take the reported value of China's exports to the United States, it comes to less than 3.9 percent of its GDP.

This overstates the actual share of Chinese value-added in these exports, since we record the full price of a product as an export, even though much of the value-added comes from other countries. For example, we would record the full value-added of an iPhone assembled in China as an export from China, even though the vast majority of the value added in the product comes from the United States and other countries.

This is offset in part by Chinese value-added in items from third countries. For example, cars we import from Germany and electronic items we buy from Japan or Korea are likely to include a substantial amount of parts produced in China. But these items will not be affected by Trump's tariffs on China.

If we conservatively reduce the value-added of the items we import from China by 25 percent to account for foreign inputs, this means the value-added in Chinese exports to the United States accounts for less than 3.0 percent of its GDP. This means that even if Trump's tariffs reduced its exports by one third (a huge reduction), it would only imply a loss of less than 1.0 percentage point of GDP. By contrast, following the collapse of the housing bubble, residential construction in the United States dropped by almost four percentage points of GDP.

In short, the idea that Trump's tariffs are a major factor in China's economic problems is absurd on its face, just like his claim that he had the largest inaugural crowd in history or that millions of illegal votes were cast in California. Just as the NYT would not report these claims without pointing out they are not true, it should not report Trump's claim that his tariffs are doing great harm to China's economy without noting that it is false.