Well, the big reason we have a trade imbalance in China is because we're a very large economy. We're about three times as large as China. We're about six times richer than China. So for those reasons, we buy more goods from China than we export to China.That should immediately set off your BS detector, as it did mine. Yes, our economy is larger than China's, but our economy is larger than any other nation's economy is as well. Relative to the rest of the world, China's economy is enormous.
If the size of the US' economy relative to the size of the economy of the country in question influenced whether or not the US ran a trade surplus or a trade deficit with said country in the way Geithner suggests, if we're running trade surpluses with anybody, it should be with China, the world's second largest economy as measured by GDP. Conversely, we should, using the same logic, be running deficits with--arbitrarily using the small countries beginning with "A"--Albania, Antigua and Barbuda, Armenia, and Aruba. In reality, we are running surpluses with all of them.
Including all countries with which the US did at least $50 million in trade during 2010, I ran a regression using US trade balances by country and national GDP. The correlation is a very robust inverse .83 (p = 0). That is, the US runs deficits all over the place with large (and generally, though not necessarily, advanced) economies while running surpluses with smaller (and again, generally less advanced) ones. The reality is exactly the opposite of what Geithner says.
What about Americans being more affluent than the Chinese are? Is Geithner correct in asserting that our relative wealth is a big reason for why we're running a perpetual trade deficit with China? Do we tend to run deficits with countries where the populations are poor and surpluses with countries where the populations are rich? No. Correlating US trade balances and purchasing power parity by country reveals no correlation at all between the two (r = .03). We run deficits with many poor countries like Sri Lanka and Ecuador and many wealthy countries like Germany and Japan. And we run surpluses with several poor (Peru, Ghana) and wealthy (the Netherlands, Australia) countries alike.
I'm certainly not an expert on trade balances nor their implications, in either an abstract economic sense or from the perspective of an American patriot, but it's depressingly humorous to me that a top government official who should be an expert on both accounts is able to get away with making assertions that are so blatantly fallacious.