I'm curious to see how broadening or narrowing a trade deficit would affect a currency pair.
The "US-China trade deficit" isn't a real thing. Yes, there are some transactions classified as "exports from US to China" and others classified as "exports from China to the US", and you can subtract the latter from the former and get a negative number, but that doesn't represent anything fundamental about the world economy. Suppose that the US were to stop buying widgets from China and buy them from Taiwan instead, and the country that was buying them from Taiwan were to start buying them from China. Everyone would end up buying/selling the exact same amount of widgets, yet the "US-China trade deficit" would go down despite absolutely nothing fundamental about the world economy changing.
The overall trade deficit of the US does have an effect on the USD, but higher trade deficits make a currency go down in value, not up. Of course, a decrease in currency value tends to decrease trade deficits, which means that this effect tends to be cancelled out.
Both the exchange rate and the trade balance are equilibrium outcomes. One does not cause the other. Whether they comove depends on the source of the shock. Two hypothetical examples:
- The shock is an increase in the productivity of US investment. The result is (could be) capital inflows as domestic investment exceeds domestic saving. The dollar appreciates and we get a trade deficit (the flip side of capital inflows: the US is selling assets, so it gets goods in return).
- The shock is a reduction in U.S. tradeable output. Consumer demand for foreign goods may increase. The dollar depreciates and we get a trade deficit.