During a trade deficit, the U.S. dollar generally weakens. Of course, there are numerous inputs that determine currency movements in addition to balance of payments, including economic growth, interest rates, inflation, and government policies. A trade deficit is a negative headwind for the U.S. dollar, but it can still appreciate due to other factors.
A trade deficit means that the United States is buying more goods and services from abroad than it is selling abroad. Foreign firms end up with U.S. dollars. Typically, they use these U.S. dollars to purchase Treasury securities or other U.S.-based assets, particularly during periods of financial stability and growth.
If imports continue to exceed exports, the trade deficit continues to worsen leading to more outflows of U.S. dollars. The flow of dollars out of the country leads to a weakness for the currency. As the dollar weakens, it makes imports more expensive and exports cheaper, leading to some moderation of the trade balance. As the currency continues to weaken, it makes U.S. dollar-denominated assets cheaper for foreigners.
The U.S. has run persistent trade deficits since the mid-1980s, but this has not translated into significant dollar weakness as would be expected. The primary reason is the U.S. dollar's status as the world's reserve currency. Dollar demand continues, as it plays a major role in global trade and reserves for central banks all around the world.
Major economies that issue their own currency, such as the European Union, Japan, and England are in a similar space, where they can run persistent trade deficits. Countries that do not have the faith of the investing community are more prone to seeing their currencies depreciate due to trade deficits.