The Irrelevance of Bilateral Trade Balances below comes directly from Greg Mankiw's intermediate macroeconomics textbook (6th edition):
The trade balance we have been discussing measures the difference between a nation's exports and its imports with the rest of the world. Sometimes you might hear in the media a report on a nation's trade balance with a specific other nation. This called a bilateral trade balance. For example, the U.S. bilateral trade balance with China equals exports that the United States sells to China minus imports that the United States buys from China.
The overall trade balance is, as we have seen, inextricably linked to a nation's saving and investment. That is not true of a bilateral trade balance. Indeed, a nation can have large trade deficits and surpluses with specific trading partners, while having balanced trade overall.
For example, suppose the world has three countries: the United States, China, and Australia. The United States sells $100 billion in machine tools to Australia, Australia sells $100 billion in wheat to China, and China sells $100 billion in toys to the United States. In this case, the United States has a bilateral trade deficit with China. But each of the three nations has balanced trade overall, exporting and importing $100 billion in goods.
Bilateral trade deficits receive more attention in the political arena than they deserve. Most economists, however, believe that bilateral trade balances are not very meaningful. From a macroeconomic standpoint, it is a nation's trade balance with all foreign nations put together that matters.
The same lesson applies to individuals as it does to nations. Economist Robert Solow once explained the irrelevance of bilateral trade balances as follows: "I have a chronic deficit with my barber, who doesn't buy a darned thing from me.” But that doesn't stop Mr. Solow from living within his means, or getting a haircut when he needs it.
Contents Based on Greg Mankiw's Blog.