The mighty US dollar continues to reign supreme in global markets. But the greenback’s dominance may well be more fragile than it appears, because expected future changes in China’s exchange-rate regime are likely to trigger a significant shift in the international monetary order.

For many reasons, the Chinese authorities will probably someday stop pegging the renminbi to a basket of currencies, and shift to a modern inflation-targeting regime under which they allow the exchange rate to fluctuate much more freely, especially against the dollar. When that happens, expect most of Asia to follow China....