Short version: During the World Wars the U.S. made so much money selling weapons to the allies that they essentially had all the world’s gold (since their money was backed by gold) allowing the U.S. to still be on the gold standard while other countries had abandoned it. So, the easiest way for them to stabilize their own money was to peg it to the U.S. dollar, which was in turn pegged to gold and thus stable. Eventually the other countries took their gold back this was less literally true and the U.S. eventually went off the gold standard itself, but the system stayed in place basically by inertia.
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