Well, the US is a major economy on the world stage, which explains part of those comparisons- as does the fact that many other countries hold large amounts of dollars in reserve. You can trace this back to the days when the US dollar was backed in gold and when the US head the most gold, near the end of World War 2. There was a deliberate choice made to pin many other currencies on the dollar, reassuring other countries and their banks that they could exchange their reserves of dollars for gold.
Of course, the dollar is fiat now, and ‘floats’ without being pinned to gold, silver, or otherwise, but the influence of that decision, along with US hegemony, keeps the dollar important.
At a meeting at the Mount Washington Hotel in Bretton Woods, New Hampshire in 1944 a man named Harry Dexter White (assistant secretary of the United States Treasury and later a suspected Soviet spy) snuck wording into an agreement that countries would link their currencies to a gold based currency and replaced it with the US Dollar.
https://en.m.wikipedia.org/wiki/Bretton_Woods_system
https://www.npr.org/transcripts/526051566
Victory in WW2. Active discouragement of the previous standard: pound sterling. Most other countries were in ruins.
Being a reserve currency is a blessing and a curse. A blessing when other countries were still in ruins and light years to catching up technologically. A curse now when US trade surpluses are no longer in the positive; it’s now imperative for US to maintain the status. The biggest threat is China – something all the highly paid analysts haven’t been able to raise to the politicians awareness till recently. The digital yuan and China’s edging for the Yuan to be used as a currency for trading petroleum, banking will reduce the US global strength. I think there are people in power who understand it, pivoting isn’t the easiest with the political discourse in current state.
Lots of good answers here on why the USD is a benchmark currency, but the second part of your question is based on a false premise…other country’s currency value is *not* determined by the USD’s value.
There is an exchange rate between every currency and every other currency that determines the relative value. It’s really common to see exchange rates presented against USD just because USD is so common and basically accepted anywhere at anytime, so it’s a convenient “intermediate” to compare any two currencies but that does *not* set a particular currency’s value. That’s set by relative demand and supply for that particular currency.
In the old days there was the Gold Standard, governments would keep a fraction of their currency in the form of Gold. You could show up to a government place and trade in their money for gold. However they sometimes needed to spend a whole lot more like, for example, having to fight a big war. After that, they would buy back some gold and go back on the gold standard.
During World War 1, all the big major European powers first spent all their gold on stuff from America, than went off the gold standard. After WW1, they didn’t have any gold left, and America had all the gold. And they were all wrecked pretty bad, so they couldn’t afford to buy back the gold from America to get back on the gold standard.
So instead of buying back the gold, they decided to just use US dollars, since they had all the gold anyway.
Later on after WW2, the leader of the French decided to finally trade in their US dollars the gold, so instead the US president dropped the gold standard themselves, so they couldn’t trade in their US dollars.
So everyone just kept using the US dollars.
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