There’s no eligibility criteria. They just unilaterally decide to do it. It’s as simple as a country saying, “one unit of our currency is equal to 1 US dollar” or whatever exchange rate they set. Not having an actual market in their currency where its exchange rate is determined by market participants could have bad economic and pricing impacts locally. But that has no bearing on whether a country can set an exchange rate pegged to any currency it wants to.
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