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No it doesn’t, the petro-dollar isn’t a real thing. Forcing USD denomination for a transaction doesn’t help USD because there is a buyer of USD and an equally sized seller of USD.

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However, there does seem to be an outsized effort applied to defending this not-real thing. A leader who defies the petrodollar has a good chance of getting killed or kidnapped. In a way, the same principle makes any god real: he doesn't have to exist, as long as people who will beat up non-believers do.

Total USD reserve involved in that transaction is not zero. They have to already hold dollars to do the transaction at all, which means a benefit has already been provided to the US. The transaction doesn't change the US's position, but enabling the transaction to occur does.

Petrodollar hypothesis is debunked. The total volume of petrodollar trade approximates minutes in stock markets. This simply isn’t a real factor anymore; a lot of people think it is because there are writings from the 70s that are compelling.

As you said, trade volume doesn't drive valuation, it's reserve size.

Which goes up with inflation btw, so you can export inflation. Actors who maintain reserves of your currency will have to keep buying more from you, providing you with benefits.

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