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Correlation does not imply causation. Richer countries have less need for minimum wage. How do you know it's not how rich the country is that causes the minimum wage and not the other way around?

Causality direction is indeed debatable. But while correlation does not imply causation, but the absence of correlation does imply the absence of causation.

I think, as a general rule, the burden of proof should be on those who want to create a new legal restriction rather than on those who oppose it. So if minimum wage laws are not correlated with any real positive effect, there is no reasonable justification for them.
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