Cowen rightly identifies the advantage of local minimum wages: localities are heterogeneous, and locally set wage floors can better match local conditions.

In the federalism literature, this is a typical benefit of locally set policy. But there are usually costs as well.
In our model, factor mobility (we use high-skilled labor for tractability) depresses the incentives for localities to set minimum wages, since they don’t want productive factors to leave. The central government, on the other hand, internalizes all this movement.
So there is a classic federalism trade-off: decentralization matches local conditions and preferences, while centralization internalizes externalities or inter-government competition.
In all of our simple experiments, the mixed regime, i.e., one in which local governments can “top off” a floor set by the central government, seems to be the best one. Here’s one example, where “US” is the mixed regime:
Note that none of this says what the federal minimum wage should be. 15 may be far too high for Mississippi. I am mostly taking issue with the phrase “all economic theories” from the post. In a country where these states are interconnected, it’s a more complicated question.
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