Paul, he's not. This is standard statistics. You shouldn't control for a collider. See page 74 of this textbook: http://scunning.com/cunningham_mixtape.pdf …
There is no way to discover if someone is earning less because they work less or because they are being paid less for the same work?
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Yes. Because if you are being paid less you will work less hours. Labor supply curves slope up.
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Yes, there is no way?
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There is a way - find a case (or create one) where there is an exogenous shock to the marketplace. That's why the paper I linked earlier by
@PikaGoldin and Rouse is compelling. Also see audit studies done by@NeumarkDN.
End of conversation
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