Gregory Mankiw has an Op-Ed piece in the New York Times about how progressive US taxation is, contrary to the uniformed consensus. It is very interesting, and surprising to me how progressive it actually is.
But I don't agree that taxation is clearly sufficiently progressive (or even overly progressive). I suspect 4.5% is a bigger deal to someone on the bottom of the heap than 31% is to someone on the top of the heap. And personally I find it rather depressing that someone earning $15,400 a year is taxed at all. I sure hope the vast majority of that bottom 20% is part-time.
My point is that the actual income numbers matter and have an impact on how progressive we think something is. As Mankiw, says it all depends on how you define "fair".
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