[rwl]

> Did you read the linked article? It measures the ratio (% of taxes paid) / (% of income earned). In this US, this ratio is 1.35%. In Norway, it's 0.95. Inequality would increase the denominator, not the numerator.

Right, sorry, I should have been more clear. Yes, inequality increases the denominator. But what I meant was that I would expect the numerator to grow faster than the denominator, at least some of the time, as both inequality and regressivity increase. So I would expect the ratio to be higher for some countries with higher inequality and relatively less progressive taxes (it seems likely that the U.S. is one example). Thus, one should not necessarily understand a higher ratio as indicating a more progressive tax system, which is what the original commenter was claiming.

[yummyfajitas]

But what I meant was that I would expect the numerator to grow faster than the denominator, at least some of the time, as both inequality and regressivity increase.

Not possible. Define P = progressivity index = tax rate for top 10% / tax rate for bottom 90%. Define R = income of the top 10%, B = income of the bottom 90%, and inequality I = R/B. Tax paid by the rich = RP x tax rate for bottom 90%.

% of taxes paid by rich = RP / (RP+B) = IP/(IP+1). (Tax rate for bottom 90% factors out)

(% tax paid by rich) / (% income earned by rich) = [IP/(IP+1)] [(R+B)/R] = P(I+1)/(IP+1)

Simple calculus shows this quantity always increases with increasing P and decreases with increasing I. So a higher ratio implies either a) a more progressive tax system or b) less inequality.