> It's valuable to look at different statistics in metrics in most endeavors.

Well, sure. The question is which statistics are useful. If Mankiw had proposed dividing the total tax revenue by, say, the number of parrots in the country, obviously "well, it's another statistic" wouldn't be enough justification for looking at it. My point is that Mankiw really hasn't given any reasons to take total tax per person much more seriously than total tax per parrot, and that he therefore hasn't justified his claim that for some purposes it's appropriate to say that the US is not a lightly taxed country.

(I'm sure tax per persion is more sensible than tax per parrot. It could hardly not be. But why not tax divided by sqrt(population), or tax divided by land area, or tax per corporation, or population / (GDP - tax), or a thousand other statistics that kinda-sorta measure tax relative to other things that might be somehow relevant? Mankiw really doesn't say.)

> If you did an analysis of taxation that showed you could have higher tax yields without taxing a higher percentage of GDP, that'd be well worth knowing.

Indeed it would. At high enough tax levels, it seems very likely that you can. What levels those are is highly debatable. Maybe Mankiw has some evidence that it's true even at the US's tax levels. But Mankiw hasn't offered any such analysis or evidence, or pointed at anyone else's analysis, or explained why such an analysis would make it appropriate to take tax/population as a measure of how highly taxed a country is rather than tax/GDP, or anything.

> Actually, the largest reason taxes reduce GDP is[...] that the government doesn't invest in the same thing as individuals.

Presumably you mean it's that the government invests in less growth-producing things than individuals do. That might be true, though again neither you nor Mankiw offer any evidence. (In particular I am not convinced either that politicians determine public spending to maximize their chance of being re-elected, or that spending chosen to maximize their re-election chances would generally produce less growth than spending chosen to maximize whatever average taxpayers want -- which isn't by any means only investment growth, since people don't typically invest all their income and don't put all their investments into maximum-expected-growth assets.)

> The purpose of taxation is to increase the revenues that the taxing authority collects.

Nope. (If you'd said "the meaning of taxation is ..." you'd be nearer the truth, but only by virtue of saying something content-free.) Of course it's a simplification to say that the purpose of taxation is to benefit the public; let's say, instead, "the point of taxation", acknowledge that yes, some tax revenues are in fact spent on things that don't benefit the public, acknowledge that you're not going to agree with my opinion that on the whole democratic governments do tend to try to spend tax revenues with that purpose and I'm not going to agree with (I'm guessing) yours that all governments are basically kleptocracies that use tax revenues only to benefit the politicians, and move on.

> another number we can look at and take into consideration.

Just like the tax revenue per parrot. Seriously: presenting another number, per se, is trivial and uninteresting. What would make it interesting would be if Mankiw offered grounds for thinking that his number is a good one to look at. He didn't.