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I don't understand why GDP is part of this calculation. It can be done more directly with (taxes/persons). Also, although greater taxes may depress GDP somewhat, there are other factors at play that makes the U.S. the home of the most productive workers. I still think the more interesting metric is tax burden as a proportion of total income, not absolute taxes paid per person.
Im not convinced by those figures; it doesn't reflect my experience of paying tax here in the uk (for example: I am above averagely paid and still not hitting the 13,000 quoted here)
He's looking at total tax revenues. Some things you might not be taking into account, from most likely to least:

1. Corporation tax. You wouldn't be paying that directly.

2. Value added tax. You do pay that kinda-directly, every time you buy something with VAT on it, but unless you keep more careful records than most people it's hard to assess just how much you pay.

3. National insurance. Effectively an addition to income tax that doesn't get reported as income tax and that (unlike income tax) is regressive rather than progressive.

Back of envelope: Consider someone paid £30k/year (modestly above the national average). They'll pay about £7k in income tax and a bit less than £3k in national insurance. The corporation tax rate is comparable to the income tax rate, and nationally profits are something like half of wages, so probably this person's share (so to speak) of their employer's corporation tax is about £3k or so. Call it £3k. This person's take-home pay is about £20k. Perhaps half of that will go to things like food, utility bills, mortgage/rent payments, etc., that aren't subject to VAT, leaving £10k; perhaps they'll manage to invest £3k of that, leaving £7k; then VAT at 17.5% on the remainder is about another £1k. So, crude estimate: this person accounts for about £14k of tax. That seems to fit well enough with Mankiw's figures.

Ah gotcha. I included NI but not the other two.

Based on the tax I'm paying currently your figures do seem about right.

EDIT: actually your income tax figure might be a bit high. I'd say it's about 4.5-5K

Personal allowance is ~£6.5k, leaving £23.5k. Then basic rate is 20% of that which is, er, £4.7k. I have absolutely no idea where I got £7k from. Sorry about that. So yes, my numbers are too high by ~£2k. So presumably it matters that I didn't include some other more obscure taxes -- inheritance tax, stamp duty, import duties, etc. Key point: there are lots and lots of taxes, and what Mankiw is looking at is the ratio of total tax revenue to GDP, or population, or whatever.
Oh yes, sorry, I wasn't querying the total :) just thinking out loud as it were.

(thinking tangentially are we including employers contribution to NI as individuals tax? because that could account for any defecit)

I was deliberately not including it, because I was thinking the employer's contribution is quite a bit smaller than the employee's. But I was wrong; they're about the same size.
You forgot to take VAT and other indirect taxes into account.
By the definition Mankiw is offering:

1. a vastly rich country with GDP $1M/person and taxes at 2% of GDP would be a "high tax country";

2. an impoverished country with GDP $1k/person and takes at 99% of GDP would be a "low tax country".

Mankiw's only justification for this is that "high tax rates tend to depress GDP". Perhaps they do, but it seems to me that his proposal waaay overcompensates for any such effect.

The question of whether moderately higher tax rates depress GDP at all seems to be controversial among economists, which seems like good evidence that they don't depress GDP much.

What would you say about this correlation between GDP growth and government spending? http://mol-eng.com/growthsm.png (taken from: http://www.foresight.org/nanodot/?p=3012 )
I'd say that there's a lot more variables that you didn't control.

It seems fair to say that a big contributor to our economic success in the 50's and 60's was due to every other first world nation having been reduced to rubble in the 1940s.

Manufacturing and innovation in Japan and Europe didn't really roar back until the late 60s and 70s.

That chart looks at all countries in the OECD (not just the US) and also looks at the 60's and 70's (not the 50's).
Not very much until I know the source of the data and whether I can actually trust it. However, it's certainly not inconceivable that such a correlation might be highly misleading. Here are two simple thought experiments to illustrate this.

1. Suppose that in every country, in every year GDP growth is exactly proportional to government spending the previous year. In other words, spending more produces immediate GDP gains. And suppose that government spending generally changes quite slowly, within certain limits.

Then low spending at the start of a decade will correlate with increasing spending over the decade (because of regression to the mean) and therefore with increasing GDP growth over the decade (because of the assumed relationship between spending and GDP growth). So we'll get a graph rather like that one despite the fact that the real relationship between spending and GDP growth is positive.

2. Suppose that GDP growth is entirely independent of government spending, and that it depends on some other characteristics of a country; that high-growth countries tend also to be rich ones (as they would, having grown faster in the past); that all countries would (with equal patterns of taxation and government spending) have roughly equal levels of inequality, so that poorer countries have more really poor people; and that government spending is dominated by attempts to give the poorest people a decent life.

Then the poorer countries will spend more, because they have more people who need government assistance to keep out of severe poverty; they will also have less growth (by our assumptions); so we'll see a correlation like the one in the graph, even though there is (by assumption) no causal relationship between government spending and GDP growth.

Of course these are both likely to be much simpler than the truth. But then, so is the model you're implicitly relying on if you point to the graph and say "see, government spending inhibits growth" without further analysis. (That model would be something like: GDP growth is purely a function of government spending over the previous decade, and nothing else.)

He answered that:

> The most common metric for answering this question is taxes as a percentage of GDP. However, high tax rates tend to depress GDP. Looking at taxes as a percentage of GDP may mislead us into thinking we can increase tax revenue more than we actually can. For some purposes, a better statistic may be taxes per person

He said taxes per person might be a better statistic "for some purposes" - apples and apples comparisons like modern, Western economies might be a good purpose. Apples and oranges comparisons like Japan and Cambodia probably wouldn't be a good purpose.

My point is that he hasn't given any reason to think that tax / person really is a better statistic for any purpose. I know that he says something that looks, in terms of sentence structure, like a reason, but there isn't actually any connecting logic there.

Mankiw's a clever chap, so let's give him the benefit of the doubt and try to see if there's any argument he might be hinting at. Perhaps it's something like this. "Higher taxes tend to reduce GDP. The way this works is that people will work less hard, or take less trouble to do more lucrative and presumably more valuable work, if their taxes are higher. The way this works is that people compare the effort they have to exert with the goods and services they can get, which assuming sensible exchange rates is basically the same thing as absolute income; so demotivation is, so to speak, a function of income; so to measure how demotivated our workers are by tax we should look at their taxes in absolute terms."

(I don't know whether that's what Mankiw has in mind, but it's the most plausible argument I can come up with that looks at all like what he said.)

I'll also mention another argument for measuring tax per person, which I don't think Mankiw hints at at all but which seems at least as persuasive as his argument: the purpose of taxation is to provide the people with benefits, typically somewhat evenly spread across the population or a substantial fraction of it; so the benefit provided per person is roughly a function of tax per person.

There seem to me to be several substantial problems with (what I'm guessing to be) Mankiw'sargument, and also with the other argument I mention above, even if we consider only "modern Western economies". Here are some:

1. The prices of goods and services are not at all constant across countries. Unfortunately, there also isn't any simple relationship between these prices and GDP, so it's not clear how to correct for this. (If relevant goods have prices perfectly constant across countries, demotivation is a function of tax per person. If they have prices exactly proportional to GDP, demotivation is a function of tax over GDP. Neither of these simple cases is common.)

2. Some particular goods, including some of great importance for the sort of demotivational effect I think he has in mind, have prices that correlate very strongly with GDP. Notably, houses tend to be more expensive in more affluent countries and cheaper in less affluent countries.

3. It's well established that most people care a lot about status, which goes along with relative income. So one particular and important "good", namely one's level of relative wealth, does in fact vary more or less in proportion to GDP. This observation is relevant to both arguments: the demotivational force of a given level of taxation will (in so far as it depends on status) be determined by tax / GDP rather than tax / population, and the cost of ensuring that no one is too poor in relative terms will also be determined by tax / GDP.

4. The diminishing marginal utility of money means that the richer a nation is, the more effective an average tax dollar is when spent on scalable things (e.g., infrastructure) or benefits for the worse-off, relative to the benefit it would have provided if it hadn't been taken in tax. (And, hence, also relative to the demotivational effect of taxing it.)

> My point is that he hasn't given any reason to think that tax / person really is a better statistic for any purpose.

It's valuable to look at different statistics in metrics in most endeavors. No statistics are perfect, but it's good to check out different ones. Take baseball, for instance. You have batting average (the percent of times a hitter gets a hit) and you have runs scored (runs are baseball's equivalent of "points" or "goals" for people unfamiliar; you win by having more runs than your opponent). The usual way people look at tax burden is looking at percent of GDP - batting average, so to speak. But it's also worthwhile to look at runs scored.

Why is that? Well, maybe batting average isn't the only way to win games. Baseball used to be obsessed with batting average, but neglected a more subtle and advanced statistic called "on base percentage" for years. If you did an analysis of runs scored, you'd find you need on base percentage more than batting average. If you did an analysis of taxation that showed that you could have higher tax yields without taxing a higher percentage of GDP, that'd be well worth knowing.

At the very least, it's a number worth looking at.

> Perhaps it's something like this.... so demotivation is, so to speak, a function of income; so to measure how demotivated our workers are by tax we should look at their taxes in absolute terms.

Actually, the largest reason taxes reduce GDP isn't motivation. It's that the government doesn't invest in the same thing as individuals. When you take taxes from, say, Sergey Brin, and put them under the control of the Senate, that money is going to be spent differently. Brin's money is far more likely to grow the GDP of the United States for the future than whatever the Senate spends it on. The Senate funds some things that produce returns (quality infrastructure, science), some things that help maintain things (a bit of law enforcement, courts), and then a lot of things that don't produce returns. Individuals reinvest in productive endeavors at a much greater rate. Taxation moves resources from the control of people who are more interested in reinvesting and growing their investments to politicians, who are primarily interested in getting re-elected.

> the purpose of taxation is to provide the people with benefits

The purpose of taxation is to increase the revenues that the taxing authority collects. How those revenues are spent are up to the authority. Some governments provide benefits to the people, some buy weapons and try to take over their neighbors, some just steal the money outright. Taxation is sold as providing benefits to the people, but that's not necessarily how the tax yields are spent.

> 1... 2... 3... 4...

I agree with some of those arguments, disagree with others. But the main point is he's not offering a Swiss Army Knife that measures everything, he's just pointing out another number we can look at and take into consideration. To go back to baseball, it's good to look at batting average, on base percentage, isolated power, runs scored, pitches taken, and a number of other factors - there's some great players that have a low average and low on base, but hit with lots of power so they're good. All things being equal, you'd like to have your players take more pitches and wear the other side out. There's a hidden value in a player that takes 1 extra pitch per appearance even if he's just an average player - he'll take 4-5 extra pitches a game, which might mean wearing the opposing pitcher out who has to be taken out. That means your teammate will face a worse pitcher. If you can get a full team of players that take a lot of pitches, you might see spend 10% of the game facing the opposing team's worse reliever when the guy who started the game gets tired and has to be taken out very early.

But if you said - "let's only look at pitches taken", you'd be crazy, because it's useless by itself. If you said, "let's only look at runs scored" you'd be crazy, because it's also about how your teammates do after you ...

> 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.

I thought the comment at http://www.bigstartups.com/wac6/blog/1273/Will-the-Last-Star... by "heretic" was someone merely trolling the comments.

However using the equation and data sets from this blog post (http://gregmankiw.blogspot.com/2010/03/taxes-per-person.html) results in:

  * Ireland:  34.0% × 39,441 = 13,409.9
  * New Zealand:  36.5% × 26,625 = 9,718.1
Add to the above data that both countries score better than the United States in the Economist Intelligence Unit's "Democracy Index" (http://en.wikipedia.org/wiki/Democracy_Index), the Reporters Without Borders "Press Freedom Index" (http://en.wikipedia.org/wiki/Worldwide_Press_Freedom_Index), and the Transparency International "Corruption Perceptions Index" (http://en.wikipedia.org/wiki/Corruption_Perceptions_Index). The only bright spot for the United States are the two indices of economic freedom: the Heritage Foundation's "Index of Economic Freedom" (http://en.wikipedia.org/wiki/Index_of_Economic_Freedom) and the Fraser Institute's "Economic Freedom of the World" (http://en.wikipedia.org/wiki/Economic_Freedom_of_the_World); wherein Ireland and New Zealand alternate in bracketing the United States.

I'm beginning to think "heretic" wasn't trolling the comments.

A professor of economics ought to know that if your equation is x/y * y/z, then it doesn't matter at all what Y is. He could use anything he wants for GDP and it won't make a difference in the result.

A more interesting point, which I think he was trying to get at, is the idea that US citizens pay around the same taxes per person as other countries, but we produce a much higher GDP per person. We're more productive. Is that good or bad? Is it cause or effect? Discuss.

I think the point is that x/y and y/z is the readily available input data.
I wanted to see the results of this calculation for more countries. Using the data available on the Wikipedia entries Mankiw used I have created a Google spreadsheet: https://spreadsheets.google.com/ccc?key=0ApvbK1Yd5hPzdFhSZVZ...

It has the information for all the countries listed.

OECD average for tax revenue as a percentage of GDP is 36.0 -- I have not calculated the OECD average for GDP per capita.

I think his idea is to measure how much tax income the government has per person, which basically means how much money it can spend on services per person. The problem is that goverment costs for the same services differ. I imagine a doctor in the U.S. cost more than a doctor in Italy, so 12,478 in Italy can pay for more doctor time than 13,097 in the U.S. His tax level measure is also very sensitive to currency valuations. If the U.S. dollar goes up, then the tax level relative to other countries will appear to go up, even though the economy has not actually changed.
What's incredible is that Americans pay all these taxes, but get few of the benefits. The average UK citizen pays $617 more tax, but gets healthcare, and decent public infrastructure (see ASCE's infrastructurereportcard.org). Also, US healthcare eats up 16% of GDP, compared to ~10% in the UK and ~12% in France (source: Economist).
> Also, US healthcare eats up 16% of GDP, compared to ~10% in the UK and ~12% in France (source: Economist).

Would you rather live in a country with $1M/person GDP that spends 50% on healthcare or one with $1K/person GDP that spends 5% on healthcare? Feel free to assume equal lifespans.

I ask because that difference in healthcare spending is dwarfed by the difference in after-tax income.

Also, the US spends a lot of money on things that those other countries don't, specifically obesity and "right before death" spending. The former can't be reduced with healthcare spending and the latter is a choice, albeit one that doesn't significantly affect lifespan. However, changing it is "treating grandma as shovel-ready".

Why does anyone think comparing tax rates across countries makes any kind of point? The methods of taxation, and the benefits provided, are different across countries.

Europeans pay higher taxes. They also get a lot more in terms of government services. I'd gladly pay 7-10% more in taxes for cheap transporation, free healthcare, and free higher education in this country.

Few Europeans, except for rich right-wing assholes, seriously complain that they pay too much in taxes (aside from the nonspecific gripe that everyone has against taxes). If anything, we pay too much in taxes in the US when you consider how little we get and how much is squandered (e.g. the Iraq war).

The problem with taxes per person is it doesn't take into account how a country spends its money. If, as a percentage, we spent as little on the military as those other countries our taxes per person would drop significantly.
If what matters is the money you take home at the end of the day, the USA is still vastly superior to any other countries in his list.

If you look at the % of USA GPD/Person and compare that against the % of USA take-home/person, only Japan has an increase (from 70.7% to 71.4%). What does this mean? That it's pretty d@mned good to live in high-income/low taxes USA. I'm going to take a look at the rest of the G8 countries.