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Comment by gjm11 | Hacker News Reader

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.

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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 get on. But that doesn't mean you should only look at batting average either - or you won't have a complete picture. It's worth looking at all the numbers, so I'm happy this number was brought up for thinking about.

> 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.

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