## Friday, April 2, 2010

### Mankiw and Yglesias on Taxes

Greg Mankiw suggests that taxes/person is a useful number for evaluating the efficiency of tax systems and (by implication) the optimal tax rate (my emphasis):

“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, which we can compute using this piece of advanced mathematics:

Taxes/GDP x GDP/Person = Taxes/Person

Here are the results for some of the largest developed nations:

France   .461 x 33,744 = 15,556

Germany   .406 x 34,219 = 13,893

UK  .390 x 35,165 = 13,714

US  .282 x 46,443 = 13,097

Canada  .334 x 38,290 = 12,789

Italy  .426 x 29,290 = 12,478

Spain  .373 x 29,527 = 11,014

Japan  .274 x 32,817 = 8,992

The bottom line: The United States is indeed a low-tax country as judged by taxes as a percentage of GDP, but as judged by taxes per person, the United States is in the middle of the pack.”
Matthew Yglesias jumps all over the suggestion that tax/person tells you anything about what tax rates ought to be, even to the point of questioning Mankiw’s good faith (emphasis in the original):

“[W]hile I’m sure Mankiw believes the conclusion that raising taxes isn’t as viable as I (or, say, Paul Krugman) think, I seriously doubt that he believes this mode of analysis is correct. After all, why should the bottom line relate to the United States at all? Does Mankiw really think that Italy has more scope to increase taxes and the size of its public sector than does the United States? Or consider that in Slovakia per capita GDP is just \$20,000. By Mankiw’s logic, Slovakia could raise taxes up to 65 percent of GDP and it would still count as a country with a below-average tax burden!”
I’m no economist, so take what follows with a grain of salt--believe me, I do. But I think Yglesias is missing a point that should matter to liberal egalitarians.

Suppose we have a metric (call it “WUs” for “wellbeing units”) that enables us to make interpersonal welfare comparisons of people within a society and across societies. Assume, moreover, that: (1) the more money a person has, the higher his WU score; and (2) that level of marginal tax rates have some supply-side effects such that, all other things being equal, productivity varies inversely with tax rates. Now imagine four two-person societies that are exactly alike except of their tax rates having the following WU scores:

Society A—4/1; Society B—3/1; Society C—1/1; and Society D—3/2

Which society, and therefore which tax system, should a liberal egalitarian prefer? That depends on whether, roughly speaking, the relevant measure of equality is the size of the WU gap between people or the absolute number of WUs enjoyed by the least-well-off person. An envious egalitarian would embrace the former view and a non-envious egalitarian would embrace the latter. (For present purposes, we'll ignore all intermediate conceptions of equality). Which view of  these two ideas of "equality" a liberal embraces should depend mostly on how reasonable he thinks it is to be envious.

The envious liberal will rank these societies as follows: C>D>B>A even though the least well-off person in D is better off than the least well-off in C and people are, on average, better-off in A than in B. Accordingly, he’ll prefer the tax system which, having the highest marginal tax rate, maximizes taxes as a percentage of GDP.

Non-envious liberals will rank these societies as follows: D>A>B>C because, although they want the worst-off person to be as well-off as possible, they aren’t indifferent to increases in the well-being of better-off people or a society’s average well-being. They won’t be indifferent to the supply-side effects of marginal tax rates because what ultimately matters to them is the absolute number of dollars they have to redistribute to the least-well-off people.

All of this suggests, although taxes/person shouldn't be the only thing about a tax system that matters to a non-envious liberal, it should matter a lot. Having a higher taxes/GDP rate tells you very little about how many dollars a society has to spend on disadvantaged people. That France, Germany and UK collect more taxes/person than we do counts as a prima-facie (non-envious) egalitarian argument in favor of their tax system because they have more public dollars to spend on every disadvantaged person. (Granted, that needn’t mean that those tax systems are better than ours all things considered: if having higher tax rates means having higher unemployment, for example, France, Germany and the UK may have to provide publicly for more disadvantaged people, and have to spend more on each disadvantaged person to bring them up to the level of our disadvantaged people).