Progressivity

Greg Mankiw (rhymes with "thank you") says that there's no one way to measure the progressivity of the tax code, giving as an example:

There are two people. A rich guy earns $200,000. A poor guy earns $20,000. At first, the rich guy pays $50,000 in taxes, and the poor guy pays $1,000. Then a new President takes office and cuts the rich guy's taxes to $48,000 and the poor guy's taxes to $800.

  • You could say the rich guy gets the better deal: The rich guy gets an extra $2000 in take-home pay, while the poor guy gets only $200. After the tax cut, the difference in take-home pay between the two guys is larger.
  • You could say the deal is evenly balanced: Everyone gets to keep an extra 1 percent of his income.
  • You could say the poor guy gets the better deal: The poor guy gets a 20 percent tax cut, while the rich guy gets only a 4 percent tax cut. After the tax cut, the rich guy pays a larger share of the total tax burden.

It is impossible to say on purely economic grounds which of these perspectives is better. All of these statements are mathematically correct, even if they leave the reader with very different impressions. If you are a politician or a journalist trying to argue that this tax cut is good for the rich, good for the poor, or somewhere in between, you can do it!

I disagree. There is one clear problem with the first two metrics: They both allow us to eliminate the poor guy's tax burden altogether while making the system less "progressive." For example we could cut the poor guy's taxes by $1,000 (5% of his pre-tax income) and the rich guy's taxes by $12,000 (6%). I don't see how any metric of progressivity which suffers from this flaw can be considered valid.

Via Asymmetrical Information

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I disagree with the

I disagree with the contention that there could be a measured 'fairness' or 'progressiveness' when it comes to robbery and the legalized form of banditry known as taxation.

I see no point in being pragmatic about it either, as one will only be wasting ink or breath, when attempting to argue rationality and ethics with an egalitarianist, whose primary principle is not an abstention from coercion and violence.

Also, the whole concept of measurement requires an objective baseline for the purpose of comparison, which is precluded in this case by the fact that intersubjective comparisons of utility are quite worthless. Even though we can express our costs in monetary terms, they are valid for only the subject, and only at the time of action.

The best measure of

The best measure of progressivity is to compare cumulative distribution of income versus cumulative distribution of tax burden. So, for instance:

Old tax regime: top x% earn I(x)% of all income but pay t1(x)% of all tax.

New tax regime: top x% earn I(x)% of all income but pay t2(x)% of all tax.

If t2(x)>t1(x) across all x<100%, then clearly the new tax regime is "more progressive" than the old regime.

The only problem -- which is ancillary to the question -- is that, in a time series analysis, I(x) may not be a univariate (i.e., fixed) function (e.g., it might change significantly in a recession).

The whole "subjective

The whole "subjective utility" thing is a social construct designed by rich people to make the poor stay poor. Everyone knows that rich people don't need yet another buck as much as poor people. The Austrian school is just obscurantism in defense of the rich.

I'm taking the piss of course with the above statement. But there is a bit of this attitude among left libertarians, a camp of which I'm an increasingly a fan. Call it populism.

Dain, The whole "objective

Dain,

The whole "objective utility" thing is a social construct designed by [insert egalitarian-minded group which know squat about economics] which will make the poor even poorer, but will yet neglect the fact that their wishful-thinking policies are much the cause of so much needless suffering. The only consolation that they will have, is that they will think their struggle is a noble cause, so that they can give themselves a nice pat on the back for their unblissful ignorance.

Everyone [may pretend to] know that rich people don’t need yet another buck as much as poor people, but yet this says nothing on the fairness of theft, two terms that do not belong in the same sentence. The Chicago/Keynesian/Marxist school is just obscurantism in defense of fleecing the rich for popular, political vote-buying, and in essense a state-sponsored advertisement to jusitify "an advanced auction of stolen goods."

I'd like to apologize to the

I'd like to apologize to the blog editors and readership, for allowing myself to succumb to writing an ad hominem in response to the same. In the future, I will try to better control my tongue, er... fingers, and will avoid responding to what I'm now thinking was just a troll.

Dain's not a troll.

Dain's not a troll.

Yea, it's all good. I was

Yea, it's all good. I was just seeing what kind of response I'd get. Is that called "trolling"? Learn something new everyday...

I'm more or less in

I'm more or less in agreement with iceberg's first comment. Taxation is theft, and arguing about the degree of progressivity as if it equalled the degree of fairness is pointless.

Brandon: I can't read Mankiw's article (the site is down right now or something), but at least the part that you quoted doesn't discuss "progressivity". It discusses "betterness", saying that it's not clear which of the three perspectives is better, leaving room for anyone to claim that a particular tax cut is better for the rich or better for the poor, and thus by implication "better" (because the standard for "better" in the popular political discussions seems to be: if it's good for poor people then it's good but if it's good for rich people then it's bad).

I think "progressivity" is a straight-forward and uncontroversial measure, more or less equal to the slope of the curve plotting income vs. percent of income paid as taxes. What's in dispute is "fairness". Liberals say a progressive tax is fair, conservatives (well, some of them, anyway) say a flat tax is fair.

I say no tax is fair.

What's interesting is that the Bush tax cuts were "good for the rich" because of Mankiw's reason number one, even though they made the system more progressive (reason number three) and thus were presumably "bad for the rich". Anyone arguing simultaneously against the Bush tax cuts and for progressive taxation (as liberals do) is either deeply confused, or illogical, or is deliberately exploiting those who are confused and illogical to score political points.

The main problems with

The main problems with trying measuring progressivity accurately or fairly:

1. It's an abstract concept, and therefore has no "measure" only suggestive statistics. Just like the "distribution of income" is a statistical artifact constructed from a billion individual transactions, so the "progressivity of a tax" is not a property of the tax itself but rather a philosophical evaluation of it.

2. Most such discussions take as given that greater progressivity is desirable. This is a normative choice and inevitably clouds any and all thinking on the matter. In my view progressivity is a bug rather than a feature and I freely admit that for the purposes of argument this will lead me to define it in such a way as to make it look as nasty as possible. The typical view comes at it from the opposite angle, attempting to cast it in as good a light as possible. Realize this in light of #1 above and we see how futile the exercise is.

For example we could cut the

For example we could cut the poor guy’s taxes by $1,000 (5% of his pre-tax income) and the rich guy’s taxes by $12,000 (6%). I don’t see how any metric of progressivity which suffers from this flaw can be considered valid.

There is a way. All you have to do is allow negative numbers. I.e., welfare. That is, somebody could argue (and people do argue) that a tax cut of $X for a corporation is "corporate welfare" (somebody did that recently in a Usenet discussion I participated in). So someone could say, "Reducing this corporation's/rich man's tax by $1 is welfare, is handing him $1 that doesn't really belong to him because that money is his proper due to society yadda yadda, and so to be fair, his poor neighbor who previously was not paying taxes must now be given $1 to match the $1 that the rich man is getting".

I don't agree with the idea that taxation is not theft (I think taxation *is* theft), I don't agree with the idea that a tax cut is "welfare", so don't shoot the messenger. Once you allow that taxes are not theft, then you are open to the claim that a tax cut is a gift from the government to the taxpayer, and so you are open to the claim that in order to be fair, such a tax cut must be accompanies by an outright welfare check to a poor man.

The only way out of this bind is to allow that taxes are theft. And I do that, and so I am not in that bind.

I'm trying to follow this

I'm trying to follow this "taxation is theft" meme to it's logical conclusion.

If taxes are by definition theft, then do you see no legitimate role for government whatsoever? Or do you have some other way to pay for policing, courts, etc.? Are you assuming ancap, where everyone pays for their own, and there are (with hope) good systems for getting similar economies of scale on a private basis?

It looks "taxation is theft" is logically equivalent to a claim that pure ancap is the only ethical (natural? unquestioned?) form of societal organization.

Am I in the ballpark?

Michael, I think You're in

Michael,

I think You're in the ballpark. I've never known anybody to say taxation is theft who wasn't an anarchist.