Arnold Kling  

Taxation and Instrumental Variables

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Greg Mankiw links to a new paper that he co-authored with Matthew Weinzierl that says,

Should the income tax system include a tax credit for short taxpayers and a tax surcharge for tall ones? This paper shows that the standard utilitarian framework for tax policy analysis answers this question in the affirmative.

At first glance, this seems silly. On further reflection, it also seems silly.

I can't really follow the math in the paper--maybe because I'm only 63-1/2 inches tall. But it strikes me as sort of like an instrumental variables argument.

The theory is that income taxes are sub-optimal because they tax both ability and effort. A certain sort of social planner might want to levy a highly progressive tax on ability, as long as this tax did not adversely affect effort. I gather that this is called "optimal taxation" in some of the literature--it's not my field.

When you have a variable that is a combination of what you want and what you don't want, the big fad in economics these days is to use instrumental variables. So, if income includes both effort and ability, why not instead use an instrumental variable that is correlated with ability but not effort? Based on some previous research, height comes to mind.

The thing that economists seem to forget too often is that instrumental variables are not necessarily highly correlated with the variables for which they are instruments. Yes, there is a correlation between height and ability, but it is nowhere near perfect.

So, if you tax tall people and subsidize short people, what you will end up with is giving a real windfall to (the minority of) short folks who have lots of ability and a real penalty to (the minority of) tall folks who have minimal ability.

I think that one can reject that notion of taxing height without rejecting the "optimal taxation" framework. I think this is just a case where use of a weak instrumental variable causes more problems than it solves.

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CATEGORIES: Economic Methods

COMMENTS (6 to date)
GregN writes:

Mankiw quoted this passage from the paper.

This result has two possible interpretations. One interpretation is that individual attributes correlated with wages, such as height, should be considered more widely for determining tax liabilities. Alternatively, if policies such as a tax on height are rejected, then the standard utilitarian framework must in some way fail to capture our intuitive notions of distributive justice.

Assume the math works out, reject it on distributive justice grounds.

Matt writes:

He is full of bullshit on this.

We have shown over and over, especially at Delong's site, that the monopoly bank and government give first preference to wealthier groups. The system that Mankiw deals with is designed to tilt toward the rich.

Essentially the problem is that for wealthier groups, future asset prices are overvalued and interest rates subsidized. While for the less wealthy, future assets are undervalued and they pay an interest penalty.

You need not go far to realize this. The federal reserve and the conservative government still evaluate national missile defense at 500 billion when its real asset value is about a negative 60 billion.

The income tax is designed to balance this deliberate subsidy to the rich.

Matt C writes:

Arnold, if the tax is phased in and out, the problem you cite can be avoided.

They also should consider a "hot or not" rating system, perhaps carried out using a computer model to assess beauty.

Karl Smith writes:

I think Arnold is largely correct. The reason it seems unjust is because height is a poor correlate for ability.

The secondary question is why it that a poor correlate is worse than no correlate at all. I go into detail here.

TGGP writes:

Matt, are you claiming that we do not have a progressive tax system (taking into account both what the government takes and what it hands out)? I'm not sure how you would define "tilted toward the wealthy", for me it would be something more regressive than a head tax. Also, I think you are misreading Greg's post. He doesn't actually expect this tax to get passed and he is not seriously proposing it, it's just a goofy idea for egg-heads.

radek writes:

Is this a case of economists forgetting basic economics? You're always supposed to ask the question "compared to what?".

So, if you tax tall people and subsidize short people, what you will end up with is giving a real windfall to (the minority of) short folks who have lots of ability and a real penalty to (the minority of) tall folks who have minimal ability.

This isn't a good argument at all.
Sure Mankiw's height tax (am I the only one who's doesn't find this idea crazy, provided it's revenue neutral and all that?) would have the result described above. So would a tax based solely on income. The point is that if there's positive correlation between height and ability, the above situation is LESS LIKELY under a height tax than under the alternatives.

I think people might find this tax morally objectionable because, well, because they're probably uncomfortable with the underlying idea of taxing ability as well - just don't want to admit it to themselves.

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