Thursday, May 3, 2007

A Simple Objection To Greg's Height Tax

Greg is getting some press for his and Matthew Weinzierl's working paper on height taxation and its affront to standard notions of equity. Yet, I think the paper falls short when it fails to recognize the importance of the height-income effect mechanism.

Here is a simple example that shows why the mechanism is relevant. This is written in a tone familiar to economists. If there is enough interest among non-economists I can do a more thorough explanation.

Suppose that base income is drawn from a normal distribution. Then nature distributes a bonus to 50% of all tall people. This introduces a strong height-income effect.

Wanting to correct for this economists suggest that the social planner institute a tax on the tall and redistributes the income to the short.

However, she rejects the proposal because it fails her Rawlsian analysis.

The distribution of income for tall people conditional on not have received the bonus is the same as the distribution of income among the short. Therefore, the poorest tall person has roughly the same income as the poorest short person. Therefore, if she takes income from all tall persons the poorest tall person will likely become poorer than the currently poorest person.

Since her objective function is max min(all agents) the tax decreases social welfare.

12 comments:

Anonymous said...

dear karl,

it seems to me like the majority of your posts relate to something greg mankiw posted on his blog; you're typically refuting whatever greg says, or adding your take on whatever greg says; i like your blog, but i think all the readers here would agree that we are more interested in what you have to say (meaning, other than refuting or commenting on mankiw posts). for instance, what about that paper you said you were writing that was inspired by this blog? your readers would like to see that

Karl Smith said...

Thanks for you comments. You make a good point.

YouNotSneaky! said...

Of course the key here is that Rawls != utiliterianism.

Karl Smith said...

Then what it implies is that our innate sense of fairness may be a little more Rawls and a little less Mills.

Also, I would add that there is some set of weights that will make the utilitarian outcome equivalent to the Rawlsian. In fact if you know who the least well off person is then you just give her all the weight.

YouNotSneaky! said...

Well, I meant utilitarian in the classical sense of "equal capacity for pleasure" - i.e. equal weights.

Also I think this is wrong:

“The distribution of income for tall people conditional on not have received the bonus is the same as the distribution of income among the short. Therefore, the poorest tall person has roughly the same income as the poorest short person. Therefore, if she takes income from all tall persons the poorest tall person will likely become poorer than the currently poorest person.”

The key here is that the Rawlsian economist (or the taxing authority) either has no way of knowing who the poorest person is, or does. If she knows, then just redistribute income by taxing others to that person – why go through taxing height? If she doesn’t know then the probability that the poorest person is short is higher then the probability that the poorest person is tall (“Proof”: Draw an income distribution – label it “short people”. Now draw another one which looks exactly like the first one except it is shifted right and label it “tall people”. They gotta cross. So for a particular low level of income the density of short people at that income is higher than the density of tall people at that level of income.) If the only variable – the instrument – that the Rawlsian economist has to go by is height, and height is correlated with income then in expectations you want to transfer income to (some) short person.

Greg’s and Matthew’s point is somewhat different than this though because there income is not just determined by nature (ability) but also by effort. So you observe income but not how it is determined by these two sources. And you want to tax ability – since, in essence, it’s inelastically supplied – but not effort, since that’s where distortions come from. So in that case a tax based on BOTH income and height is optimal.

Like I said on my blog, I don’t see what the problem is with this proposal, given that one doesn’t have a problem with taxing ability in the first place. I think though that a lot of people DO have a problem with taxing intrinsic ability – what if Michelangelo had to pay a tax every time he picked up a paint brush? – and that’s why the proposal seems unfair. That’s the point where the rabbit is stuffed into the economist’s hat.

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