## July 28, 2004

### Measuring Inequality-- Kaplow 2003 working paper

A bad back and access difficulties are slowing down my blogging, but I have gotten a bit more reading done. One stimulating paper is "Why MEasure Inequality?" by Louis Kaplow of Harvard Law. The theme is that standard measures of inequality in income distribution are flawed because they are not related to any purpose for which you would want such a measure. I've got lots of comments, enough of which are of general interest that I'll write some of them up here.

First, of all, some numerical examples would be useful. Imagine the following income distributions.

A1: Andrew gets 10 dollars per hour. Belinda gets 10 also.

A2: Andrew gets 11 dollars per hour. Belinda gets 1000.

By any measure of inequality, A2 is "worse". Yet most people would prefer society A2 to society A1. In particular, a utilitarian would say A2 is better, because everybody is better off, and a Rawlsian would say A2 is better, because Andrew, the poorest person, is better off in it.

It is true, though, that someone who values Utility and Equality as separate good things, and puts a very strong weight on Equality, would say that A1 is better. That would be true egalitarianism, which although it sounds silly to me, at least has logical consistency.

Most people, however, who say they think inequality is bad don't really mean it. Instead, they are confused utilitarians, who do not mind inequality per se, but think it is inefficient for one person to have a lot more income than another because the rich person doesn't get as much value from his last dollar as the poor person would.

If, however, you really do think inequality is unfair, you are on your way to preferring Society A1-- you should be willing to make everybodypoorer if that will reduce unfairness, after all. If something is evil, it is worth everybody paying something to get rid of that evil.

Muich of Kaplow's working paper is about situations where it is hard to define whether Society X or Society Y has more unequal income distribution. He starts off, though, by saying (roughly) that any definition should say that if distribution B1 is the same as distribution B2 except that if the richest person in B2 has transferred money to the poorest person to reach B1, then B2 is more unequal.

I would dispute even that. Consider the example below.

Society B1. The king has 750 in wealth. Each of 4 dukes has 55. Each of 1000 peasants has 5.

Society B2. The king has 950 in wealth. Each of 4 dukes has 5. Each of 1000 peasants has 5.

B1 can be reached from B2 by taking 200 from the king and splitting it equally among the 4 dukes. But is B1 a more equal income distribution? In society B2, the king is the only rich person, and there is otherwise perfect equality. Aristocrats are no richer than peasants. In daily life, most people are on terms of perfect equality, as a result.

In society B1, on the other hand, an aristocracy has emerged. The king is still vastly richer than anyone else-- that has changed very little. But now there are 5 times as many "rich people". It looks to me as if B1 is much more unequal.

This is not an unrealistic example. In international comparisons, we often will want to compare a tyranny == which levels people out-- to an aristocracy or a market economy-- which tends to create a large class of rich people.

This example illustrates Kaplow's big point nicely. To figure out a good measure of inequality, we have to think hard about what we mean by inequality, which will boil down to what kind of question we are trying to answer.

I've lots more to say, but I'll defer the rest till another day.

Posted by erasmuse at July 28, 2004 08:09 PM

http://www.rasmusen.org/mt-new/mt-tb.cgi/56

Eric:
I am quite sure you are wrong when you state that:

"Yet most people would prefer society A2 to society A1."

I'm not saying that they should or that A1 is better in some abstract sense, but I think the great bulk of survey research shows that as a matter of empirical fact, the substantial majority of people would rather live in A1 than A2.

You add: "In particular, a utilitarian would say A1 is better, because everybody is better off, and a Rawlsian would say A1 is better, because Andrew, the poorest person, is better off in it."

This is certainly true and simply adds to my conviction that neither utilitarianism or Rawlsianism has any close relation to how real people think or act. Nor can I see any compelling reason to GET people to act in these strange ways

Posted by: Chris Atwood at July 29, 2004 04:25 PM

Any particular surveys you have in mind, Chris?

I wonder why you think it strange. Spite is common, but would someone neutral (i.e., not Andrew himself, before knowing he is the one who only gets 11) really be willing to throw Belinda into poverty just because of the thought that Andrew ought to have company in misery?

It might help to think of the health analogy. Suppose we have a choice between two situations:

1. Andrew and Belinda both have their right legs and their left big toes amputated.

2. Andrew has his right leg amputated, and Belinda has all her limbs safe.

Is (2) an unjust situation? If so, does that mean social progress would be made by cutting off Andrew's left big toe and Belinda's left big toe and right leg?

I can see Andrew, if he were particularly vicious, being willing to cut off his toe if he could cripple Belinda as a result, but would anybody else approve?

Posted by: Eric Rasmusen at August 1, 2004 04:14 PM

Oops-- I see that I mixed up A1 and A2 in my discussion. I've fixed that in the original post, but keep in mind that Chris Atwood's comment was based onthe original mixed-up notation.

It's taking me a while to get the hang of Movable Type. Viewing a newly created post is lot harder than with my home-grown HTML. Moveable Type needs a very obvious button for Viewing a new post, rather than having to go to VIEW SITE and view the entire weblog. Maybethere is one and I haven't seen it yet, or maybe there is a way to customize. Or perhaps I should just try out the Preview feature.

Posted by: Eric Rasmusen at August 1, 2004 04:21 PM

I suppose which land Andrew is better off in depends on how much Charlie charges for a Ham and Cheese sandwich.

If Charlie charges \$1 in both A1 and A2 then Andrew seems to be better off in A2. If he charges \$1 in A1 and \$2.50 in A2 because Belinda is easily able, and willing, to pay \$2.50, then Charlie makes more money dispite the fact that Andrew doesn't buy one, and I suppose Andrew was much better off in A1 land.

Posted by: Steve at August 2, 2004 08:58 AM

Eric:
I don't have the studies in hand, but I know I've seen them. Which should be good enough for a blog comment box :^)

But in any case I'll stand by my assertion that most people do see "Utility and Equality as separate good things". Have you ever been out with some people and they decide to go to a restaurant you know you can't easily afford? Suddenly, although your income hasn't changed, it feels a lot smaller and more cramped.

The reality is Andrew's life would be far more humiliating in situation A2 than in A1 even with a slightly higher income. To claim that people don't put a value on relative wealth that is independent of absolute wealth is just absurd. Of course neither is absolute. People would be willing to accept deprivation of some relative wealth if the absolute wealth gain is large enough, and vice versa.

Part of the problem with your example is the absurdly large disparity between the two in your example and the absurdly small benefit to Andrew. If it was smaller, say
Andrew has 13, Belinda has 25,
people would probably feel differently about it.

The limb analogy is totally bogus and just confuses the issue. Limbs are part of normal human endowment. Income (when viewed under the "veil of ignorance" which you are evidently positing) is not. For me to deprive (our imagined) Belinda of the normal human body she would have a right to expect would of course be spiteful. But to deprive our imagined Belinda of income which (by the hypothesis itself) she would have no prior right to expect (remember we're designing society ab initio) is something else entirely. By contrast if you were to create ask, Belinda worked really hard and gets amazing skills and so EARNS 1000, should we deprive her of it to make Andrew happy, I think most people would say no.

Which raises the point that by speaking of income in the abstract, you're actually making egalitarian instincts stronger than they would be in a real world situation. Which again I would say is true of most people: they are more disapproving of wide disparities of income in the abstract (when they see no reason for them) than they are in the concrete (when they see all the possible reasons).

Posted by: Chris Atwood at August 2, 2004 03:57 PM