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Friday, August 18, 2006

Greg Mankiw : Krugman's a Flip-Flopper! [sound of glass wall breaking]

I'm putting together some materials for general interest audience for a class on social insurance I'm teaching this fall. I've had an easy time finding stuff written by economists more inclined toward the government-can-help/inequality-is-rising-and-that's-a-problem views. Because I want to add some materials from the other side of the political spectrum, I went to Greg Mankiw's blog.

As I scrolled through some recent posts, I came up with
this one from about a month ago
. In it, Mankiw criticizes Paul Krugman for
  1. Allegedly being wrong in Krugman's claim that
    "There's a persistent myth, perpetuated by economists who should know better -- like Edward Lazear, the chairman of the president's Council of Economic Advisers -- that rising inequality in the United States is mainly a matter of a rising gap between those with a lot of education and those without."
  2. Supposedly writing the opposite in his textbook ... copyright 2005, no less!
Well, I couldn't help myself. Here's the text of my comment (number 61, I believe):

Jonah B. Gelbach said...

Professor Mankiw

You criticize Paul Krugman for writing in the NYT that returns to skill are not the most important source of rising inequality, given his apparently contradictory statement in his 2005 textbook:

I suppose that Paul has changed his mind since this book (copyright 2005) was written. It is a bit harsh, however, for Paul to be so hard on Eddie for believing what Paul believed not very long ago.

This criticism shows an considerable chutzpah.

I used the first edition of your textbook to teach my principles class and well remember your reference to the Arthur Laffer/George W. Bush/GOP Congressional leadership types (you know, the ones who claim that tax cuts pay for themselves) as "Charlatans and Cranks".

Anyone who has followed this story knows that you removed this reference in later editions (can't remember if it was in the 2nd or not, but it sure wasn't in the third!). Interesting to note that shortly thereafter you became head of the Bush CEA.

So please, spare us the lectures about consistency---glass houses and stones, they don't go together so well.

On the merits, there really isn't any contradiction between the Lemieux paper you cite and the point Krugman makes in the NYT. There are (at least) two reasons for this fact. First, as you should know, Professor Mankiw, the CPS has top-coded data. Thus top earnings values (from which wages have to be recovered for salary workers) have to be adjusted somehow. Lemieux addresses this problem, as is typical in this literature, by multiplying topcoded values by 1.4. That method is not very likely to help you characterize right-tail concentrations.

The second problem is probably worse: as you no doubt also know, the CPS is only a sample, with roughly 50,000-60,000 households in a given month (even using the ORG samples gets you only 3 times that sample size). One can hardly hope to get a sense of what's going in, say, the top 1% of the overall income distribution of 100+ million households from such a sample---there just aren't going to be enough observations *there*, even if they weren't top-coded. [See JG Update below]

None of this is to criticize Lemieux's paper -- it just doesn't address the rising inequality point to which Krugman's NYT statement refers (if memory serves, anyway).

Krugman's point is that income inequality is largely being driven by the extreme right tail of the income distribution, not by the increase in returns to a few more years of education.

Thus it is not impossible for returns to skill to explain a substantial amount of the increase in wage inequality in a dataset like the CPS even as ever greater concentration of income and wealth at the very top totally swamps this effect, which I believe that this is Krugman's NYT point, tho it's been a while since I read it or his textbook.

On the concentration point, go look at Figure B of Piketty and Saez's THE EVOLUTION OF TOP INCOMES: A HISTORICAL AND INTERNATIONAL PERSPECTIVE (http://papers.nber.org/papers/w11955.pdf), and you will see that as an accounting matter, the growth in the top decile's share of income since about 1987 has been driven largely by a striking increase in the income of the top 1%. It's difficult to think of a story that (a) can explain this trend and (b) involves simple solutions like "get a BA" for low-to-moderate-income folks.

Jonah Gelbach

JG UPDATE: On reflection, I think this second point may not be so important, though its importance depends on the question being asked. 500 observations is often enough to estimate a mean with some precision, so if the data weren't top-coded it would probably be possible to estimate avg income in the top 1% reasonably well. On the other hand, the estimation of the top 1% cutoff point itself might still be challenging: it's known that the variance of the qth quantile of a distribution is q*(1-q)/(nf2), where n is the sample size and f is the density of the distribution at the qth quantile. in this case, f is likely very small, so one over its square is likely very big. Thus the precision of estimating the top 1% cutoff point from the CPS may well be quite low. Moreover, the earnings/income distribution above the top 1% cutoff is extremely right-skewed and has enormous variance. Thus it may be that very large sample sizes (i.e., much larger than usual Central Limit Theorem arguments suggest) would be needed to measure what's going on at the very top with any precision; this point is even more relevant when interest involves estimating trends from repeated independent cross-sections, in which case the variances essentially need to be summed across years. So my second point above might or might not be practically relevant if there were no topcoding (which there is, in any case).

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