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Wednesday, May 28, 2014


Somebody named Chris Giles has published a big attack in the Financial Times on Thomas Picketty's data calculations, writing that "unlike what Prof. Piketty claims – wealth concentration among the richest people has been pretty stable for 50 years in both Europe and the US."  Paul Krugman remarks about this criticism, "OK, that can’t be right," and proceeds to get into the weeds a bit further than I am competent to follow.  Why can it not be right?  Using the data I dredged up on income quintiles for my "New Conversation," I carried out a little thought experiment which convinced me that Krugman's reaction is correct.  Thought experiments, I should explain, are what philosophers do when the alternative is actually going out and finding facts.  Thirty years ago, the thought experiment du jour was "brains in a vat," Hilary Putnam's gift to the philosophical world.  The latest thought experiment clogging the journals is "the trolley and the fat man" [don't ask]. 

Let us go back to that breakdown of household income by quintiles.  The upper bound of the lowest quintile, you will recall, was $20,260 in 2011.  That year, there were 121,084,000 households in America, so the lowest quintile was roughly 24 million households, all of which had income that year of $20,260 or less.  I don't know exactly how the actual incomes were spread between zero and $20,260, but let us assume that six million of them [one-fourth] checked in at $20,000 a year.  [Right away, you can see how much easier it is to carry out thought experiments than it is to go looking for data.  By the way, the most famous thought experiment in the history of science was Einstein's gedankenexperiment that led to the Theory of Relativity, so don't knock all thought experiments.]   Simple multiplication tells us that those six million households had total annual income of $120 billion.

Up in the stratosphere at the other end of the income spread, it took roughly $10 million a year in income to shoe horn your way into the top one one-hundredth of one percent of households.  [You can find the figures here].   One one-hundredth of one percent of all households is 12,100 households [division this time, not multiplication].  At ten million apiece, this group of deserving worker bees took in $121 billion, which is just about as much as those six million slacker households down in the pits.

Now, let us think about the saving habits of these two groups.  This will lead us to see why Krugman's immediate response to the Giles claim was, "That can't be right."  How much do we figure a $20,000 a year household saves each year?  My instinctive response is a snort of unbelieving laughter.  Saves?  We might more plausibly ask how much more each $20,000 household goes into debt each year!  Well, don't they put anything away? 

I am reminded of a poignant little vignette from my first year of marriage to Cynthia Griffin, which was 1962-63.  Cynthia's father was then a vice-president of Sears, Roebuck and Co.  Jim Griffin did not like me, so for the first several years of my courtship of Cynthia he did not speak to me at all, but after the wedding -- held in Cambridge, MA because I was a scandal to the faithful in Jim's seriously Catholic circles -- he relented to the extent of giving me occasional pieces of advice, as well as a collection of his old ties [the deeper Freudian significance of which was not lost on me.]  During one of the Griffins' infrequent visits to our small apartment in Hyde Park, where I was teaching at the University of Chicago, Jim took me aside and said, "Bob, let me give you some advice.  Every month, put a little bit away in stocks -- two or three hundred -- and don't touch it.  Over the years it will grow."  I was touched by his solicitude, but unfortunately was unable to take the advice.  At that time, I was making $10,000 a year as an Assistant Professor [no kidding], and "two or three hundred a month" was roughly a quarter of my annual before-tax income.

I am tempted to guess that when increasing credit card debt is balanced against money salted away in a savings account, the typical $20,000 a year household has net savings of zero, but let us give Chris Giles the benefit of the doubt and assume that those 24 million households manage to save 1% of their income each year.  That is $200 per household put into savings rather than spent on food for the children or for the co-pay on medicine that they really should be taking.  Well, $200 isn't much, but when six million households manage to save that much, it adds up -- to $1.2 billion, to be exact.

Now turn your attention to the roughly 12,000 ten million dollar a year households.  How much do you suppose they save?  If Giles is right, they also save, as a group, $1.2 billion, which works out to $100,000 a year for each household.  Is this plausible?  Hardly!  Remember that as these folks pay off their mortgages on their first, second, and third homes [not to mention the car elevator], they are saving an amount equal to the reduction in principal.  Do they have 401(k)s?  Are they buying stock?  Surely they manage to save half a million of the ten million, even in the magical year when they throw a five million dollar wedding for the family daughter.

Well, if they do succeed in paring enough cheese and scrimping on enough necessities to salt away 5% of their income, then at the end of the year they will have saved $6 billion, which means that at the end of the year they will, as a group, have increased their total wealth by $4.8 more than the six million homes at the bottom of the heap.

Over time, this surplus of accumulated wealth really adds up.   As the late unlamented Senator Everett Dirksen of Illinois said during a floor debate about the annual budget, "a billion here, a billion there, and pretty soon you have some real money."

It is transparently obvious that soaring income inequality, which Giles does not dispute, must lead to soaring wealth inequality as well, which was, after all, the central point of Piketty's book.


Chris said...

"the trolley and the fat man" [don't ask]

But it's so much to ask people for their response to this problem :)

Chris said...

so much *fun

Robert Paul Wolff said...

I have always wondered whether Putnam's brain in a vat was the inspiration for THE MATRIX. Will there be a movie emerging from the fat man and the trolley? Maybe MISSION IMPOSSIBLE XI.

Chris said...

I know in The Matrix Neo hides his stash of hacker disks in a copy of Jean Baudrillard's Simulacra and Simulation. That was the book the creators claim inspired The Matrix. I believe JB said they didn't properly understand his book if that movie was their inspiration.

Robert Paul Wolff said...

Yes, I felt the same way about THE TEN COMMANDMENTS. :)

Jacob T. Levy said...

This proves too much, doesn't it? The thought experiment as stated doesn't even depend on increasing income inequality. What it seems to show is "*any* income inequality must lead to increasing wealth inequality," since even at static income inequality, the rich will save more than the poor, year after year.

But if things were that simple, presumably we wouldn't have needed Piketty at all.

Of course, there's a lot more to it-- losses as well as gains in the value of stocks or real estate are concentrated at the top; taxes and spending matter; new fortunes aren't typically the result of ordinary savings behavior; etc. But all of that means that, *regardless* of whether income inequality rises or not, it can't be axiomatic that wealth concentration increases.

Krugman's "that can't be right" is, and had better be, based on a sense of what various data have looked like for a generation, not on pre-empirical certainty about what *must* be true.

David Auerbach said...

Actually the Trolley problem originates in 1978. And I think it peaked (and piqued) a while ago. I think it's Dennett who has the funniest version of the brain in the vat; but of course the underlying epistemological issues go back to Descartes and I think that Putnam did a better job than René.

Robert Paul Wolff said...

I am afraid that shows how out of touch I am!

David Auerbach said...

Oh, everyone is in touch with that with which they're in touch.

i.e., different strokes for ...