
Piketty, inequality and volatility: How can r exceed g? - zootar
http://www.chrisstucchio.com/blog/2014/piketty_inequality_and_volatility.html
======
jfager
I'm only through the introduction right now, but assuming that it's
representative of what's coming later, Piketty isn't saying 'r > g' as
mathematical fact, he's saying ' _when_ r > g, divergence in the distribution
of wealth happens' and 'empirically r has frequently been and is again moving
towards > g'. And his concern with this is the same as the problem you state,
that r > g implies, eventually, r = g, which translated back to English means
economic activity devolves into rent paying.

Quoting:

"When the rate of return on capital significantly exceeds the growth rate of
the economy (as it did through much of history until the nineteenth century
and as is likely to be the case again in the twenty-first century), then it
logically follows that inherited wealth grows faster than output and income...
Under such conditions, it is almost inevitable that inherited wealth will
dominate wealth amassed from a lifetime's labor"

"Forces of convergence also exist, and in certain countries at certain times,
these may prevail, but the forces of divergence can at any point regain the
upper hand, as seems to be happening now, at the beginning of the twenty-first
century"

"My conclusions are less apocalyptic than those implied by Marx's principle of
infinite accumulation and perpetual divergence... In the model I propose,
divergence is not perpetual and is only one of several possible future
directions for the distribution of wealth"

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themgt
First off you're I believe incorrectly using g rather than r in your "how
volatility changes things" section. Secondly you seem to be assuming not only
that r will be more volatile than g, but that it will be so much more volatile
that medium/long-term r will drop enough to match g.

And lastly you're ignoring the actual history Piketty is describing, in which
dynastic families very often tend to accumulate and pass on vast empires of
wealth. When your speculative theory doesn't match reality ... perhaps it's
time to reconsider the theory.

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zygomega
> To begin, I’m going to illustrate a mathematical fact.

'growth' rate is likely to be a geometric constant, not an arithmetic one. A
0% growth rate followed by a 6% growth rate is not 3% geometric growth on
average. 100% growth followed by -100% growth isn't 0% growth on average.

Many a quant manager has gotten rich off of spruiking the reverse of this
story.

The market price of capital is the discounted value of future production
(which will be equal to consumption). If the discount rate declines, then the
price of capital goes up and at least some of this effect finds its way into
measures of capital growth (and capital return).

Windfalls accrue to the current generation of risk capital holders and, to
some extent, the current generation of consumers. Losers are everyone else -
current savers and future generations.

~~~
igonvalue
> 'growth' rate is likely to be a geometric constant, not an arithmetic one.

I agree. I find it unlikely that Piketty's thesis rests on such an elementary
mistake as interpreting arithmetic means as geometric ones. Academic
economists are basically applied mathematicians. (In the book, Piketty
actually bemoans the fact that economists are preoccupied with proving
mathematical theorems at the expense of engaging with the real world.)

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lifeisstillgood
Is it just me or does the economics-mathematics remind anyone else of doing
three or four decimal place calculations at school after measuring things with
your hand because the ruler got broken.

It is an old argument but really came home in that article.

------
arghbleargh
Disclaimer: I have not read the book either.

One thing I don't understand about the r and g thing is how it makes sense to
compare these two values at all. Isn't capital a measure of accumulated
wealth, while GDP is a measure of wealth produced in a certain unit of time?
For example, what if we just maintained a perfectly steady GDP that exceeded
our consumption needs; wouldn't that yield a positive r and explain r > g?
Does someone who read the book have a better understanding of exactly what
these two numbers mean?

P.S. I find it implausible that Piketty would make such an elementary mistake
as the arithmetic mean vs. geometric mean issue discussed in the article. But
again someone who has actually read the book should weigh in.

~~~
yummyfajitas
For the record, I (author here) also think it's unlikely Piketty simply
ignored it. I think the reviewers of the book are either ignoring it or
failing to understand it.

See this comment I wrote on HN discussing the book review which inspired this
post:
[https://news.ycombinator.com/item?id=7619412](https://news.ycombinator.com/item?id=7619412)

 _...most reviews of Piketty, have to be misrepresenting...r > g...I don't
think it's actually what Piketty is pushing._

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wazoox
There is a very extensive (60 pages or so) analysis of the book in french
here:

[http://www.les-crises.fr/piketty-le-capital-1/](http://www.les-
crises.fr/piketty-le-capital-1/)

[http://www.les-crises.fr/piketty-le-capital-2/](http://www.les-
crises.fr/piketty-le-capital-2/)

[http://www.les-crises.fr/piketty-capital-3/](http://www.les-
crises.fr/piketty-capital-3/)

Check the unforgiving and long conclusion here:

[http://www.les-crises.fr/piketty-capital-4/](http://www.les-
crises.fr/piketty-capital-4/)

------
davidiach
Nassim Nicholas Taleb has also debunked the math in Piketty's book. Here is
the paper:
[https://docs.google.com/file/d/0B8nhAlfIk3QIbzRrRkhhc1RNY0U/...](https://docs.google.com/file/d/0B8nhAlfIk3QIbzRrRkhhc1RNY0U/edit)

~~~
alnafie
One of the best and most accessible pieces I've ever read on inequality is
PG's essay on the subject:
[http://paulgraham.com/gap.html](http://paulgraham.com/gap.html)

My all-time favorite quote on inequality: "You need rich people in your
society not so much because in spending their money they create jobs, but
because of what they have to do to get rich. I'm not talking about the
trickle-down effect here. I'm not saying that if you let Henry Ford get rich,
he'll hire you as a waiter at his next party. I'm saying that he'll make you a
tractor to replace your horse." -PG

Also see:
[http://paulgraham.com/inequality.html](http://paulgraham.com/inequality.html)

~~~
czr80
So the thesis is that technological progress relies on us incentivizing people
with the hope of extreme wealth?

Seems unlikely - for one counter-example, a large part of progress in society
rests on investment in basic research, and most of the scientists engaged in
that work have no real expectation that they will get rich.

~~~
ArkyBeagle
I don't think any of that is necessarily true. The Henry Ford that we know of
is a myth, an aggregation of ... "process engineers" and engineers-in-general
that worked for him, not to mention the army of line workers. He's a "macro".

The real Henry Ford was modestly ... nuts. But in a _good_ way... well, mostly
a good way... the Rouge Plant is the Neuschwanstein Castle of American
industry...

But who gets identified with a machine that is as iconic as a horse? Perhaps
you have to have know someone who used a 40-horse Ford in anger for decades -
there were a handful of my paternal grandfather's brothers, who I knew, who
did ( guys who were fully adults at the onset of the Depression) . As a
suburban brat raised by somebody who was not going back to the farm, they were
like priests of the Old Religion.

In order for a narrative to make any sense, we have to have a two-legged
archetype. The truth is closer to "we (collectively) stumbled into using
tractors and Haber-Bosch* process related fertilizers to make Malthusian
scarcity/crises go away as a potential force of history."

*yes, that's James Burke's "Connections" voice you hear there.

Of course, the equal but opposite counter to that is these things also made
way for machine guns and tanks. Might some extra CO2 outta it; we're not 100%
sure...

Even modest wealth has a lot of fantasy tied up in it.

The whole point of markets is to enslave Vast quantities of inscrutable
information. When we make up stories about this information, we should expect
to fail.

I don't think it's been said better than by Talking Heads - "You may find
yourself behind the wheel of a large automobile You may find yourself in a
beautiful house with a beautiful wife You may ask yourself, well, how did I
get here? "

If anything, what hubris it is to think we can shape that to order.

------
ivan_ah
If I understood correctly (me too judging only from secondary sources) Piketty
is concerned about uneven distributions---the relative share of the total pie
of all that is measurable economically (GDP+capital) is becoming more
concentrated in very few hands.

He's an economist and I don't generally trust economists' calculations[1], but
the concern he raises relates more to the fact that the long-tail wealth
people are better at hiding their revenue offshore. As more of the pie goes to
them, there is less tax revenue for the state.

He proposes more International laws be put in place to prevent off-shore
stashing (Hollande's of the world unite!). Also, some of his research papers
are about "optimal" inheritance taxation.

I find these to be interesting lines of thought---not so much as they will
happen, but because it brings the 0.001 into the lime light, and I bet they
don't like that at all...

__________

[1] my reasons being that you can pretty much use _any_ model and it _might_
come out true ;)

~~~
rtpg
It's not just inequality, he also fights the statement " everyone's getting
richer, even if inequality's increased"

------
igonvalue
I think there are two flaws in your premise.

First, I think Piketty is merely making the claim that whenever r is greater
than g, inequality tends to increase.

From the book:

> When the rate of return on capital exceeds the rate of growth of output and
> income, as it did in the nineteenth century and seems quite likely to do
> again in the twenty-first, capitalism automatically generates arbitrary and
> unsustainable inequalities that radically undermine the meritocratic values
> on which democratic societies are based.

Second, r is actually the return to capital, not the "growth rate" of capital.
That is, the owners of capital can (and will) choose to spend some of it
rather than reinvesting all of it. You can imagine a steady state where the
return to capital is tremendous but wealthy oligarchs are also profligate and
reinvest only enough so that their investment keeps pace with g.

~~~
yummyfajitas
Your second point is an interesting theory, but seems unstable. What if one
capital owner decides to consume a smaller amount of his wealth, and thereby
increase his share of the economy?

Eventually he would rule the world.

~~~
igonvalue
Yes, I'm not saying that's where society is actually headed. It's just a
hypothetical to illustrate how r can diverge from capital's "growth rate". To
rephrase the last sentence, "In the extreme case, you can imagine a
hypothetical equilibrium where..."

------
carlob
I read this as an overly complicated statement of Jensen's inequality [1]: if
f is convex <f(x)> ≥ f(<x>). Where <> denotes the expected value.

This can be used to prove that the geometric mean is always smaller or equal
than the arithmetic mean; obviously equality holds for x constant. So
_volatility drag_ is really just restating this very fundamental inequality.

[1]
[http://en.wikipedia.org/wiki/Jensen's_inequality](http://en.wikipedia.org/wiki/Jensen's_inequality)

------
bhouston
I am not sure I trust someone disproving a book that they didn't read. I mean,
come on.

------
jzila
From the article, "Suppose that r and g are both fixed quantities which do not
change over time." This is a straw man that I didn't get in the book. The idea
I understood from Piketty is that whenever g is greater than r, _no matter how
different_, inequality grows. Since you can have g > r, with g approaching r
with time (g = r at infinity), capital simply continually takes up a larger
piece of the economic pie.

~~~
yummyfajitas
I only got that "straw man" from the book reviews.

It's incorrect that r > g implies inequality grows. You need r - volatility >
g.

~~~
mrow84
So is your thesis that inequality will increase in periods of economic
stability, where the volatility is low?

Also, can you provide a ballpark figure for (abs(r - g) / volatility)?

(edited to improve phrasing)

~~~
yummyfajitas
_So is your thesis that inequality will increase in periods of economic
stability, where the volatility is low?_

Yes. Some data vaguely suggesting this is directoinally correct:

[http://www.nytimes.com/2011/12/13/business/economy/recession...](http://www.nytimes.com/2011/12/13/business/economy/recession-
crimped-incomes-of-the-richest-americans.html?_r=2&pagewanted=all)

Recessions tend to hurt the rich the most.

I don't have a ballpark figure - I'd need to dig into Piketty's data and it
would take a while to come up with that. I'm kind of hoping someone who
actually read the book can tell me it's in there, since I think it's a bit
crazy that everyone is talking about Piketty's book without mentioning this.

~~~
mrow84
Take individual income as (l + c), where l is the return on labour, and c is
the return on capital, and assume a recession reduces both. The rich are rich
(long term) through large c, not a balance of l and c, and so as a group they
will inevitably be hurt the most during a recession. The only way this
wouldn't be the case is if the reduction in returns to capital was negligible
which, given what recessions are, seems unlikely. Also, whilst the rich are,
undoubtedly, proportionally hurt the most be recessions, I presume you
wouldn't claim that they were hurt the most in absolute terms (on average)?

And a follow up to my previous question: I realise it's difficult to guess a
figure for (abs(r - g) / volatility), and it inevitably varies with economic
conditions, but I'm interested in your sense for how it changes. Are you
suggesting that it is mostly less than 1, mostly greater than 1, or that it
spends roughly equal amounts of time greater than and less than 1?

edit: Sorry, after re-reading my post I realise that my use of absolute could
easily be misinterpreted - I meant that although those with large capital
portfolios will lose proportionally more of their income, they will still, on
average, have significantly more wealth in absolute terms than those who
started with small capital portfolios; and so the suggestion that they are
'hurt' more is, itself, fairly misleading.

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RivieraKid
1\. Of course that over the long term, r will become equal to g (well, it's
actually mathematically possible that r > g forever). But the point is that we
don't want to live in a world where 90% of the GDP goes to people who own
capital.

2\. The volatility argument says, that even if r = g over the long-term, the
per-year average of r can be bigger than the per-year average of g. What
Piketty's claim does it debunk?

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bayesianhorse
Maybe I am naive, but if g is the growth rate of an economy, and r the growth
rate of a smaller part of it, doesn't this mean that if r>g the portion of
capital growing at rate r increases? This would also mean that g increases.

~~~
RivieraKid
r can be positive and g negative at the same time. Total growth consists of
labour and capital growth. Piketty's point is that capital is growing faster
than labour – if that continues forlong enough, we can end up in a world where
99% of income goes to owners of capital.

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apsec112
In a fast-paced, industrial society, like the one we live in, long dynasties
tend to get wiped out by high volatility. I don't know exactly what happened
to the aristocrats of Russia as of 1910, or the businessmen of Germany as of
1935, but it can't have been good. Likewise for China, France, Poland,
India...

In a stagnant, agricultural society, like medieval Europe, dynasties tend to
get weighed down by the problem of reproduction. If you've inherited a
fortune, there's no reason not to have ten kids, especially before birth
control. And those ten kids will then want to fight over or divide the family
fortune, and so on with their kids, etc. Queen Elizabeth is a descendant of
Charlemagne, but so are millions of others whose distant ancestors were
slightly less lucky in the power game.

~~~
bayesianhorse
The businessmen of Germany from 1935 eventually got to use slave labor to
build lucrative weapons... Quite a few corporations and individuals survived
the war.

~~~
_delirium
The Krupps are perhaps the most famous. They profited handsomely from both WW1
and WW2, managed to escape losing their fortunes during denazification (for
unclear reasons), and the family still controls large amounts of wealth today:
[https://en.wikipedia.org/wiki/Krupp](https://en.wikipedia.org/wiki/Krupp)

~~~
bayesianhorse
I have a personal beef with the "profiting from war" story. In the particular
case of Krupp it stands to reason whether or not spending for the war, getting
their factories bombed to the ground and the lost opportunity for peace time
development (and even peacetime production of arms) wasn't making the world
wars a lot less "profitable" than a peace would have been. Leaving aside the
discussion if peace throughout the 20th century would have been possible in
slightly different circumstances.

------
davidgerard
tl;dr: "I haven't read the book, but I'll disprove the headline from first
principles without looking at the data."

Yay praxeology! Gives so much more pleasing results than the annoying "look at
the world" step, doing the damned legwork with the data, as Piketty did.

