Piketty, inequality and volatility: How can r exceed g?
chrisstucchio.comI'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"
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.
> 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.
> '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.)
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.
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.
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
...most reviews of Piketty, have to be misrepresenting...r > g...I don't think it's actually what Piketty is pushing.
He explains all the terms at the start of the book. He has his own definition for capital which also includes real-estate etc...
OP's post is just an argument against a straw man. BTW. Piketty also says that the problem with modern economics is too much focus on fancy math.
It's pretty simple if I understand it correctly. GDP = total income in the economy = income that goes to labour + income that goes to owners of capital.
g is the absolute growth of GDP, r is the absolute growth of income that goes to capital. If r > g, then the share of income that goes to labour is shrinking as a ratio of GDP.
Another problem is that the income that goes to labour is increasingly unevenly distributed.
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-2/
http://www.les-crises.fr/piketty-capital-3/
Check the unforgiving and long conclusion here:
Nassim Nicholas Taleb has also debunked the math in Piketty's book. Here is the paper: https://docs.google.com/file/d/0B8nhAlfIk3QIbzRrRkhhc1RNY0U/...
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
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
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.
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.
Piketty's worry is not about earned wealth; his worry has to do with inherited wealth.
Disclaimer: I don't mindlessly believe everything pg says just because he is a co-founder of YC.
"Replacing a horse with a tractor with a horse" is 'g'. Any action that reduces the incentives of the next Henry Ford to create will reduce both 'r' and 'g', and have very little effect on the relationship between r & g. Piketty realizes this. It's the heirs of Henry Ford, who did nothing but get lucky in the genetic lottery, who have the most to worry from broad adoption of Piketty's book. It may be the actions of Bill Gates and everybody else who signs and propagates the giving pledge who do the most to prevent the doom that Piketty prophesies.
Piketty's book is about rentiers and rentier capitalism; the comment you quote is an intellectually weak justification of why riches do exits. In the real word is not like that.
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 ;)
It's not just inequality, he also fights the statement " everyone's getting richer, even if inequality's increased"
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.
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.
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..."
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.
I am not sure I trust someone disproving a book that they didn't read. I mean, come on.
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.
I think you've reversed r and g vs ops notation, but yes, agreed. R can exceed g with no trouble, right up to the point where all economic growth is directly absorbed by capital accumulation (or whatever terminology you want to use for piping an annual measure into a cumulative one) at which time g must equal r... a fact of small comfort to the millions of people who, empirically, are getting a tiny slice of pie to live off. At this point volatility may well rear up and change the returns to owners of capital in the form of a revolution (as has happened again and again and again), but that's hardly an ideal form of society. You'd think if we know the mechanism and the result we could implement a fix. On the other hand, if you'd been paying any attention at all to climate change mitigation actions you'd probably be unsurprised that we haven't.
I only got that "straw man" from the book reviews.
It's incorrect that r > g implies inequality grows. You need r - volatility > g.
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)
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...
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.
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.
No, volatility can increase as well as decrease returns.
Downward volatility hurts you more than upward volatility helps you (on average). That's where the -sigma^2/2 term comes from.
Yes, so you could write
r + (amount that upward volatility helps) - (amount that downward volatility hurts) > g
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?
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.
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.
Yes, that's entirely the point of the first section.
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.
You really think that? There are a lot of families that got rich in the early 20th in the US who are still controlling huge stakes in production of the country. After a 100 years I'd start calling those dynasties.
Countries you cited have had the bad luck of having much of their means of production wiped out through war/political turmoil. But the places that haven't blown up... well the wealth doesn't seem to be moving as fast as you seem to imply .
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.
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
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.
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.