Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Piketty, inequality and volatility: How can r exceed g?

chrisstucchio.com

Post reply on HN
Print view View original

11–20 of 46 posts

Re: Piketty, inequality and volatility: How can r exceed g?

#11

Post by yummyfajitas »

arghbleargh wrote: post #2

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 >…

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.

Re: Piketty, inequality and volatility: How can r exceed g?

#12

Post by dojomouse »

jzila wrote: post #7

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.

Re: Piketty, inequality and volatility: How can r exceed g?

#13

Post by yummyfajitas »

jzila wrote: post #7

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 only got that "straw man" from the book reviews.

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

Re: Piketty, inequality and volatility: How can r exceed g?

#14

Post by carlob »

I read this as an overly complicated statement of Jensen's inequality [1]: if f is convex ≥ f(). 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

Re: Piketty, inequality and volatility: How can r exceed g?

#15

Post by 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.

Re: Piketty, inequality and volatility: How can r exceed g?

#17

Post by 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.

Re: Piketty, inequality and volatility: How can r exceed g?

#18

Post by igonvalue »

zygomega wrote: post #17

> 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 fu…

> '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.)

Re: Piketty, inequality and volatility: How can r exceed g?

#19

Post by dojomouse »

yummyfajitas wrote: post #13
jzila wrote: post #7

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 only got that "straw man" from the book reviews. It's incorrect that r > g implies inequality grows. You need r - volatility > g.

No, volatility can increase as well as decrease returns.
Post reply on HN