[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.

[dojomouse]

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.

[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...

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.

[dojomouse]

No, volatility can increase as well as decrease returns.

[yummyfajitas]

Downward volatility hurts you more than upward volatility helps you (on average). That's where the -sigma^2/2 term comes from.

[dojomouse]

Yes, so you could write

r + (amount that upward volatility helps) - (amount that downward volatility hurts) > g