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

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"

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.

'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.

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

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.

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:

http://www.les-crises.fr/piketty-capital-4/

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 ;)

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.

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

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?

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.

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.