Notes and Finger Exercises on Thomas Piketty's "Capital in the Twenty-First Century"

Brad DeLong attempts to answer a question many people have been asking. Can the Summers claim of secular stagnation due to the real interest rate being too low be reconciled with Piketty's argument that the real interest rate is too high, high enough to generate rising inequality (larger than the growth rate of the economy)?:

Notes and Finger Exercises on Thomas Piketty's "Capital in the Twenty-First Century": When I look at Thomas Piketty's big book, I see one thing that he failed to do that I think he really should have done. A large part of the book is about the contrast between "r", the rate of return on wealth, and "g" the growth rate of the economy. However, there are four different r's. And in his book he failed to distinguish between them.

The four different r's are:

1. The real interest rate at which metropolitan governments can borrow: call this r₁.
2. The real interest rate that is the actual average return on wealth in the society and economy: call this r₂.
3. The real interest rate that is the average risky net rate of accumulation--what capital receives, minus the risk of confiscation or destruction or taxation, plus appreciation in valuation multiples, minus what is spent in order to keep the world in the appropriate social position: call this r₃.
4. A measure of the extent to which capital and wealth serve as an effective claim on income independent of how much capital there is--a standardized measure of what the society and economy's return on wealth would be at some standardized ratio of wealth to annual income: say, 4: call this ρ.

These four r's are very different animals.

The first r, r₁, is what Larry Summers is talking about when he talks about secular stagnation. When that r₁ falls to a level equal to minus the rate of inflation, the economy is in big trouble. At that point, wealthholders would rather become coupon-clipping rentiers holding government bonds then invest in industry of any sort. Full employment can then be attained only via:

1. A bubble that produces unrealistic and unsustainable expectations of the profits from investing in industry.
2. The government borrowing money and buying stuff on a large scale.
3. A higher rate of trend inflation that relaxes the zero lower bound constraint on safe government debt interest rates. .

Larry Summers is worried that this is the dilemma we face: that we are in a world in which r₁ is too low...

Thomas Piketty, by contrast, says that he is worried about the world in which r₂ is too high.

But it is not r₂ but rather r₃ that he should be talking about. And r₃--the average rate of accumulation--is r₂ to which there are a good number of sociopolitical factors plus and minus.

Are Piketty and Summers Reconcilable?

We have a world in which some eminent economists (Larry Summers) say r₁ is too low, and other eminent economists (Thomas Piketty) say r₂ is too high. Can this compute?

Yes.

The difference between r₁ and r₂ is the risk premium. In a well-functioning market economy with well-functioning financial markets, there are powerful reasons to believe that this risk premium should be small: less than 1%-point per year. The fact the risk premium appears to me to be 7%-points per year today is a powerful evidence of the profound dysfunctionality of our financial markets, and of their failure to do their proper catallactic job. But that is a separate and largely independent discussion: that is a dysfunction of our modern market economy which is different from either the dysfunction feared by Summers or the dysfunction feared by Piketty. For the moment, simply note that it is perfectly possible for all three of these major dysfunctions to occur together.

What Does This Neoclassical Economist Say? Build a Mathematical Model

When a conventional American post-World War II neoclassical economist--somebody, that is, like me--tries to make analytical sense of Piketty's big book, he says:

Ring-ding-ding-ding-dingeringeding!

No, that's not it... He says something like:

Piketty talks a lot about eras, and about times when r--his r, r₂--r₂ > g, and wealth concentration and the wealth-to-annual income ratio is rising, and times when r₂ < g, and wealth concentration and the wealth-to-annual-income ratio is falling. But how much? And in what periods, exactly? Let's see if we can do some finger exercise to figure it out. ...