A tale of 2 r’s

The Piketty data problems are the huge talk right now, but I want to point out something entirely different.

Brad Delong points out there are 4 different rates and Piketty does not do a great job differentiating 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 wealthin 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.


Brad points out that by definition r2 > r1, because r2 contains a risk premium, and r1 is the closest “r” to a risk free rate we can find.

Fortunately, I have a bit of experience with what Brad calls r1. r1 happens to be the variable which fits into the Intertemporal Government Budget Constraint math.

Over at Traders Crucible, I did a deep dive into how this math works, mostly by following Scott Fullwilers excellent paper on the topic.

It turns out if g > r1, then the government can deficit spend in perpetuity! This follows from the math. If the economy is growing faster than the interest rate on its debt, the debt becomes smaller in real terms. I recommend reading Scott’s paper pages 7-9 very closely – this is where he explains how this imbalance works.

This is really pretty straightforward thinking, and nobody in their right mind questions this at all.

So far, this g > r1 has held up pretty well. The average real borrowing rate for the U.S. government is extremely low. I’ve pointed out if you think inflation is higher than the stated rates, these real interest rates are even lower. We can almost certainly deficit spend without much consequence right now.

We are left with something interesting about Piketty’s Capital. Piketty shows if r2> g, then capital will grow relative to the economy. Some people are critiquing Piketty on the grounds g > r2.

If g <r2,then by definition, r1 <g. This implies governments can deficit spend in perpetuity and not go broke.

My point today is simple. Either r1 > g, or r1<g for the government budget constraint. We know r1 and r2 are related values, and r1 < r2. If people are claiming r2 < g, then certainly r1 < g.

Hammering down r2 by pointing out errors with Piketty’s excel sheets only helps the case the government can deficit spend in perpetuity.



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8 Comments on "A tale of 2 r’s"

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3 years 2 months ago

I think this is a typo “If g <r2,then by definition, r1 r1, if g < r2 then g could also be less than r1: g < r1 < r2 still satisfies g r2 (in which case by definition g > r1). So I think you meant “If g > r2 …”

3 years 2 months ago
beowulf: ” I haven’t read Piketty’s book, but if he doesn’t touch on these points, I’d wager its not worth reading.” The orthodox-heterodox dilemma is that heterodox views get no media attention even though on point. So to get the attention of the mainstream, it is necessary to enter the mainstream universe of discourse, which is loaded toward economic liberalism. Piketty only got noticed by stepping into the mainstream universe of discourse to attack the consequence of economic liberalism which is more appropriately characterized economically as monopoly capital and politically as the asymmetric power leading to privilege rather than “inequality,” which is difficult to define other than normatively. First, heterodox economists, sociologists and political scientist have put forward more on point and trenchant analyses than Piketty’s, and this is a point that many heterodox economists have been making along with criticizing Piketty’s essentially neoclassical approach. Secondly, Piketty’s data set was bound to lead to problems for the reasons that Piketty himself gives. It’s extremely difficult to collect good data across different countries and over historical time for a variety of reasons. Moreover, there is the underlying problem of different contexts. In addition, several commentators have pointed out that its nearly impossible to put together a large data set without some errors creeping in. The question is what difference it makes to the argument when the errors are corrected. This was bound to provide some ammunition for the opponents, who don’t really have to win the argument but only mount it to create enough FUD to muddy the waters, which is SOP in the propaganda world of the so-called news. The good thing is that the overall economic and political universe of discourse has shifted since the publication of Piketty’s book and related work. So it’s main contribution has been as… Read more »
3 years 2 months ago

“I find it very strange that he put all of his excel sheets online and there are obvious errors.”
sloppy thinking > dishonesty, so I guess its to his credit.

The point Brad makes for 4 is interesting–
“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.”

This is important because the ratio of wealth to annual income (or to put it another way, the capital share versus labor share of national income) is not in fact, a fixed ratio. It waxes and wanes like the tide but unlike ocean waves it can be changed by public policy. As Jared Bernstein (underrated, really, as the most on the ball economist serving in Obama’s first term) noted:
“profits as a share of income are at or near record highs while the compensation share is around a 50-year low… I submit that increasing labor’s share of national income is neither mysterious nor beyond our scope (it is beyond our current politics, but so is pretty much anything useful). It takes getting rid of the persistent slack in the labor market, which in turn means policy makers must plot a course toward full employment.”

Of course, these policies are beyond our current politics because of deficit hysteria. And the first step to curing that is recognizing, as Jamie Galbraith has said for years, that the long term deficit problem more or less evaporates if the r1 (the rate which Uncle Sam can borrow at) is kept near 0 or below, in real terms. I haven’t read Piketty’s book, but if he doesn’t touch on these points, I’d wager its not worth reading.

Detroit Dan
3 years 2 months ago

Wow! That puts Piketty’s thesis into perspective quite nicely…