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:
- The real interest rate at which metropolitan governments can borrow: call this r1.
- The real interest rate that is the actual average return on wealthin the society and economy: call this r2.
- 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.
- 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.