On Piketty and Growth

John Aziz has a critique of Piketty over at The Week. It starts with a somewhat confused take on Piketty's point about the rate of return of capital being higher than the growth in national income (r > g) and ends with an optimistic projection of future growth that does not take account of any of the growth-reducing trends Piketty identifies.

r > g

He starts:

Piketty's main theory is that inequality grows or shrinks based on two key quantities: G, the level of economic growth in the entire economy, and r, the rate of return on capital in the economy. If G exceeds r, then inequality tends to shrink, as the growth in the wealth of capital holders is outpaced by growth in the economy at large. But if r exceeds G, then inequality tends to expand.

This is fine enough as a gloss of an explanation, but is it not strictly true. Piketty's actual point that the larger the spread between r and g, the more forcefully the dynamics of capital income pushes in the direction of increasing wealth inequality.

This is easiest to see when talking about capital income growth. If the rate of return is 5 percent and the growth rate is 4 percent, then capital owners will have to save 80% of their returns each year to ensure their capital income grows at the same rate as national income. However, if the rate of return is 5 percent and the growth rate is 1 percent, capital owners will only have to save 20% of their returns each year to keep pace. This same basic dynamic is true of wealth as well: the larger the spread between r and g, the easier it is for savings dynamics to concentrate national wealth into fewer and fewer hands.

Feudal-era Spreads

Keep this in mind as we turn to Aziz's big move in the piece:

History shows that the major systemic driver of inequality is not capitalism, but low-growth feudalism — and the hereditary privilege and lack of widespread economic opportunity that feudalism ensures — that preceded it. For Piketty to look at his own data and conclude that capitalism is the driver of inequality after 1700 years of low-growth feudalism and massive inequality is, quite simply, bizarre.

This is an incredible paragraph. Aziz notes that if you actually look back before modern capitalism, inequality was higher. Why was that? Because it was low-growth. Why would that make inequality higher then? Because with growth that low ... the spread between r and g is very high! That's Piketty's entire point!
 
Piketty spends plenty of time in the book talking about low or no-growth agricultural societies and the way in which the wealth accumulation dynamics of such societies will drive severe wealth inequalities. His main point about wealth inequality going forward is that declining growth will make us more similar to those societies than we are used to. There is nothing bizarre about this. If your theory is that growth will decline, it actually makes incredible amounts of sense to compare it to periods where growth was lower.
 
Aziz seems caught up in feudalism versus capitalism for some reason here, when Piketty's point is about the spread between r and g in both systems. His point is that the spread between the r and g in the future is going to be closer to feudal-era spreads than the exceptionally narrow spreads we've seen in the last few decades.
 
Growth
The way to actually contest Piketty on this point is to either say that r is going to be lower than he thinks it is (as many have done) or that g is going to be higher than he thinks it is. And when you move past the somewhat confusing analysis above, this is actually the only point Aziz has. He questions Piketty's projection that growth is going to be lower:
 

As I wrote last month when I first looked at Piketty's ideas, while there has definitely been a stagnation in growth in some countries, like Japan, in recent years, it is not right to assume that the soaring growth and wealth creation that brought down inequality in the middle of the last century will never return. In fact, growth continues apace worldwide, rising in 2013. New technological innovations like renewable energy, 3D printing, robotics and the internet of things have the potential to severely boost growth in the 21st century as innovations like fossil fuels, automobiles, the radio, computing, and rubber did in the 20th. [...]

He spends two more paragraphs highlighting his optimistic projection of a high-growth future. And that's all well and good. Nobody knows the future. Piketty is clear about that. But Aziz fails to address any of Piketty's arguments for why growth is going to decline.

Piketty argues firstly that population growth is going to decline and population levels will stabilize. This is actually a pretty common view among demographic experts who predict such things. In developed countries, you already see this. Population increases, Piketty claims, have generally accounted for around half the overall growth rate. If that's true, then the leveling off of world population will mean, all else equal, a halving of economic growth. Per-capita growth will become the only growth. Aziz says nothing about this.

Piketty argues that, absent shocks, economies at the technological frontier tend to grow pretty slowly. Economies that are not at that frontier (or who have faced shocks that destroyed a great deal of its wealth) can grow much faster, but that's only catch-up growth and it will tumble down when they hit the technological frontier as well. Aziz also fails to mention this, and even runs right into the trap by noting that global growth rose in 2013, a fact which is true only because of exceptional catch-up growth, largely from China.

Conclusion

Once you bracket out the somewhat odd foray into feudalism versus capitalism, what Aziz's critique amounts to is a challenge to Piketty's growth projections. But the challenge doesn't actually respond to Piketty at all.

Piketty argues growth will decline because global population growth will decline and level off, and Aziz has no response to that. Piketty argues that, with the exception of catch-up growth and rebuilding after shocks, per-capita growth rates are fairly modest at the technological frontier, and Aziz's response is to cite data that reflects the exceptional catch-up growth of countries not at the technological frontier.

None of this is to say you should believe Piketty's growth projections. It is impossible to say what the future holds. An exceptional wave of technological innovation (like some of the innovations Aziz talks about) might be so great that it can push high growth even when the half of growth usually driven by population increases has disappeared and when global catch-up growth has largely subsided. But that's a pretty speculative and optimistic guess. Aziz shouldn't be so confident, especially when those growth-boosting innovations are having to push against the growth-reducing tides Piketty has identified but Aziz has ignored entirely.

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