K21

What Larry Summers Gets Wrong On Piketty's 'Capital' by Matt Bruenig

In his discussion of the first point, Summers just talks about substitution elasticities (i.e. when the capital stock increases, by how much does the rate of return to capital decrease?), as many other economists have also done. He accuses Piketty of confusing gross returns to capital with returns net of depreciation. But in the book, Piketty specifically says that his figures are net of depreciation. If you want to quibble with his specific data or how he accounts for depreciation in it, then you can do that, but you can't just say "I think he misreads the literature by conflating gross and net returns to capital." He doesn't conflate them. He's careful to explain the importance of depreciation and tries to account for it. 

Additionally, when economists start going into the substitution elasticity stuff (on which Summers himself admits there is not good data), they appear to me to be pushing Piketty into a physicalist capital framework that is totally different from what he is talking about. As I explained in a prior post, Piketty has a social constructivist account of capital. The "capital" he is discussing in his book refers to all tradeable assets that deliver passive returns, not just physical buildings and machines and the like. Models that try to show adding more machines will cause the rate of return to fall proportionally such that the owners of the machines won't grab increasing shares of the national income do not actually address Piketty's "capital." Summers falls into that trap here.
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Read the entire post for the overall point, but the gist here is that those who hold big piles of wealth see their wealth and capital income increase each year by r * s. They don't need their s to be 100% to see their holdings grow at a faster rate than those without big piles of wealth (i.e. those who only make money by working). So long as their savings rate is sufficiently higher (how much is sufficiently higher depends on the spread between r and g) than those with only labor incomes, they will perpetually gain on those people in terms of wealth and income. Piketty has not mistakenly assumed all capital income is saved at 100%. Summers has that wrong.