Department of “Huh?!”–I Don’t Understand More and More of Piketty’s Critics: Per Krusell and Tony Smith

As time passes, it seems to me that a larger and larger fraction of Piketty’s critics are making arguments that really make no sense at all–that I really do not understand how people can believe them, or why anybody would think that anybody else would believe them. Today we have Per Krusall and Tony Smith assuming that the economy-wide capital depreciation rate δ is not 0.03 or 0.05 but 0.1–and it does make a huge difference…

Per Krusell and Tony Smith: Piketty’s ‘Second Law of Capitalism’ vs. standard macro theory: “Piketty’s forecast does not rest primarily on an extrapolation of recent trends…

…[which] is what one might have expected, given that so much of the book is devoted to digging up and displaying reliable time series…. Piketty’s forecast rests primarily on economic theory. We take issue…. Two ‘fundamental laws’, as Piketty dubs them… asserts that K/Y will, in the long run, equal s[net]/g…. Piketty… argues… s[net]/g… will rise rapidly in the future…. Neither the textbook Solow model nor a ‘microfounded’ model of growth predicts anything like the drama implied by Piketty’s theory…. Theory suggests that the wealth–income ratio would increase only modestly as growth falls…

And if we go looking for why they believe that “theory suggests that the wealth–income ratio would increase only modestly as growth falls”, we find:

Per Krusell and Tony Smith: Is Piketty’s “Second Law of Capitalism” Fundamental?
: “In the textbook model…

…the capital- to-income ratio is not s[net]/g but rather s[gross]/(g+δ), where δ is the rate at which capital depreciates. With the textbook formula, growth approaching zero would increase the capital-output ratio but only very marginally; when growth falls all the way to zero, the denominator would not go to zero but instead would go from, say 0.12–with g around 0.02 and δ=0.1 as reasonable estimates–to 0.1.

But with an economy-wide capital output ratio of 4-6 and a depreciation rate of 0.1, total depreciation–the gap between NDP and GDP–is not its actual 15% of GDP, but rather 40%-60% of GDP. If the actual depreciation rate were what Krussall and Smith say it is, fully half of our economy would be focused on replacing worn-out capital.

It isn’t.

Graph Net national product FRED St Louis Fed

That makes no sense at all.

For the entire economy, one picks a depreciation rate of 0.02 or 0.03 or 0.05, rather than 0.10.

I cannot understand how anybody who has ever looked at the NIPA, or thought about what our capital stock is made of, would ever get the idea that the economy-wide depreciation rate δ=0.1.

And if you did think that for an instant, you would then recognize that you have just committed yourself to the belief that NDP is only half of GDP, and nobody thinks that–except Krusall and Smith. Why do they think that? Where did their δ=0.1 estimate come from? Why didn’t they immediately recognize that that deprecation estimate was in error, and correct it?

Why would anyone imagine that any growth model should ever be calibrated to such an extraordinarily high depreciation rate?

And why, when Krusell and Smith snark:

we do not quite recognize [Piketty's] second law K/Y = s/g. Did we miss something quite fundamental[?]… The capital-income ratio is not s/g but rather s/(g+δ) no reference to Piketty’s own explication of s/(n+δ), where δ is the rate at which capital depreciates…

do they imply that this is a point that Piketty has missed, rather than a point that Piketty explicitly discusses at Kindle location 10674?

One can also write the law β=s/g with s standing for the total [gross] rather than the net rate of saving. In that case the law becomes β=s/(g+δ) (where δ now stands for the rate of depreciation of capital expressed as a percentage of the capital stock)…

I mean, when the thing you are snarking at Piketty for missing is in the book, shouldn’t you tell your readers that it is explicitly in the book rather than allowing them to believe that it is not?

I really do not understand what is going on here at all…