The Theory of Growth and Inequality: Piketty, Zucman, Krusell, Smith, and “Mathiness”

Paul Romer inquired why I did not endorse his following Krusell and Smith (2014) in characterizing Piketty and Piketty and Zucman as a canonical example of what Romer calls “mathiness”. Indeed, I think that, instead, it is Krusell and Smith (2014) that suffers from “mathiness”–people not in control of their models deploying algebra untethered to the real world in a manner that approaches gibberish.

I wrote about this last summer, several times: Department of “Huh?!”–I Don’t Understand More and More of Piketty’s Critics: Per Krusell and Tony Smith; The Daily Piketty: Ryan Avent on Housing in the Twenty-First Century: Wednesday Focus for June 18, 2014; In Which I Continue to Fail to Understand Why Critics of Piketty Say What They Say: (Late) Friday Focus for June 6, 2014 – Washington Center for Equitable Growth; Depreciation Rates on Wealth in Thomas Piketty’s Database: Monday Focus: June 9, 2014 (Brad DeLong’s Grasping Reality…);

This time, I replied to Paul Romer’s question with a Tweetstorm. Here it is, collected, with paragraphs added and redundancy deleted:

.@paulmromer My objection to Krusell and Smith (2014) was that it seemed to me to suffer much more from what you call “mathiness” than does Piketty or Piketty and Zucman.

Recall that Krusell and Smith began by saying that they:

do not quite recognize… k/y=s/g”…

But k/y=s/g is Harrod (1939) and Domar (1946). How can they fail to recognize it?

And then their calibration–n+g=.02, δ=.10–not only fails to acknowledge Piketty’s estimates of economy-wide depreciation rate as between .01 and .02, but leads to absolutely absurd results:

  • For a country with a k/y=4, δ=.10 -> depreciation is 40% of gross output.

  • For a country like Belle Époque France with a k/y=7, δ=.10 -> depreciation is 70% of gross output.

It seemed to me that Krusell and Smith had no control whatsoever over the calibration of their model at all.

Note that I am working from notes here, because no longer points to Krusell and Smith (2014). It points, instead, to Krusell and Smith (2015), a revised version.

In the revised version, the calibration differs. It differs in:

  1. raising (n+g) from .02 to .03,

  2. lowering δ from .10 or .05 (still more than twice Piketty’s historical estimates), and

  3. changing the claim that as n+g->0 k/y increases “only very marginally” to “only modestly”

(The right thing to do would be to take economy-wide δ=.02 and say that k/y increases “substantially”.)

If Krusell and Smith (2015) offers any reference to Piketty’s historical depreciation efforts, I missed it.

If it offers any explanation of why they decided to raise their calibration of n+g when they lowered their δ, I missed that too.

Piketty has flaws, but it does not seem to me that working in a net rather than a gross production function framework is one of them. And Krusell and Smith’s continued attempts to demonstrate otherwise seem to me to suffer from “mathiness” to a high degree…

May 18, 2015

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