In Which I Continue to Fail to Understand Why Critics of Piketty Say What They Say: (Late) Friday Focus for June 6, 2014

Per Krusell II

So I wrote this on Friday, and put it aside because I feared that it might be intemperate, and I do not want to post intemperate things in this space.

Today, Sunday, I cannot see a thing I want to change–save that I am, once again, disappointed by the quality of critics of Piketty: please step up your game, people!

In response to my Department of “Huh?!”–I Don’t Understand More and More of Piketty’s Critics: Per Krusell and Tony Smith, Per Krusell unfortunately writes:

Brad DeLong has written an aggressive answer to our short note…. Worry about increasing inequality… is no excuse for [Thomas Piketty’s] using inadequate methodology or misleading arguments…. We provided an example calculation where we assigned values to parameters—among them the rate of depreciation. DeLong’s main point is that the [10%] rate we are using is too high…. Our main quantitative points are robust to rates that are considerably lower…. DeLong’s main point is a detail in an example aimed mainly, it seems, at discrediting us by making us look like incompetent macroeconomists. He does not even comment on our main point; maybe he hopes that his point about the depreciation rate will draw attention away from the main point. Too bad if that happens, but what can we do…

Let me assure one and all that I focused–and focus–on the depreciation assumption because it is an important and central assumption. It plays a very large role in whether reductions in trend real GDP growth rates (and shifts in the incentive to save driven by shifts in tax regimes, revolutionary confiscation probabilities, and war) can plausibly drive large shifts in wealth-to-annual-income ratios. The intention is not to distract with inessentials. The attention is to focus attention on what is a key factor, as is well-understood by anyone who has control over their use of the Solow growth model.

Consider the Solow growth model Krusell and Smith deploy, calibrated to what Piketty thinks of as typical values for the 1914-80 Social Democratic Era: a population trend growth rate n=1%/yr, a labor-productivity trend growth rate g=2%/yr, W/Y=3. Adding in the Krusell-Smith depreciation assumption of 10%/yr means (always assuming I have not made any arithmetic errors in https://www.icloud.com/iw/#numbers/BAJQ8MCS-CfQAKyIcIOBR6yniZzZlgmFu3qF/20140606_Krusell-Smith_Comment.numbers) that a fall in n+g from 3%/yr to 1%/yr holding the gross savings rate constant generates a rise in the steady-state wealth-to-annual-net-income ratio from 3 to 3.75–not a very big jump for a very large shift in economic growth: the total rate of growth n+g has fallen by 2/3, but W/Y has only jumped by a quarter. Adopting a less ludicrously-awry “Piketty” depreciation assumption of 3%/yr generates quantitatively (and qualitatively!) different results: a rise in the steady-state wealth-to-annual-net-income ratio from 3 to 4.708–the channel is more than twice has powerful.

We have a very large drop in Piketty’s calculations of northwest European economy-wide wealth-to-annual-net-income ratios from the Belle Époque Era that ended in 1914 to the Social Democratic Era of 1914-1980 to account for. How would we account for this other than by (a) reduced incentives for wealthholders to save and reinvest and (b) shifts in trend rates of population and labor-productivity growth? We are now in a new era, with rising wealth-to-annual-net-income ratios. We would like to be able to forecast how far W/Y will rise given the expected evolution of demography and technology and given expectations about incentives for wealthholders to save and reinvest.

How do Krusell and Smith aid us in our quest to do that?