Krusell answers Brad DeLong

4 Jun, 2014 at 18:53 | Posted in Economics | 3 Comments

Yes, Brad DeLong has written an aggressive answer to our short note. We consider the subject of Piketty’s work really important and we really worry about increasing inequality and its determinants (and in fact we have devoted a good part of our own joint research to studying inequality). This worry, however, is no excuse for using inadequate methodology or misleading arguments.

reallyPiketty’s book is a really solid piece of research and our point is merely that the theory of saving he is employing in his predictions is unreason-able. As an illustration of our points, we provided an example calculation where we assigned values to parameters—among them the rate of depreciation. DeLong’s main point is that the rate we are using is too high (we use 10% in one place and 8% in another place in the paper where we actually perform some calculations about how the capital-to-output ratio responds to changes in the growth rate under different assumptions about saving behavior). It might be reasonable to assume lower rates (we conducted a quick survey among macroeconomists at the London School of Economics, where Tony and I happen to be right now, and the average answer was 7%). We already did some calculations based on lower rates and, not surprisingly to us, our main quantitative points are robust to rates that are considerably lower. (For example, Alex Tabarrok does some back-of-the envelope calculations here:, with a depreciation rate equal to 5%, and finds quantitative results similar to the ones we report in the paper.) Within a week or two we will update our document and include these calculations and also include some additional text addressing other feedback that we have received.

It is, however, disappointing that 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.

Our main point, to be clear, has two parts. First: if the net rate of saving remains positive as the economy’s growth rate falls toward zero, as Piketty assumes in his second fundamental law of capitalism, the gross saving rate in the economy must approach 100%. This observation is a way of illustrating how unreasonable the behavioral assumptions underlying his theory of saving really are. Second: according to standard, and much more reasonable, saving theory (based either on the standard textbook Solow growth model or on the permanent-income model), the net saving rate must fall with the rate of growth, and become zero when growth is zero. This makes Piketty’s ”second fundamental law” inapplicable/misleading, as it now reads K/Y = 0/0 (in fact, there is a well-defined limit, as we show in the paper). These points are key because Piketty’s predictions are all about what happens as growth falls during the 21st century, as he argues it will. As we explain in detail in the paper, both of these results hold no matter what the depreciation rate is (so long as it is positive).

DeLong also mentions that Piketty is aware of our main point—that his theory of saving is a non-standard one with implausible implications as growth rates fall—as if we were not aware of this. We have read Piketty’s book and papers, and so we of course know that Piketty knows; our note is thus not written for him but instead, as we say in the introduction to the paper, for all of those who might be puzzled by the striking result that he derives from his non-standard theory, namely, that the capital-to-output ratio will go to infinity as growth approaches zero. Actually, in an early version of our note we did include a couple of sentences about the fact that Piketty is aware that his assumptions are extreme, with references to his texts. But we feared that a reader of our paper might misinterpret us as wondering how Piketty could have made these assumptions, knowing full well that they vastly exaggerated his results. We deleted these sentences because we did not want our paper to be interpreted in that way.

Per Krusell

“We have read Piketty’s book and papers …”

Hmmm … I wonder if that includes Piketty’s and Zucman’s 2013 article Capital is Back:

Our results also suggest that the focus on the possibility of a balanced growth path that has long characterized academic debates on capital accumulation … has been somewhat misplaced.cartoon_economic_growth1It is fairly obvious that there can be a lot of capital-labor substitution in the long-run, and that many different β can occur in steady-state. But this does not imply that the economy is necessarily in a stable or optimal state in any meaningful way. High steady-state wealth-income ratios can go together with large instability, asset price bubbles and high degrees of inequality – all plausible scenarios in mature, low-growth economies.


  1. Lars, in your earlier post, Robert Solow described pretty well what this anti-Piketty nittpicking is all about:
    ” Suppose someone sits down where you are sitting right now and announces to me that he is Napoleon Bonaparte. The last thing I want to do with him is to get involved in a technical discussion of cavalry tactics at the battle of Austerlitz. If I do that, I’m getting tacitly drawn into the game that he is Napoleon. Now, Bob Lucas and Tom Sargent like nothing better than to get drawn into technical discussions, because then you have tacitly gone along with their fundamental assumptions; your attention is attracted away from the basic weakness of the whole story. Since I find that fundamental framework ludicrous, I respond by treating it as ludicrous – that is, by laughing at it – so as not to fall into the trap of taking it seriously and passing on to matters of technique.”

  2. Brad Delong answers in return to Krusell and Smith:

    “Krusell and Smith favor a deprecation rate of 10%/year–and I genuinely do not understand why they think it is appropriate. We are not, after all, dealing with short-run business-cycle fluctuations in which the pieces of the capital stock that vary are made up mostly of inventories and machines here. We are talking about land, very durable buildings, powerful property rights and the ability to summon the police to protect them–claims over future output that do not, I think, erode away at anything like 10%/year. And, indeed, if you try to understand the pre-WWI northwest European economies with such an assumed depreciation rate, you get results that strike me as completely nonsensical: 46.1% of gross output in gross investment; I think we would have noticed if, in pre-WWI northwest Europe’s economies, two out of every five workers spent their days simply keeping society’s collective capital stock from depreciating by repairing rust and wear-and-tear. That is simply not what the pre-WWI northwest European economies looked like.

    But the Belle Époque comes to an end. World War I, the Bolshevik Revolution, the Great Depression, and World War II wreak their effects on the North Atlantic. The wealth-to-annual-net-income ratio falls to 300% or so as the growth acceleration of the twentieth century raises the rate of growth of income to 3.0%/year. And then during the Thirty Glorious Years of post-WWII social-democracy and growth the wealth-to-annual-net-income ratio shows no signs of rising swiftly back to its previous equilibrium of 700%. Viewed from the perspective of the Solow growth model, the economy of the generation after 1950 is and remains much less capital-intensive than the economy before World War I, and to support this lower capital-intensity equilibrium requires savings rates out of gross output reduced by a third from their pre-WWI shares:

    Starting around 1980, Piketty argues, the North Atlantic shifted out of its Social-Democratic Era and is now moving into a new configuration, with increasingly-concentrated wealth, savings no longer reduced by highly progressive capital taxation and fear of expropriation, and slower rates of population and labor productivity growth. Piketty expects the consequence to be a rise in the savings rate back to Belle Époque levels and a return to the capital intensity and inherited-wealth dominance of those days. In my view, the next questions are two:

    Would this be a good thing? More savings and wealth accumulation by the rich that increase the capital intensity of the economy increase real wages for the working class and the poor, no? Here I think the answer is perhaps–and I think this is what the debate over Piketty should be about. Unfortunately, that is not the debate we are having. Instead, we have:

    Can this happen? And Krusell and Smith and company are saying: no, it cannot. As the capital-output ratio rises, the desire to consume wealth pushes the gross savings rate goes down and the fact that capital depreciates at 10%/year pushes the net savings rate down much further, and so there are no macroeconomic forces in play that could push the wealth-to-annual-net-income ratio far up above its current value of 300%.

    But if the savings rate necessarily falls as the wealth-to-annual-net-income ratio rises, why was the (gross) savings rate half again as high back before World War I when the economy was wealth-dominated as it is today? And from where comes the 10%/year depreciation rate assumption?

    What we clearly have here is a failure to communicate. And I really, really do not think that it is the result of a failure to try on Thomas Piketty’s part.”

    Calculations here: ”

  3. […] ‘Second Law of Capitalism’ fundamental? Brad DeLong comenta. Y James Hamilton critica a DeLong. Krussell tambien le responde. The Economist tambien […]

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