On Piketty and Capital

Important disclaimer: I have not read Thomas Piketty‘s book on Capital in the Twenty-First Century, and therefore cannot possibly have given it a fair reading.

I do, however, trust Per Krusell and Tony Smith to have given it a fair reading, because Krusell and Smith have long track records as diligent and thoughtful scholars. And their analysis appears to devastate both Piketty’s model and his prediction that income inequality is destined to grow explosively over time.

Here’s why:

All of Piketty’s predictions depend on his assumptions about how much people save. The simplest respectable model (that is, a model that economists generally feel comfortable using for many purposes, and which fits fairly well with observations) says that we save a fixed percentage of our incomes — say 30%. (There are also more sophisticated models in which this percentage can change as economic conditions change.)

Piketty, by contrast, assumes that our net saving is a fixed percentage of our net incomes, where “net” means “after subtracting depreciation of our assets”. That’s a very different assumption, and, according to Krusell and Smith, not at all a plausible one. It’s implausible first because it has extremely odd implications. Most notably, it implies (though this is not immediately obvious) that if economic growth slows to zero, we will eventually choose to save 100% of our incomes(!!). Beyond that, Krusell and Smith argue in considerable detail that, compared to the more traditional models, Piketty’s does a poor job of fitting the last seventy years’ worth of data.

According to Krusell and Smith, Piketty demonstrates correctly that under his assumptions, slowing economic growth must lead to massive inequality over time. But under the far more plausible assumptions found in modern textbooks and modern research papers, that conclusion goes away. In fact, after substituting those assumptions, Piketty’s arguments yield something like the opposite conclusion — as growth slows down, changes in inequality become pretty much negligible.

If this analysis is right — and given the identities of the authors I’ll be very surprised if it’s wrong — then there appears to be very little reason to buy into Piketty’s story. That doesn’t mean he’s wasted his time. We learn a lot by making a variety of different assumptions and figuring out where they lead us, even when the assumptions are ultimately unsupportable. But a serious intellectual exercise is not the same thing as a serious prediction.

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22 Responses to “On Piketty and Capital”


  1. 1 1 Brandon Berg

    we save a fixed percentage of our incomes — say 30%.

    Just based on my own experience and introspection, this doesn’t really seem plausible. Right now my income is split roughly three ways between taxes, consumption, and savings. But my consumption is fairly insensitive to changes in my income. If I get a raise, the lion’s share of the after-tax increase will go to savings, rather than being split evenly between consumption and savings. Conversely, if my income were at subsistence level, I wouldn’t be able to save at all.

  2. 2 2 RichardR

    I’m sure you’re very busy but I find it strange that an Economics professor hasn’t read the most talked about Economics book in a generation.

  3. 3 3 Jim WK

    I’m not surprised Steve Landsburg hasn’t read it – it’s a weighty tome that libertarians pretty much know they’re going to disagree with – and thus it’s quite disenchanting to put aside time for something you feel is going to be full of holes, particularly when you know there will always be reliable people on the economic right that will save you the bother.

  4. 4 4 Jim WK

    By the way, readers might like to note The Chamley-Judd Redistribution Impossibility Theorem which surpised many by arguing that the optimal tax rate on capital is zero (

    https://www.blogger.com/blogger.g?blogID=2678383177049754916#allposts/src=dashboard)

    Why isn’t this proof more widely known? I suspect the reason is the same reason a lot of libertarian qualities are not wdely known – they involve lateral brainpower to work out, but also they are largely unappealing to the majority of people who prefer leftist delegation rather than laissez faire individual responsibility.

  5. 5 5 Steve Landsburg

    Jim WK:

    it’s a weighty tome that libertarians pretty much know they’re going to disagree with

    Expecting to disagree with something would be, I think, a pretty poor reason not to read it.

  6. 6 6 Jim WK

    Steve, I agree in conditions under which you have good intuition that you might be in the wrong. Under those conditions it is always good to read contra-views that might challenge your own and prove you wrong.

    However, in conditions under which you have good intuition that you’re going to spend a few hours reading something that’s bound only reaffirm what you already know, one has to be more selective and discerning with one’s time.

  7. 7 7 tb

    Jim WK,

    Can you check the link? Doesn’t seem to work.

  8. 8 8 Jim WK

    Ooops, it’s broken…

    Try this one tb,

    http://econlog.econlib.org/archives/2013/03/redistributing.html

  9. 9 9 Bob Murphy

    Not to be obnoxious, but here I have a review of Piketty’s book. It’s a “punchy” piece but it is filled with hyperlinks to more formal discussions on each of the points I raise. In short: Piketty’s book is chock full of theoretical and empirical problems, several of which are independently devastating to his enterprise.

  10. 10 10 Capt. J Parker

    I’d like to put in a plug for Larry Summers’ review of Piketty’s “Capital” The piece that caught my eye was:

    Piketty argues that the economic literature supports his assumption that returns diminish slowly (in technical parlance, that the elasticity of substitution is greater than 1), and so capital’s share rises with capital accumulation. But I think he misreads the literature by conflating gross and net returns to capital. It is plausible that as the capital stock grows, the increment of output produced declines slowly, but there can be no question that depreciation increases proportionally. And it is the return net of depreciation that is relevant for capital accumulation. I know of no study suggesting that measuring output in net terms, the elasticity of substitution is greater than 1, and I know of quite a few suggesting the contrary.

    . So mark that down as another possible net vs gross problem with Piketty.
    I’d also like to plug all the stuff Bob Murphy has written and linked to.

  11. 11 11 Ted Levy

    Is it the result of the internet? I must say I can’t recall a famous book that has been so completely trashed on multiple levels by both practical and theoretical arguments AS QUICKLY AS this one, by multiple independent sources.

  12. 12 12 Twofer

    @ Ted Levy #11 — Actually, I’m surprised in the other direction. The criticism has not held up well at all. Piketty thoroughly rebutted the FT, and now this:

    http://equitablegrowth.org/2014/06/02/department-huh-dont-understand-pikettys-critics-per-krusall-tony-smith/

  13. 13 13 dullgeek

    [blockquote]That doesn’t mean [Piketty has] wasted his time.[/blockquote]

    Certainly not. He’s created a treatise that will be lauded for decades as gospel by politicians seeking it’s lessons to enrich themselves. Meanwhile well reasoned criticisms will fall by the wayside.

    We’ve seen this [url=http://www.amazon.com/Keynes-Hayek-Defined-Modern-Economics/dp/0393343634]before[/url].

  14. 14 14 AMT buff

    I’m surprised Piketty did not address the criticism by four French economists that his use of house prices, rather than their rental values, as capital was incorrect, See their full paper at http://spire.sciencespo.fr/hdl:/2441/30nstiku669glbr66l6n7mc2oq/resources/2014-07.pdf

    These economists conclude that “The capital/income ratio has therefore increased only because of the choice made to measure the value of capital as indexed on the housing price and not indexed on rental price.”

  15. 15 15 Mike H
  16. 16 16 Robert

    Twofer, Mike H
    What you link to does not contradict Krusell & Smith at all.

  17. 17 17 Robert

    http://larspsyll.wordpress.com/2014/06/04/krusell-answers-brad-delonng/

    I am getting annoyed at the refusal of some left-leaning economists to engage in substantive, reasonable debate. Yah boo sucks does not, in my view, pass for research.

    (Not that I want to impugn either Mike H or Twofer, who were simply pointing us to an opinion piece.)

  18. 18 18 Twofer

    Robert,

    There’s probably a lot to debate in Piketty. I’m just not sure this is quite it — but if there is an attack to be made it will be on the r side of the equation. Krussell and Smith seem to be treating the second law as an identity.

    Piketty’s Second Fundamental Law is not an identity or an approximate identity. It is, as Piketty makes clear at some length on pages 166-170, a long-term asymptotic law. For the benefit of the general reader, Piketty writes it in the form “β = s/g”. But it might more carefully be stated this way: “For a fixed savings rate s and growth rate g, the capital-to-income ratio β converges over time to s/g.” He might have written it in more conventional fashion in the form β(t) –> s/g. He sketches an elementary proof of this convergence theorem in his technical appendix. Like any limit theorem true in the real numbers, it requires an implicit restriction on the range of the variables to avoid singularities.

    Refer to the example on page 351. It requires nothing like the savings rate that Krussel and Smith imply is required.

  19. 19 19 Robert

    Twofer,

    I don’t think 351 helps.

    First, his own data show no increase in capital’s share even as r is greater than g for 1820-1910 France. Second, net savings over growth as the limit to which the capital share tends requires some rather funky things to happen as g approaches 0. I rather think that’s K&S’s whole point.

    There is a third possibility – I’m just too dumb. This s not to be discounted.

  20. 20 20 Twofer

    Robert wrote: “There is a third possibility — I’m just too dumb. This is not to be discounted.” It made me laugh, because I could have written the same. So me too Robert.

    I studied Econ as an undergrad. David Friedman was my prof. I am NOT an economist. But I read it and try to understand as best as I can, and attempt to judge the arguments. But in the end, I count on real economists to make the real cases, and to help us amateurs along. Frankly, IMO, the profession looks like crap right now, talking past each other, sniping, long on theory, short on empiricism…

    DeLong is snarky. K&S are equally so, and if anybody can make any sense of what they are saying in the last paragraph of the rebuttal, please translate.

    In the meantime, DeLong answers K@S here:

    http://equitablegrowth.org/2014/06/05/trying-yet-communicate-arithmetic-scaffolding-pikettys-capital-twenty-first-century-thursday-focus-june-5-2014

  21. 21 21 Robert

    Twofer
    :-)

  22. 22 22 Bigjeff5

    Gist of K@S vs DeLong on Piketty, from the perspective of someone ignorant on the subject just trying to parse the arguments:

    K@S: Piketty’s model doesn’t work when depreciation is 10%! It gets plain wacky! Traditional models (e.g. Solow) work fine at 10%, and way lower (more reasonable?) percentages too.

    DeLong: Fools! 10% is too high!

  1. 1 On Piketty and Capital feedly | Daniel J. Smith
  2. 2 *Yawn* Two More Experts on Growth and Inequality Say Piketty Is Totally Wrong
  3. 3 Some PIketty-Related Links
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