31 May 2014

*Yawn* Two More Experts on Growth and Inequality Say Piketty Is Totally Wrong

Capital & Interest, Inequality, Piketty 42 Comments

Steve Landsburg links to this Note by Krussell and Smith on Piketty. These guys are experts in this field; for example here’s one of their joint papers on wealth and income inequality in the JPE. Short version of their current Note: Like Larry Summers, they claim that once you account for depreciation, Piketty’s whole case falls apart. Some excerpts:

Piketty’s predictions are not mere extrapolations from past
data but, instead, rest importantly on the use of economic theory. This is important, since
for the predictions to be reliable, one would want to feel some comfort in the particular
theory that is used. Our main point is to make clear that there are strong reasons to doubt
the specific theory that Piketty advances.

We argue that one of the key building blocks in this theory—what he calls the second
fundamental law of capitalism—is rather implausible, for two reasons. First, we demonstrate
that it implies saving behavior that, as the growth rate approaches zero, requires the aggregate economy to save 100% of GDP each year. Such behavior is clearly hard to square with
any standard theories of how individuals save, and it is inconsistent with the findings in the
empirical literature on how individuals actually save.

[Piketty’s] argument [for predicting an explosion in capital’s share of income], in its disarming simplicity, may look attractive, but it is worrisome to those of us who have studied basic growth theory based either on the assumption of a constant saving rate—such as in the undergraduate textbook version of Solow’s classical model—or on optimizing growth, along the lines of Cass (1965) and Koopmans (1965) or its counterpart in modern macroeconomic theory. Why? Because we do not quite recognize the second law, k/y = s/g. Did we miss something important, even fundamental, that has been right in front of us all along?

I just love the opening of that one sentence: “This argument, in its disarming simplicity, may look attractive, but it is worrisome to those of us who have studied basic growth theory…” Pretty much.

I’m going to go out on a limb and say that this won’t faze Piketty’s fans at all. Who cares if his theory is totally at odds with the existing literature and can’t be squared with historical data? Damnit Jim the man’s a visionary, not an accountant.

42 Responses to “*Yawn* Two More Experts on Growth and Inequality Say Piketty Is Totally Wrong”

  1. Tel says:

    First, we demonstrate that it implies saving behavior that, as the growth rate approaches zero, requires the aggregate economy to save 100% of GDP each year.

    I think the theory is that you end up with a small handful of individuals owning most of the world’s wealth and because of the return on investment they earn vastly more than they can possibly consume. At this point they have no choice but to reinvest something very close to 100% of their earnings. The rest of humanity are presumable impoverished down to subsistence level, and have no choice but to consume everything they earn with zero savings.

    Mathematically it is self-consistent, but kind of difficult to imagine the physical mechanism allowing this to happen.

    • Major-Freedom says:

      Almost 100% or 100%?

      If 100% GDP, then everyone would die because there would be no consumption.

      If it is close to 100% GDP, then the standards of living of both rich and poor, ans everyone in between, would be growing at a very, very high rate. It is not true that production passes the workers by. In a division of labor, you don’t need to own a factory in order to benefit from the factory.

      • Tel says:

        I don’t believe that in any real world society it would get anything remotely close to 100%. For a start, the rich are not entirely stupid. If your workers are coming in half fainting from hunger, then they probably won’t be doing a good day’s work.

        What’s more, there’s no point owning the factory if you can’t sell the produce, so this “wealth” is entirely dependent on maintaining at least some level of consumption.

        • Major-Freedom says:

          0.00000000001% of GDP going to workers is not itself sufficient to conclude that workers would be malnurished and fainty. Maybe in today’s economy, but in principle we could have a situation where 99.99999999999% of GDP is invested wealth production, and everyone could be thousands or millions or whatever more wealthy.

        • guest says:

          … so this “wealth” is entirely dependent on maintaining at least some level of consumption.

          More fundamentally, all wealth is produced in pursuance of consumption.

          That’s what “wealth” means: a thing’s ability to satisfy preferences (consumption). Capital derives its value from its ability to supply such things.

          This is why “production” or “output” is only meaningful to the extent that it satisfies consumer preferences.

          “Output” isn’t necessarily “wealth”. And to the extent that capital is not employed toward the satisfaction of consumer preferences, it’s a malinvestment.

          (Note that this is true even if the capital owner destroys his capital for fun; He has become the consumer.)

          • Rick Hull says:

            > That’s what “wealth” means: a thing’s ability to satisfy preferences (consumption).

            Well put. It’s all either present consumption or some form deferred future consumption.

            Even your home, whether owned, rented, or squatted, is consumed like a gumball: it starts shiny and round, and then it is put to your exclusive use (though you can share it), and it becomes chewed up by your usage. It may even lose most of its flavor, but you can keep chewing on it for a long time. Then you either swallow it, or spit it out to be reformed into a new gumball.

  2. Major-Freedom says:

    Marx treated long term, fixed capital, or in his expression “constant capital”, as adding nothing to the value of output. To him, only “variable capital” was responsible for value.

    If one ignores how constant capital adds value, then it is inevitable that one would ignore the costs (depreciation) of it as well.

  3. Unlearningecon says:

    “I’m going to go out on a limb and say that this won’t faze Piketty’s fans at all. Who cares if his theory is totally at odds with the existing literature and can’t be squared with historical data? Damnit Jim the man’s a visionary, not an accountant.”

    The paper you link to claims that as g tends to zero, conventional economic theory implies the savings rate must tend to 100% for Piketty’s ‘law’ to hold. They then show that, surprise surprise, savings rate aren’t usually 100%, as if this is somehow a central tenet of Piketty’s book. The idea this somehow ‘refutes’ Piketty rests on two clearly debatable propositions: that g will actually tend to zero, and that conventional economic theory is right. Neither are justified by the authors.

    Piketty fans aren’t phased by these criticisms because they are almost all incredibly weak (and that goes for Galbraith et al, too). Until people actually tackle his work head on (and without messing it up like Chris Giles did), this will continue.

    • Tel says:

      So, each new economics article is now required to re-establish economic theory from first principles.

      Hmmm, Bob has some semi-permanent links on the left hand side of the page, including one to the Mises Institute. Does that suffice?

      • Unlearningecon says:

        No, each economics article is required to establish that its empirical implications actually hold before using them as an argument against an empirical claim.

        Claim: conventional economic theory says growth will tend to 0, which requires that s will tend to 100% for Piketty’s thesis to hold.

        Counterclaim: growth has never been observed to tend to 0, and Piketty never claimed it would when discussing his thesis. This suggests that the theory they are using is wrong and that their point is irrelevant as a critique of Piketty.

        • Transformer says:

          Unlearningecon,

          I don’t think your claim/counterclaim is at all relevant to the paper..

          The “savings will be 100% when g falls to zero” is just an extreme conclusion to be drawn from “savings will increase as a proportion of GDP as g falls”. The latter (it is claimed) is implicit in Piketty’s model.

          It is not being said that Piketty believes that g will tend to 0, but only that he claims g will slow. And the paper claims to show that in his model as g slows savings will increase This seems counter-intuitive to me.

          If you don’t think this is part of Piketty’s model then you need to say what is wrong with the paper not just dismiss it as ‘conventional economic thinking”.

        • Bill Woolsey says:

          Conventional macro theory doesn’t say that growth will fall to zero.

          It is Picketty that says that growth will fall substantially.

          The conventional theory is that _if_ the net saving rate is constant, _and_ growth falls to zero, then in the long run all of current output will be the production of new capital goods to replace worn out capital goods. Gross income will equal depreciation, net income will be zero, and so the constant saving rate out of that zero net income will also be zero. The total capital stock will be constant. There will be no consumption. Again, all productive effort will go to replace the existing capital goods as they wear out.

          If profit, the net return on capital remains constant, then the gross return on capital will need to rise enough to cover that ever increasing depreciation–the need to replace existing capital goods that wear out. There will be more and more to replace as more and more exist.

          It seems to me that it is impossible obvious that the “profit” the net return on capital can remain constant if net income is zero and total output equals depreciation. And so, r>g cannot persist as the total capital stock and so its depreciation (the capital goods wearing out each year) gets bigger and bigger.

          • Unlearningecon says:

            Let me make myself clear:

            The authors completely straw man Piketty. First, while he does claim growth will fall to 1-1.5%, this is not even close to zero. Unless you have serious reason to believe zero growth is a possibility, discussing it is irrelevant. It’s entirely possible for the capital-income ratio to rise/stabilise at a high level with plausible savings rates at the kind of growth levels Piketty is talking about

            Second, Piketty never claims capital to income will “explode”; only that it will rise compared to now. So their entire interpretation of his ‘law’ seems to be incorrect.

            And I’m not inherently bothered that they use conventional economic theory. What bothers me is that they claim to have disproved Piketty’s claim, which is empirically supported, with pure theory (the only data they present is on savings rates). Indeed, it’s quite telling that they reference only the predictions of their model, rather than actual data, for their claims about how inequality will evolve. Even if they’d characterised his argument correctly, I don’t see how this would be an especially noteworthy critique.

            • Major-Freedom says:

              “they claim to have disproved Piketty’s claim, which is empirically supported”

              No it isn’t.

            • Transformer says:

              Even if Piketty doesn’t think g will actually ever be 0, doesn’t his use of a theory which “implies saving behavior that, as the growth rate approaches zero, requires the aggregate economy to save 100% of GDP each year” concern you at all?

              Even if his empirical claims about rising wealth disparity are true surely this aspect of his work would cause one to question whether he has identified the correct theory to explain it.

            • Eduardo Bellani says:

              > What bothers me is that they claim to have disproved Piketty’s claim,
              > which is empirically supported, with pure theory (the only data they
              > present is on savings rates).

              I suggest you talk to a commenter here called Lord Keynes about the need for a correct theory to interpret any data.

          • Bob Murphy says:

            This was a good summary of the situation, Bill. I knew what K and S were saying, but you made it really “jump out.”

    • Bob Murphy says:

      Unlearningecon wrote:

      The paper you link to claims that as g tends to zero, conventional economic theory implies the savings rate must tend to 100% for Piketty’s ‘law’ to hold. They then show that, surprise surprise, savings rate aren’t usually 100%, as if this is somehow a central tenet of Piketty’s book.

      Just in case there are onlookers who have an open mind, let me point out: Unlearningecon, what you’re doing here is totally backwards. No, standard economic theory doesn’t predict that as g–>0, then savings–>100%. On the contrary, they’re saying *that’s what Piketty’s “law” implies*. And since it’s crazy, Piketty’s “law” must not be right.

      Further, they are saying that the type of behavior the law implies, does not match the actual data. People don’t constantly save the same percentage (net of depreciation) of their net income.

      And in any event, are you actually saying Piketty should be given a pass on what he calls a “fundamental law of capitalism” because the situations in which we all agree it would be false, probably won’t come to pass?

      • Rick Hull says:

        It’s amazing (to me) that you have to explain this, Bob.

        Maybe I can put it a slightly different way:

        To call something a Law in the sciences implies that it is universal — that it holds in all possible (even seemingly unlikely) circumstances.

        What Piketty has is more of a hypothesis, and we can test it. We can see what it implies, for some various (even seemingly unlikely) scenarios.

        This sort of analysis dovetails with logic and proofs, philosphy and mathematics. We start with some premises, and we try to drive them to absurdity. Then we can disqualify one (or more of the premises).

      • Unlearningecon says:

        I’ll reply to everyone here because the threads are getting too small.

        Look, I just can’t believe that anybody, including K & S, have read the book properly with this characterisation. Let me quote Piketty:

        “First, it is important to be clear that the second fundamental law of capitalism, β = s / g, is applicable only if certain crucial assumptions are satisfied. First, this is an asymptotic law, meaning that it is valid only in the long run: if a country saves a proportion s of its income indefinitely, and if the rate of growth of its national income is g permanently, then its capital/income ratio will tend closer and closer to β = s / g and stabilize at that level. This won’t happen in a day, however: if a country saves
        a proportion s of its income for only a few years, it will not be enough to achieve a capital/income ratio of β = s / g.”

        He is not claim that the identity will be satisfied at all times or even ever. He is simply claiming it is a tendency – and a slow, rather than explosive one, as the authors seem to be making out. He also goes on to give a number of qualifications, and explicitly contrasts it with his first law, which he says is *actually* true at all times (since it’s an accounting identity). Hence the qualification that g will not equal zero (which clearly renders the basic equation mathematically undefined) is completely understandable.

        The result is that when the authors, having incorrectly interpreted the identity as a straightforward equality, and tried to make out that Piketty is arguing it really is an unassailable ‘law’, solve for ‘steady state equilibrium’, they show absolutely nothing. Don’t get me wrong: depreciation is certainly of interest, and it would offset the process Piketty has outlined, but he was right to ignore it in his general exposition.

        • Transformer says:

          So his “fundamental law of capitalism”

          1. Is applicable only if certain crucial assumptions are satisfied

          2. At g = 0 , is “mathematically undefined”

          3. At levels of g just above 0 will have extremely high levels of savings relative to GDP.

          • Philippe says:

            Piketty is quite clear:

            “this is an asymptotic law, meaning that it is valid only in the long run: if a country saves a proportion s of its income indefinitely, and if the rate of growth of its national income is g permanently, then its capital/income ratio will tend closer and closer to β = s / g and stabilize at that level.”

            • Transformer says:

              Yes, if you make those assumption you derive Pikettty’s results for β = s / g.

              Based on the Krussell and Smith paper however I’m wondering how theoretically and empirically sound these assumption are.

              • Transformer says:

                I took a look at that link.

                I’m not sure I understand what changes in Krussell and Smith critique if you use a depreciation rate of
                0.02 or 0.03 or 0.05, rather than 0.10 (or even if they are actually wrong to have used 0.1)

              • Transformer says:

                On DeLong:

                Even if KS have depreciation rate set too high in their examples this doesn’t change the fact that Piketty’s version of the model drives weird results when g is low and surely makes use of this model suspect.

                Also for KS: Does the 0.1 represent capital depreciation as a % of total output or as a % of total capital stock?

                If the first , then DeLong’s point is wrong and KS are actually underestimating the depreciation rate (which Delong shows to be 16% of GDP).

              • Bob Murphy says:

                Also for KS: Does the 0.1 represent capital depreciation as a % of total output or as a % of total capital stock?

                Everybody in this context is referring to the percentage of the capital stock. DeLong is saying capital stock is 400% – 600% of GDP, and total depreciation is estimated at 15% of GDP or so, therefore depreciation rate must be about 3%.

                However, that result obviously depends crucially on DeLong’s non-sourced assertion that capital stock is 400% – 600% of GDP. The micro-level estimates of depreciation rates on particular capital goods run the gamut, with low rates for structures and higher rates (above 20%) for certain types of equipment and durable consumer goods.

              • Transformer says:

                Thanks for the clarification.

                K&S actually talk about the ratio of capital to net output in their section on low growth:

                “Second, Piketty’s model implies that the ratio of capital to net output goes to infinity
                as g goes to zero. The textbook model implies, for the same ratio, a limit s=((1/[depreciation_rate]/ s)); for
                standard values like s = 0:3 and  [depreciation_rate] = 0:1, we thus obtain a ratio a little over 4.”

                Even with their 0.1 they come up with a ratio of 4 for capita;/output , which is not too far from DeLong’s 5 or 6 – so I’m still not convinced their 0.1 is indefensible.

                I hope they make some sort of reply to DeLong.

              • Transformer says:

                From DeLong

                “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”

                Does that make sense ? is it possible to be devoting 50% of GDP to capital goods, while the capital output ratio is 5 ?

                isn’t there a correlation between % of GDP devoted to capital goods and the capital output ratio ?

              • Transformer says:

                I mean if you are in a steady state where the capital/output ratio is 10, doesn’t that mean that you need to replace 10% of your capital each year to maintain that steady state ?

                Am I looking at this wrong ?

              • Transformer says:

                Oh. of course it would be 1% not 10% – forget my last 3 comments.

            • Major-Freedom says:

              To call something a law of X means you can’t then make it contingent on certain forms of X.

              If this “law” of capitalism is really a special case contingent on premises, at least one of which is known as false, then not only is it not a law because of it being a special case, but it also not a law because the contingent premises are false.

              You cannot fault the critics for treating Piketty’s law of capitalism as…a law.

              Couple that with the fact that Piketty is calling for a worldwide tax on wealth on the basis of this false special case, and the hubris is only more pronounced.

          • Unlearningecon says:

            OK, so now people are no longer arguing about the substance of the matter; they’re just saying that the use of the word ‘law’ is silly.

            You know what? I agree. I hate the use of the word ‘law’ in social science. But the simple fact is that Piketty explicitly points out he’s not using the law in the way he’s been interpreted by KS, and hence their characterisation of him completely misses the mark.

            These arguments about the word ‘law’ are just besides the point, and a way to excuse the continued lazy mischaracterisations (and subsequent dismissals) of Piketty by people who either haven’t read him or haven’t read him carefully enough.

            • Major-Freedom says:

              Could it be that Piketty purposefully chose the word “law” in order to present a theory contingent on a number of (false) “ifs” as something other than what it really is?

              What misses the mark is basing one’s advocacy of worldwide theft of wealth on the basis of a hypothetical set of false if statements.

            • Major-Freedom says:

              That maybe, just maybe, he knew that nobody would play along with his worldwide theft politics, UNLESS he presented his contingent claims as “laws”?

  4. Bob Roddis says:

    Unlearningecon writes:

    My Favourite Blogs of 2013

    Matt Bruenig. While there aren’t necessarily any stand-out posts (although this recent smackdown of Ezra Klein is amusing), I never fail to delight in Bruenig’s effortless dismissals of libertarian theories of…well, everything. He also does some good policy analysis (including a basic income calculator), and blogs in a similar vein over at Demos.

    Chris Dillow (Stumbling and Mumbling). There should probably be a rule against including Chris Dillow on lists like this – everyone can just agree that he’s a Really Good Blogger. His unique mixture of marxist, behavioural and mainstream economic reasoning makes him both endlessly interesting and frustratingly hard to disagree with, even when he is casually tearing your pet beliefs to pieces. Oh, and his sidebar ‘top blogging’ is always worth a look.

    Noah Smith (Noahpinion). Despite the fact that Noah’s dismissive attitude toward heterodox economics irritates me, there’s no denying that he is an excellent and consistent blogger. Naturally, I enjoy his posts on macroeconomics, but he also writes interesting things about Japan, has good overviews of economics debates and makes a lot of interesting political/miscellaneous posts.

    ‘Lord Keynes’ (Social Democracy for the 21st Century: a Post-Keynesian Perspective). This blog has always been a great source of, among other things, post-Keynesian theories and criticisms of Austrian Business Cycle Theory. However, this year LK pushed the boat out with relentless attacks on both marginalist theories of pricing and Mises’ a priori philosophy. An excellent resource for heterodox economists.

  5. Bob Murphy says:

    For what it’s worth, at this point my best guess is that Piketty simply forgot about depreciation altogether. [Rest edited out, because Keshav showed me below that Piketty didn’t forget…–RPM]

    • Keshav Srinivasan says:

      Bob, here’s a reference to depreciation on page 178:
      “I should also be clear that the notion of savings relevant to the dynamic law beta = s / g is savings net of capital depreciation, that is, truly new savings, or the part of total savings left over after we deduct the amount needed to compensate for wear and tear on buildings and equipment (to repair a hole in the roof or a pipe or to replace a worn-out automobile, computer, machine, or what have you). The difference is important, because annual capital depreciation in the developed economies is on the order of 10–15 percent of national income and absorbs nearly half of total savings, which generally run around 25–30 percent of national income, leaving net savings of 10–15 percent of national income (see Table 5.3). In particular, the bulk of retained earnings often goes to maintaining buildings and equipment, and frequently the amount left over to finance net investment is quite small—at most a few percent of national income—or even negative, if retained earnings are insufficient to cover the depreciation of capital. By definition, only net savings can increase the capital stock: savings used to cover depreciation simply ensure that the existing capital stock will not decrease.”

      • Bob Murphy says:

        OK thanks Keshav. I’m not sure if that makes things better or worse. When he’s talking about the elasticity of substitution, do you remember seeing him mention depreciation?

        • Transformer says:

          I found this post very helpful in understanding the implications of all this.

          http://marginalrevolution.com/marginalrevolution/2014/06/piketty-v-solow.html

        • Keshav Srinivasan says:

          I’m not sure, I haven’t actually read Piketty’s book. By the way, I should add that the quote I gave comes with a note, which as Delong says discusses the very equation that Krusall and Smith say that Piketty neglects:

          “One can also write the law β = s / g with s standing for the total 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). For example, if the raw savings rate is s = 24%, and if the depreciation rate of the capital stock is δ = 2%, for a growth rate of g = 2%, then we obtain a capital income ratio β = s / (g + δ) = 600%. See the online technical appendix.”

  6. Philippe says:

    Bob,

    “do you remember seeing him mention depreciation?”

    Brad DeLong:

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

    2nd June 2014

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

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