More on Piketty

I continue to agree with Paul Krugman that the Financial Times and Tyler Cowen have picked an unlikely battle with Thomas Piketty in trying to claim that wealth inequality in the United Kingdom has been decreasing rather than increasing over the last 40 years; more on this from Carter Price. As for Piketty’s broader claims of century-long trends (to perceive which the French scholar has to dismiss much of the twentieth century as an anomaly), King Banaian’s summary of some of the details in how Piketty misreported the data are troubling.

The core claim of Piketty’s book is that slower economic growth will lead to a huge increase in the capital/income ratio as a consequence of a relation that Piketty described as the “second fundamental law of capitalism”. I earlier explained why Piketty’s law is complete nonsense. Separately, James Galbraith explains why the first “law” as interpreted and applied by Piketty is also highly problematic.

Many of us believe that relatively recent globalization, rather than Piketty’s broad theories or asserted sweeping historical trends, played an important role in growing income inequality within most major developed countries over the last generation. But it should also be noted that this same globalization has also been the key factor in reducing inequality on a global scale in the sense of profoundly raising the standard of living for billions of residents of developing and emerging economies.

UPDATE: I see that Per Krussel and Tony Smith came out with a paper today elaborating on the points I made on Sunday. Hat tips to Greg Mankiw and Tyler Cowen.

50 thoughts on “More on Piketty

  1. Tyler Cowen

    Do please be clear though on exactly what I have argued. I do think it likely that wealth inequality for the UK top one percent has gone up. But if the best numbers we have, as presented by the FT, don’t show that, perhaps wealth inequality numbers are simply not up to supporting (or refuting) Piketty’s story one way or the other, Arguing “we know this intuitively” isn’t really helping Piketty’s work much, because it implies he is adding relatively little on the empirical side.

    1. BananaGuard

      “But if the best numbers we have, as presented by the FT,…”

      Hold the phone. Whether the FT got its data right is a major point of dispute. To assert that the data set that has to be right in order for your point to hold is the “best numbers we have” is a highly questionable way to support an argument.

      There must be a term for Cowen’s slick behavior. “Begging the data” perhaps.

  2. pete

    Globalization and the tech revolution explain all, from what I see. Income/wealth ratios are pretty stable till you get to Bill Gates Larry Ellison and pals. And that wealth will dissapate, and incomes will eventually normalize, much like the decline of the robber barons/Vanderbilts/Rockefellers etc. 1920 to 1968 showed gains in equality. Then globalization (China opened up thanks to Forest Gump) and the tech revolution happened. In a couple of generations all will be normalized, maybe back to 1968 levels, with higher incomes for all.

    1. mlnberger

      “And that wealth will dissipate”: that phrase hides the reason why Piketty is rousing such emotion. The redistribution of the riches accumulated during the late 19th c. did not occur naturally, but as a result of tumultuous political action and even war. The fundamental issue, for me, is the suggestion that Huey Long’s prescription that “no man is a king” is sound economics, not dangerous radicalism, and that the battlefield is the role assigned to the government, either the “ruling committee of the bourgeoisie” or as utilizing its powers to effect this necessary redistribution and restore growth to the economy.

  3. Patrick R. Sullivan

    Colombia’s Xavier Sala y Martin has a very funny, detailed, analysis of Piketty’s book, in Spanish, on his website. But since he thinks about economics in English, Google translate does a decent job making it readable;

    My cleaned up version of one paragraph from it;

    If the most famous thesis of Piketty is true and the rate of return on capital is higher than the growth rate of the economy (r > g) , it follows that we should have a capitalized social security system . I.e., with the current system of PAYGO in which young workers pay taxes on their wages to supply the pensions of retirees, the rate of return they get is the growth rate of wages, ie, ‘g’. If, on the contrary, we take the money wages of theose young and we invested it in capital would get a return ‘r’ . If, as Piketty says, “r > g “, retirees could enjoy a much higher pension if the pension system was fully funded! Which is what I argued to the union leader and former leader of ICV, Joan Coscubiela in a debate on the future of work we did on TV3 . He said the return on capital was much higher than the growth rate of wages and that meant that capital “ate” an increasing share of GDP. I warned him to be careful of that argument because the immediate implication was that the model of a fully funded pension is superior to PAYGO. I got the impression that Coscubiela did not understand the contradiction of his own argument, but Thomas Piketty does understandthat . So he devotes an entire section of his book to discussing pensions. Recognizing the validity of the argument, Piketty explains that now it is too late to change the system because at the time of the transition would have a generation that has to pay twice [My note; that’s not a valid argument, as Milton Friedman has demonstrated]. But that argument is not valid for emerging countries that do not yet have a pension system. I wonder if Piketty (and Coscubiela) advocate the introduction of a capitalized private pension scheme for poor countries that do not have social security. In fact, the argument is not valid for the rich countries: if truly the return of capital is so superior to wage growth, you could take some of the excess return, save it and grow it until you have enough money to make the transition . Why not defend that, Piketty! Then there is a second reason for not wanting a funded system: the return on capital is higher, true, but it is also vastly more volatile and uncertain! That is, after writing an entire book on the great bargain it represents for the rich to have capital, at the end of the book he confesses that some of the higher return is compensation for taking higher risk. A risk that Piketty does not want workers to take. Curiously, Piketty does not analyze the risk assumed by capitalists throughout the book. Piketty speaks of the rate of return of capital as an overpayment to a class of citizens who do little more than suck the blood of the workers. At the moment of truth, however, Piketty confesses that, at least in part, that “r” rewards risk taking by those who invest. It’s one thing simply to get a return for exploiting your fellow citizens, and quite another to reap a reward who taking a risk that the rest of society (and Piketty most of all!) is not willing to take. This lack of rigor in analyzing the relationship between return and risk of capital is one of the major shortcomings of the book.

    Which is characteristic of most of the review. Sala y Martin is one guy who could quit his day job and make it as a comedy writer.

  4. Ricardo

    I don’t think there is much doubt that there has been an increase in income inequality. As Pete notes income equality increased before Johnson’s Great Society spending binge and then Nixon leading the world on to floating, and crashing, monetary units. Any time the monetary unit declines the rich who are the holders of capital will benefit while the poor who hold what wealth they have in currency will lose.

    Additionally, with government, local, state, and federal, expropriating savings to be distributed to those who consume there is reduced capital accumulation. Those who have capital once again benefit while those desiring to accumulate capital lose.

    Then there are the redistribution efforts of government. All redistribution creates over-consumption because the market is subverted and capital is diverted away from producing goods to consuming goods.

    We always find an increase in income inequality in command economies where the political class is the parasite confiscating wealth to support their spending habits while the income producers are the hosts being bled dry. This becomes obvious when we understand that the middle-class was a creation of free markets.


    1. pt

      There are plenty of data indicating an increase in inequality since about the mid 1970s in the US, contrary to Giles’ polemics. But nearly all advanced economies have experienced a similar rise in inequality. Based on pure market forces, as measured by the before taxes and transfers Gini coefficient, the US is only 0.01 above the OECD average (OECD, 0.45; US, 0.46). So many of these countries fare worse based purely on market forces. However, after taxes and transfers we rise (or fall) to the number one ranking among those same OECD countries (OECD, 0.33; US, 0.38). It is our tax regime, conceived and voted upon by a body with a majority of millionaires, that has the crucial effect on inequality in the US. And to expect our educational system, based largely on local property taxes, to redress this inequality is more than a bit naïve.

    2. BananaGuard

      No, no, no. This is just Ricardo doing the right-wing shuffle. Everything is about taxes. Any bad trend is the result of taxes rising on (mumble). Any good trend is the result of taxes falling on (mumble). Here we have a very well regarded scholar making an argument based on years of data analysis, and Ricardo’s answer is “no, it’s taxes”. Ask Ricardo why music ain’t the same as it once was or why athletes take steroids and he’ll tell you it’s because of taxes. Knees hurt when the weather changes? Ricardo says it’s because of taxes.

  5. Bruce Hall

    Interestingly, there are those who try to point out that there is a difference between income distribution and wealth distribution. That difference is not always appreciated. One study indicates that the most wealth now are a smaller percentage of total wealth than a century ago.

    Now I’m going to throw darts in the dark, but with all of the high tech IPOs over the past 2 decades, it would seem that at least some of the wealth was “paper” wealth as IPOs for and the like were quickly gobbled up by wise investors. Another issue for the U.S. has been the substitution of machinery for human labor in higher paying skilled jobs such as those found at Ford Motor Company and General Motors. The lower need for labor along with the required higher skill sets for that labor leave your average high school graduate and many college graduates wondering what happened and why their education didn’t prepare them for what they faced. I’d guess a lot of farmers around 1900 felt the same way.

    So, we have a situation where, through information and technology, we can create wealth quickly, but incomes are harder to come by. Should we emulate those who are skillful in the 21st century dynamics or penalize them so that we can support those stuck in the 20th century? And if we choose the latter, does that solve our problems or make us less competitive and exacerbate the problems?

  6. Nick G

    A very minor correction: there’s a “Pikkety” in the article. For me, it interrupted the flow of the argument…

  7. DeDude

    The “natural” development in societies is for the rich to try obtaining as big a piece of the pie as they can get away with – not as a strategy, but as the simple sum of greedy individuals trying to get as much as they can for themselves. In that process they will try to game, rob and rape the available system the best they can. The results can be seen in dictatorships all over the world (in past and present) – a large group of people barely surviving and producing wealth for a very small group of plutocrats with the power and brutality to keep it that way. Every now and then a rebellion will smash the plutocrats, but eventually a new group of plutocrats develop and you get back to the same state. The unique thing that happened after the great depression and WW2 was the development of functional democracies in western countries, allowing the masses to succeed in demanding a fair share of wealth and income. Furthermore, enormous amounts of resources had to be used towards rebuilding of infrastructure (a increase in demand way beyond anything previous wars had produced). This gave those countries a middle (consumer) class, which allowed continued growth in demand (to levels much higher than what is possible if only the top 1% are consumers). From there came the GDP difference between south and north America. But the rich are like the scorpion, driven by who they are, and have continued to game, rob and rape the system to get more for themselves individually (not understanding or caring about the big picture). There is no doubt that with the election of Reagan and ever since, the rich have been getting the upper hand, and as a result inequality has increased. The question is how far will that go – with clueless morons like the Koch brothers, it may end up going “all the way”.

  8. T

    I’m with Tyler of the Mercatus Center — let’s wait for more results on wealth inequity.
    I’m also with the American Petroleum Institute — let’s wait for more results on global warming.
    And I’m with the American Tobacco Institute — let’s wait for more results on lung cancer.

    You can never be too careful.

  9. 2slugbaits

    JDH Not directly related to Piketty’s thesis, but don’t we get the requirement for wealth depreciation from the (sometimes hidden) assumption that capital is in some sense physical and homogeneous for purposes of an aggregate production function? It’s not obvious to me that all forms of wealth are subject to depreciation, especially as Piketty defines it (see below). Art is a form of wealth and much of it is likely to appreciate. Personal human networks are a form of wealth, and those tend to appreciate with time and use rather than depreciate. Just ask a Washington lobbyist. In fact, with some kinds of wealth the marginal value of the 101st unit exceeds the marginal value of the 100th unit…at least up to some limit. And even when some assets do depreciate (e.g., ubiquitous software like Microsoft Office), the costs of depreciation are borne by the consumer rather than through savings. And if we go back to Piketty’s Ancien Regime, major sources of private wealth were in gold (which does not physically depreciate) and titles of nobility (which tended to appreciate in value). Those two wealth assets did not produce economic growth either. Maybe what Piketty needs to show is that economies tend toward the accumulation of unproductive wealth that can be used to extract income flows.

    One minor clarification to your post. Piketty’s definition of national income includes income from overseas assets, not just net domestic product. Not trivial if you’re 19th century Britain with an East India Company or Ancien Regime France with colonies in the tropics.

    Piketty’s definition of capital or wealth (page 48), which he says can be used interchangeably: To summarize, I define “national wealth” or “national capital” as the total market value of everything owned by the residents and governments of a given country at a given point of time, provided that it can be traded on some market. So this would clearly include assets that are immune from depreciation. In fact, Piketty’s definition of capital goes beyond the kind of capital that is imagined in production functions. He means tradable assets, whether productive or not.

  10. Rick Stryker

    I wanted elaborate on the comment I made yesterday on Piketty’s “second law of capitalism.” I gave an example of odd behavior when g > 0, but didn’t have time to go through the details. I’ll do that now.

    When I originally read through Piketty’s second law of capitalism, I was struck by his handwaiving proof. I understand why he’s resorting to that, as he’s trying to write a book that can appeal to a broad audience. However, the danger in the handwaiving is that it can obscure the details of what’s really going on, as the corollary to the “law” that JDH pointed out shows. I ended up just writing my understanding of the argument out more rigorously in order to assess what Piketty’s really doing with his law.

    Let’s define Y(n) to be income at the end of period n, K(n) to the capital at the end of period n, s to the be saving rate from income net of depreciation, d to be the depreciation rate of capital, and g to be the growth rate of income over each period. Y0 is initial income and K0 is initial capital. Time is discrete.

    As I understand it, Piketty’s second law is really a set of simple difference equations.

    The first equation is Y(n) = (1 + g)Y(n-1), which says that Y grows over the period at rate g.
    The second equation is netY(n) = Y(n) – dK(n-1), which says that income net of depreciation is equal to income minus depreciation of capital over the period.
    The third equation is K(n) = K(n-1) + s*netY(n), which says that capital at the end of the period is equal to capital at the beginning of the period plus savings from net income. Note that depreciation has been implicitly added back to capital in this equation.

    So, we can write the “second law of capitalism” as the set of difference equations
    Y(n) = (1+g)Y(n-1)
    netY(n) = Y(n) -dK(n-1)
    K(n) = K(n-1) +s*netY(n) = (1-s*d)K(n-1) + s*Y(n)

    If we start with JDH’s case, we have g = 0 and Y(n) = Y0. Then, solving the difference equation for K(n) we can verify that the solution is

    K(n) =[ (1-s*d)^n][K0 – Y0/d] + Y0/d

    Now, if we let n go to infinity, the first term on the right hand side of the K(n) solution goes to zero and you get equilibrium capital K to be

    K = Y0/d

    So, if Y0 is 100 and d = 10% then K = 1000 as JDH showed.

    Also, since netY(n) = Y(n) – d*K(n-1) = Y0 – d*K(n-1) and we let n go to infinity, we have that netY = Y0 – d*Y0/d = 0. Thus, net income goes to zero while the ratio of capital to net income increases without bound. A bizarre result indeed.

    However, I wanted to emphasize in my comment that the “law” can also give very odd results when g > 0. If g > 0, we can verify that the solution to the difference equation for K(n) is

    K(n) = K0*(1-s*d)^n + sum(from j =1 to n) [(1-s*d)^(n-j)]*s*Y0*(1+g)^j]

    By using netY(n) = Y(n) – d*K(n-1), we can verify that the ratio K(n-1)/netY(n) goes to s/g as n goes to infinity as Piketty claimed. But these equations also allow us to study the dynamics of K(n) and netY(n) as the ratio converges. The behavior can be highly implausible for small g. For example, in my previous comment, I considered the case where g = 0.5% per year, Y0 = 2000, K0 = 5000, s = 10%, and d = 10% and where the step size is 1 year.

    If you look at the dynamics, you’ll see that netY initially starts to drop and continues to drop for the first 60 years or so reaching a low level of 1,363. Then it turns around and starts climbing, reaching 2,000 about 200 years out. At that point the ratio of K/netY is over 18 and as time goes on the ratio continues to converge to 20. More bizarre behavior.

    When you write out the precise assumptions and structure of the “second law of capitalism” it’s clear that it’s a surprisingly primitive theory of saving and capital accumulation. Key parameters are exogenous rather than being linked explicitly to agents’ optimal decisions in the presence of constraints. The savings and depreciation actions are imposed ex cathedra rather than emerging from the theory. No wonder the “law” can lead to such odd results.

    The “second law of capitalism” is quite a flimsy theoretical edifice upon which to base a theory of capital.

  11. Bruce Hall

    DeDude, the two wealthiest Americans, Bill Gates and Warren Buffet, have supported primarily Democratic Party candidates, but we won’t count them in your “clueless morons” with money because they don’t fit your preconceived notions.

    1. DeDude

      They are not counted as clueless morons because they have looked at the real world and understand that in the end predatory capitalism is cannibalistic and everybody lose. They are able to look at the astonishing difference between north america and south america and understand why there is such a huge difference.

    2. Nick G

      How much money have Bill Gates and Warren Buffet contributed, and how does that compare to spending by the Kochs? Don’t forget to include all of the various forms of influence, including captive “think” tanks (e.g., AEI, Heartland Institute, Cato, etc), and the more recent forms of “free speech” (Would Benjamin Franklin have agreed that writing a check counts as free speech??).

  12. Steven Kopits

    I am currently writing a book on supply-constrained oil markets forecasting. This naturally involves a good bit of researching, and I stumbled on a good summary resource for vehicle, energy, GDP and CPI numbers, all in excel tables. This is not a bad place to start in looking for oil and transportation statistics.

    From Oak Ridge National Laboratories:

  13. PeakTrader

    Capital creation results from efficiencies in production, where more output is produced with fewer inputs.

    Output = GDP = income; and income = consumption + saving.

    Using fewer inputs (or limited resources) to produce more output allows the economy to expand.

    So, both capital and output rise.

  14. Hans

    As presented by, Jason Lewis, there is an immediate solution to this
    inequality debate.

    No need for complex studies or math equations.
    Convert your labor into an equity position, just like the owner..Forgo
    a pay check, wait for revenues to stream in and then hope
    that all costs are covered, leaving the typical 5% net margins on
    gross sales; and then a satisfactory distribution.

    To compare labor (guaranty return) verses capital (risk taking)
    is abhorrent and beyond the pale.

    Remove the corporate income tax and 75% of property tax and you
    would experience a new revolution in America’s market place;
    with innovations, lower prices and higher employment/wages..
    But that would be a direct assault on Socsheviks’ dogma.

    Unfortunately, America now has a large minority, whom believe
    that daily labor is a dysfunction and a social inequality.

  15. Patrick R. Sullivan

    A little more from Xavier Sala y Martin (again translated from Spanish);

    ‘ We see that 10% of the richest population of France had 80% of the total wealth of the country in 1810. This proportion rose to nearly 90% in 1910. Thereafter, a systematic decrease is observed up to 60 % in 1970 and since then, it has stagnated (or experienced a slight increase). The richest 1% of the country, meanwhile, had 45% of the wealth in 1810, 60% in 1910. Since then, the share of wealth of the super-rich was down to 22% in 1970 and increased slightly to 25% in 2010.

    ‘The same pattern is observed in Britain and Sweden: increasing the fraction of wealth held by the rich and super-rich in the nineteenth century, the proportion falling between 1910 and 1970 and slight recovery since 1970.

    ‘In the U.S. (where the 1810 and 1870 data are much less accurate, partly because of having to assess the value of the slaves, who Piketty devotes an entire section of his book), the pattern in the twentieth century is basically the same though the numbers have been much more stable over time. The big difference is that the fraction of total wealth that had the rich and super-rich in 1800 was much lower in 1810 (57% and 25% in the U.S. compared with 47% and 80% in France). During the nineteenth century, then, inequality in America increased slightly more than in Europe. But the pattern is basically the same: increase during the nineteenth century, reduction between 1910 and 1970 and increased (mild) from 1970.’

    So, the question is what is the norm, and what is the aberration?

  16. Patrick R. Sullivan

    Everybody has fun trashing the French, including the Spanish;

    … the fundamental message of the book is; as the rate of return on capital is higher than the growth rate of the economy (and therefore wages), the “capitalists” obtained an increasing share of the pie, leaving inheritance to their children, who therefore, are born rich. The return of inherited wealth that they will get will also be higher than the growth rate …. And so dynasties; the rich getting richer relative to workers, and capital has become increasingly large relative to the rest of the economy.

    This constant increase in inequality is a major problem for capitalism because it generates political instability: per Piketty, the mass of poor workers will end up rebelling against the rich minority, and through democracy or violence will destroy the system. That is the “central contradiction of capitalism”. A contradiction that will ultimately lead to self-destruction.

    To fix the problem requires taxing inheritances and capital, to break the dynasties of billionaires and their possibly dominating the economy. Everything from the finding that the rate of return on capital is higher than the growth rate of the economy. Everything from “r> g”.
    This logic of Piketty, however, has a little problem: IT IS FALSE!

    Let the rate of return on capital, r, be greater than the growth rate of the economy, g. Far from being a “contradiction of capitalism” this is a condition that economists have dubbed “dynamic efficiency”. If an economy has “r <g", it is inefficient in the sense that it has saved too much. That is, if "r g.” And that would be true in a capitalist economy and a planned economy. so, the inequality “r> g” isn’t the “central contradiction of capitalism”, it is an aberration.

    Moreover, contrary to the claims of Piketty, the fact that r is greater than g implies neither the rich spend their savings on to their children, nor that wealth grows faster than GDP, or that rich dynasties are increasingly richer, or that social inequalities grow.

    Imagine, for example, a world in which individuals work when young and retire when old. Knowing that someday they will retire, so when young, save money and invest. When they are old they use their savings (and the rate of return on their savings) to survive. It’s no longer a dollar inheritance to their children if they die with nothing.

    The children do the same parents and, thus, generation after generation. All economists know that in this world of “overlapping generations” the rate of return on capital, r, may be higher, exceeding the growth rate, g. If the economy is dynamically efficient, then it is true that “r> g” and yet, no one leaves a euro inheritance!
    Unlike what Piketty says, logic does not dictate in any way, that “r> g” implies that inherited wealth grows faster than GDP, partly because inherited wealth can be exactly zero in worlds where “r> g”!

    In the real world, of course, the rich do not consume everything they have and leave part of their wealth in inheritance to their children. It is also true that for many of them an important part of that wealth is spent on lavish parties, boats, airplanes, luxury travel or philanthropic actions such as Bill Gates or Warren Buffet.

    Furthermore, unlike what happened in ancient times, where all the wealth went to a single heir, now the property of the rich is divided between many children (often from different marriages) so that from a very rich grandfather You can have very poor grandchildren. It is well known, the saying that the grandfather created a fortune, his children extend the fortune, and the grandchildren squandered same.

    The world could have “r> g” and, in turn, be filled with families whose grandparents create fortunes , the grown children and grandchildren destroy them. And contrary to what Piketty says, in that world there would not be more and more rich and powerful dynastie., However, it would be true that “r> g”!.

  17. Rick Stryker


    Piketty is well aware of the point you made that when g = 0 or g goes to zero, the capital to net income ratio becomes infinite. He discusses the point in the section “Back to Marx and the Falling Rate of Profit.” But reading that section, you see that PIketty thinks that this is a desirable feature of the model that’s explaining some real phenomenon. Piketty gives a Marxist interpretation of this property of the “law,” arguing that it reveals the central contradiction of capitalism. If g = 0 or is low, capitalists still desire to save in order to perpetuate their power or because they already have plenty of money. In the process where the ratio goes to infinity, the return on capital goes to zero and capitalists “dig their own graves” by fighting wars or paying labor a smaller and smaller share of income.

    Piketty seems to be suggesting that permanent productivity is the only thing that saves the economy from this fate. Marx, he thinks, didn’t realize this. Wonder what you think of this?

    1. James_Hamilton Post author

      Rick Stryker: But all these problems come from insisting that the net saving rate s has to be constant. Devoting 100% of GDP to replacing worn-out capital leaving nothing ever to consume for yourself or anybody else is not perpetuating your power, it’s pouring money into the ocean for no purpose whatever. If you assume that people pour their money into the ocean for no purpose whatever, then I agree that capitalism is going to run into problems. But a central tenet of those who see redeeming features in capitalism is the belief that people try to do what they perceive to be in their own best interests. To build a workable model of capitalism, you need to examine what is actually in somebody’s interests to do in the circumstances in which they find themselves, not make up some arbitrary rule that you assume always characterizes their behavior.

      1. Patrick R. Sullivan

        A nice example of capitalism in practice comes from this AP story;

        ‘In brewery-heavy San Diego, Green Flash Brewing Co., Stone Brewing Co., Societe Brewing Co. and others supply their spent grain to David Crane, a home brewer whose small company makes “Doggie Beer Bones” out of the beer leftovers mixed with peanut butter, barley flour, eggs and water. They’re sold in breweries and pet stores nationwide and on the Internet. But don’t worry, Fido, won’t get drunk off of them — they don’t contain alcohol or hops, which are harmful to dogs.’

        Reminding me that John D. Rockefeller built his Standard Oil fortune refining Pennsylvania’s oil into kerosene for lighting homes. Then there was this waste product that competing refiners burned off; we call it gasoline.

      2. Rick Stryker

        I agree. But I guess I’m surprised that Piketty would seriously make an argument like this. The data part of the book is good but the analysis seems very poor, and crankish in many places.

      3. 2slugbaits

        Your timing could not have been worse. Talk about plutocrats pouring their wealth into the ocean, Steve Ballmer decides to pay $2 billion for the LA Clippers…formerly the San Diego Clippers. Ugh!

    2. 2slugbaits

      Rick Stryker In a peculiar sense holding “s” constant is a kind of “fundamental” law of capitalism, albeit not necessarily in the way that Piketty said. By that I mean the way that a constant “s” was fundamental to neo-classical growth theory in the dictionary sense of the word meaning “foundation or base.” The early models assumed a constant “s.” They also assumed that it was exogenously determined. Of course, the same could be said for the capital consumption parameter; it too was treated as exogenous and constant. Just as a constant savings rate is suspect, so too is a constant capital depreciation rate. Fifty years ago the capital consumption rate as a percentage of the fixed private productive capital stock was half of what it is today. On the other hand, in the 13th century it was around 6 times higher than today. So it changes. In fact, there’s nothing that says the capital consumption parameter for non-physical capital assets couldn’t change signs and yield appreciating capital stocks.

      More recent models use savings rates that are endogenously determined, but when you look under the hood those endogenous savings models always slip in some kind of exogenous fixed factor (e.g., a fixed intertemporal substitution factor derived from some constant risk aversion assumptions). I always had the feeling of being cheated with some sleight of hand.

      I agree that the intellectual drive to find some kind of fixed constant is analogous to Marxist thinking. And as I’ve said many times before, that same craving for some kind of fixed, north star that is forever true also underpins a lot of very conservative economics. And by “very conservative economics” I mean Austrian economics and the kind of stuff you might read over at I think this emotional need for a fixed reference point is behind a lot goldbuggery. That’s why I believe that in his heart of hearts, poster Ricardo is really a closet Marxist who is suffering from a bad case of false-consciousness.

      On the other hand, I am perfectly comfortable with complete relativism in which everything is in flux. If there’s a fundamental law of capitalism, that’s probably it. I’ll go a little further. I think all of these growth models are (to use JDH’s preferred term) “bunk.” We’re kidding ourselves if we think we can really understand long-run economic growth. Technology surely has a lot to do with it, but we can’t even coherently define what “technology” means in these models in a way that doesn’t eventually come down to being a polite word for “error term.” Even “capital” and “labor” are fuzzy. Is human capital part of labor or capital? Oh wait, let’s fudge and call it “augmented labor.” Even Paul Samuelson eventually admitted that all of these growth models based on aggregate homogeneous production functions cannot really be defended in a rigorous way. I think we can use these models for insights and clues, but it’s a mistake to take the math too literally.

      Regarding Piketty, what I see as a real tension in Piketty’s argument is that in the end he doesn’t really seem to believe that what he claimed earlier was an economic law is in fact an economic law. He kind of walks it back. If he really believe that these were immutable economic laws, then why would he argue for amelioration through political reforms and global wealth taxes? Why not just spend life on nude beaches along the French Riviera and get drunk? Hmmm…come to think of it. At the end of the day my sense is that what we have is a political problem. Stupid and inattentive voters being taken in by corrupt and mendacious (and usually Republican) politicians who use their positions to secure monopoly rents for the rich. So the rich get richer and people in Kansas get Brownback governance.

      JDH this same globalization has also been the key factor in reducing inequality on a global scale in the sense of profoundly raising the standard of living for billions of residents of developing and emerging economies.

      I don’t disagree. But there’s a paradox here. On the one hand globalization and market economies have narrowed the gap between the richest and poorest countries (a good thing), but on the other hand those same forces have widened the gap between the richest and poorest within each country. In a material sense much of the most abject, conscience shocking poverty has been reduced. I would credit much of that to not just globalization and market economics, but the spread of more democratic political institutions in much of the 3rd world. In any event, it’s a good news story. But what the econ god gives with one hand he taketh away with the other. Increasing wealth and income inequalities in the developed world are undermining our democratic political institutions, and that is not a good news story. The tough moral question is whether the trade-off in better material conditions for those in other countries is worth the cost of drifting towards oligarchy in the developed world. I think that’s a genuinely tough moral and political question.

      1. Nick G

        Increasing wealth and income inequalities in the developed world are undermining our democratic political institutions

        I’m not sure I follow that cause and effect. The Kochs (and other oligarchs) are using a small fraction of their fortune to undermine our democratic political institutions: they could do just as effectively if they were worth 1/4 as much. I’d say that the Kochs, for instance, are driven by the desire to hold back the forces of change in the resource extraction/energy world. They’re threatened by the inevitable shift away from mining, drilling and raw resource consumption that they celebrate as the centre of their business model.

        What is making the wealthy so willing to embrace narrow and short term goals? Why the shift from “liberal” Nelson Rockefeller? Or, have we simply become more aware of the sociopathic behavior of a relatively small portion of the very wealthy?

        1. 2slugbaits

          Well, even with one-fourth the wealth they would still be much richer than the oligarch wannabe fifty years ago. The danger is that extreme wealth and old age tend to make for nutjobs and cranks. If they were merely wealthy (like George Romney), then their powee would be unequal, but not godlike. The merely wealthy still have to accommodate themselves to the rest of the world. Not so with extreme plutocrats. They buy media outlets, buy academics, buy state legislators, and buy protection from criminal prosecutions by threatening mutual assured destruction if a prosecutor should be dumb enough to actually consider charges. How many finance crooks from the big investment baks have gone to prison? The executives didn’t commit fraud, it was The BANK? So we get the doctrine of collateral damage. But God help the welfare mother who gets caught having her boyfriend living with her. All those things undercut respect for laws and democratic institutions. Conservatives are always comparing the US to the late Roman Empire. A better comparison would be the late Roman Republic under Crassus, Pompey and Caesar…plutocrats all.

          1. Nick G

            I agree generally with those ideas, but it’s not clear to me that the relatively recent decrease in equality is the important factor in what appears to be a dramatic increase in untoward influence over public policies and ideas.

            I have the impression that the .1%’s share of income and wealth has increased by 2-3x. Again, they would have more than enough money to buy influence with 1/2 or 1/3 as much money as they have now. So, what’s changed?

      2. Rick Stryker


        I wasn’t saying that the drive to find a fixed constant is analogous to Marxist thinking. I was pointing out that Piketty fully believes the implication of his law for g = 0 and sees it as a confirmation of what Marx was arguing less rigorously. Piketty says that directly in the book.

        I don’t mind at all that some deep parameter of a model is fixed. But the rate of saving should not be that parameter. The saving rate should be a choice that depends on the economic environment, such as the current level of income, future expectations of income, the rate of time preference, etc. Piketty just asserts that people will keep saving a constant percentage from net income in his second “law.” That assumption leads directly to the bizarre implication that net income goes to zero. Rather than see that as a problem for his theory, Piketty fully embraces this bizarre implication and bases his policy prescriptions on it.

        I don’t believe he’s walking anything back. Piketty believes his law implies that capitalism will inevitably produce higher capital to income ratios. That tendency in Piketty’s view was broken by the interruption of the world war, in which taxes climbed much higher and for a time reduced capitalism’s necessary march towards higher capital concentration and inequality. But Piketty believes that it is essential to raise taxes dramatically again, to over 80%, and to institute a world wide capital tax. After taxes have gone up very dramatically, perhaps then Piketty will go relax on the beach.

  18. Ricardo

    Reading Peter Schiff’s article on Piketty made me realize that Piketty has used the Marxist slight-of-hand to ask and answer the wrong question. If the rich are 1,000 times more wealth than the poor, but the poor have access to everything that the rich have access to only at a lower level of quality is the society better off that when the rich are only twice as right as the poor but the poor are starving? Capitalism deals with reducing uneasiness (Mises). If it is successful in this can it be criticized. Socialiam, Marxism, central planning, and any form of the commant economy promises a better world for the poor. If there is overwhelming evidence that they are total failures and their systems only make everyone less wealthy are they better than capitalism.

    There is no question that for most of the history of the United States the poorest was better off than the poorest in the rest of the world. The United States has fulfiledl the capitalist goal. Now as central planning and redistribution are forced into law is there greater want and need satisfaction.

    Today we waste ourselves asking then attempting to answer the wrong questions.

  19. baffling

    “If the rich are 1,000 times more wealth than the poor, but the poor have access to everything that the rich have access to only at a lower level of quality is the society better off that when the rich are only twice as right as the poor but the poor are starving? ”
    except that the poor do not always have access to the same things but only lower quality. health care is a prime example. yes the poor have access to aspirin, but in no way is that considered a lower level of quality than the chemotherapy drug required to treat cancer.

  20. Mark S

    Of course “r > g”….. Capital is defined, in part, by claims on debt. The reality is however, that periodically the claims on that debt get wiped out because of banking/financial collapse. (Over time, government regulators and banking institutions become infiltrated by grifters, who will sell more securities than there are available assets).

    I am mystified, that this concept (so vividly demonstrated by recent financial events), continues to be sidestepped in Economic conversations.

    1. Patrick R. Sullivan

      A big problem for Piketty’s story is (again from Xavier Sala y Martin);

      ‘Starting 1950, the capital increase [in France] occurs almost exclusively by increasing the value of homes and not productive capital! Looking at the “business capital” only, we see that the relationship between capital and GDP remains essentially constant between 1970 and 2010. All, or nearly all, the increase in Piketty data are due to home values. And the same applies to all other countries discussed in the book.

      ‘It is true that homes are part of the family wealth. But if the increase of wealth is not the result of the accumulation of productive capital by the rich but rather the increase in the price of their homes, the theory that the rich capitalists exploit the working poor and therefore capital increases growing relative to the rest of GDP seems-fetched .’

      Of course, you can quibble about how to value residential real estate, but most people don’t derive any real income that way. Back to ‘Sally Martin’;

      ‘…in the case of France [using Piketty’s data], the total capital does not increase from 1950 but remains constant between 1950 and 2010 drops slightly between 1950 and 1970, remains constant between 1970 and 2000 and increased between 2000 and 2010.

      ‘….capital in America is much lower than in France (and Europe): 300% of GDP (compared to 700% in Europe). The explanation is that the land in the United States in 1770 was much cheaper than in Europe. From 1810 to 1930, domestic productive capital increases with the great industrialization of America and peaks in 1910. Falls during World War I, recovers to the absolute maximum in 1930. The Great Depression brings down capital to a minimum of 1950 and thereafter increases again: between 1950 and 2010, the U.S. capital returns to its long-term positive trend.’

      1. PeakTrader

        When an asset, e.g. land, is sold for a gain, there’s no capital creation.

        There’s just a capital exchange.

  21. PeakTrader

    Competition tends to reduce r and raise g.

    Less risk taking (for whatever reason) and barriers to entry are examples that can cause r to exceed g.

  22. Tom

    Thank you very much Jim for the third paragraph of this article. You put it very well.

    As for Chris Giles’ argument with Piketty on wealth inequality in Britain, I don’t think it’s an “unlikely battle” at all. In a country whose elites so actively offshore their wealth, we can’t really be too certain what’s going on. Piketty is right that he couldn’t use a mix-and-match time series that sources from income tax for early decades and from surveys for recent decades. But Giles is right that the survey data raises such serious doubts about the income tax data that Piketty can’t plausibly claim his series reflects reality. The truth is we don’t have conclusive evidence, and Tyler put it very well that “we know intuitively” isn’t worth much.

    Anyway, I think empirical research should focus on income, not net worth, as the latter is subject to so much misleading fluctuation, eg the huge swings in middle class net worth during the housing bubble and crash.

    1. 2slugbaits

      Stephen Cusulos I don’t think JDH has said much one way or the other regarding the data issues cited by Chris Giles and the FT. As best I can tell, JDH has pretty much taken a “wait and see” attitude. I don’t know about JDH, but I think that Piketty has mostly answered and satisfactorily addressed the main issues. It’s still not clear why there are any differences (as opposed to small differences) between Piketty’s numbers and Giles’ numbers; but then again, anyone who has ever worked with Excel shouldn’t be too surprised by this result. Especially if you are moving across different versions of Excel. In any event, small differences are just that, small differences and don’t upset Piketty’s major claims about income and wealth inequality. You can question some of his data adjustments and it’s entirely possible that Piketty’s assumptions may be wrong. OTOH, it’s almost a certainty that Giles’ assumptions are quite wrong. So pick your poison.

      JDH’s critique wasn’t so much with Piketty’s data, but with the so called second fundamental law of capitalism. This is a juicy topic; unfortunately, I don’t think this thread has come anywhere close to extracting all of the potential juice in Piketty’s fruit. JDH criticized the assumption of a constant “s” and the fact that Piketty does not account for capital consumption. Unfortunately, most of the discussion focused on the capital consumption problem, which I think is the weaker of the two criticisms. I tried to highlight this by positing a case in which growth was strongly negative such that the denominator went to zero. This showed that you got exactly the same crazy result of a infinite capital/output ratio. It also put the focus back on the assumption of a constant savings rate, which is the real heart of the problem. I want to get back to this constant savings rate assumption in a minute, but first we need to clean up a few things regarding capital consumption.

      Some of the critiques implicitly assume that capital consumption must always be a positive number. This is no doubt the case for total (i.e., public and private) physical capital. But it is not necessarily the case if you only look at private capital. Afterall, it is not hard to think of examples in which the cost of capital consumption is shifted from the private owner of the capital to the public. Second, a positive capital consumption rate is true of physical capital used in production, but not all capital is physical and not all capital is used in production. And it’s pretty clear that Piketty includes both non-physical capital (though not human capital) and non-productive capital. I half-jokingly brought up the example of Steve Ballmer paying $2B for the Clippers; but only half-jokingly. The Ballmer example either means that many capitalists are in fact quite willing to pour their capital into the ocean, or it means that some kinds of capital are immune from depreciation through consumption in the way that neo-classical models envision. The Clippers were originally valued at something a little south of $900M. So either the estimate of wealth was grossly understated (which supports Piketty’s claim), or owners like pouring their wealth into the ocean (point to Piketty), or it is possible for some kinds of capital to either escape consumption losses through use or shift those costs onto labor. Again, the point goes to Piketty. Let’s set aside the first two possibilities. So is it possible for some kinds of capital to have negative capital consumption (I.e., increase in value with use)? Well, yes. Art is one example. And so are sports teams. My Chicago Blackhawks saw their market value increase dramatically when they started putting more games on television, which did not result in any additional capital consumption costs. You could argue that there is still capital consumption in the form of wear and tear on the bodies of athletes. True, but how much of that consumption cost is borne by capital and how much is borne by labor is a legal and political question, not necessarily an economic one. There are plenty of examples of effective negative capital consumption (I.e., capital appreciation rather than depreciation) as a function of use. This cannot be true for physical productive capital, but it can be true for other kinds of capital. Bottom line is that the capital consumption criticism is not one that necessarily poisons Piketty’s argument. Capital consumption costs are not stationary and there is no necessary reason why they must be positive for all kinds of capital.

      The more important criticism is with the assumption of a constant savings rate. That’s ultimately what drives all this. One problem I have with Piketty’s argument is why he felt it was necessary to require a constant savings rate. Afterall, he could have made his argument work if he had argued for an increasing savings with growth held constant. Or a savings rate that was increasing while growth was decreasing. It would have been relatively easy to get this result since Piketty defines net income to include both domestic income and income from foreign sources of domestically owned capital. If overseas investments result in very high NNP (as opposed to NDP), then you could get a high savings rate and a declining growth rate. You wouldn’t get that globally, but you could get it for any one country.

      Finally, the usual reasons given for growing income and wealth inequality all seem kind of pithy and not quite up to the problem. No doubt there’s a good deal of truth in them, but clearly something is missing. No one seriously believes that CEOs are thousands of times smarter than the next smartest person for the job. If someone is truly that much smarter than everyone else, then that intelligence was a gift of nature and not something that was earned in any meaningful sense of the term. Education differentials might explain the difference between the 30th percentile and the 80th percentile, but they don’t explain the huge differences between the top 1% and the top 0.01%. Capturing monopoly rents is also a big source of inequality. The point is that all of the alternative explanations for growing income and wealth inequality ultimately justify exactly the kinds of redistribution and confiscatory policies that Piketty recommends.

      1. James_Hamilton Post author

        2slugbaits: I think you are making a mistake to lump all models with some sort of constant saving rate together. Piketty’s assumption of a constant net saving rate is far, far sillier than the more standard assumption of a constant gross saving rate, though as I said, the latter can also be much improved upon by paying attention to the motives facing those who save. And as you have pointed out, it is possible to come up with pathological implications of a constant gross saving rate if the economy is rapidly shrinking every year (though again, as I noted, Piketty’s assumption of a constant net saving rate in such a setting would be even more ridiculous). In sum, Piketty deviated from a standard assumption (though one subject to potential criticism) to insist on something instead that was over-the-top ridiculous when applied to the questions in which he was interested.

        I also think you are too quick to jump to this idea that there are some assets that do not depreciate but whose returns grow faster than the overall economy. Do you own some of these yourself and can you recommend them to others who would also like to benefit from these exceptional investments? I think you will have a hard time writing down a coherent model that could produce anything like this. Think again about the zero growth g = 0 case. Where is the growing volume of real stuff coming from that is continually being transferred to the owners of these investments? Perhaps you are thinking of a bubble, but that is not going to lead to a permanent accumulation of wealth by the holders of capital.

        1. 2slugbaits

          JDH>/b> Appreciate your comments. Regarding my lumping of constant savings models. My point was that the infinity problem applies to all models with a constant saving rate. It’s a bigger problem for some than others, but in principle all models that assume a constant saving rate are vulnerable to the problem. In your example you assumed a 10% capital consumption rate, which of course meant that it would take an implausibly severe negative growth rate. But then again, a 10% capital consumption rate is unrealistic as well. As I said a few days ago, the capital consumption rate today is a little south of 5% and fifty years ago it was half of that. In the 13th century it was probably around 30%. Given where capital consumption rates were fifty years ago, I don’t think it’s implausible to imagine a world with 1.5% capital consumption rates and -1.5% sustained negative growth rates. Likely? Perhaps not. But well within the range of the possible.

          You asked if I am aware of any investments that enjoyed a zero or negative capital consumption rate. Well, yes I am. But before I give a few examples I want to nail down exactly what I mean by capital consumption. I am defining capital consumption as the amount of savings that must be reinvested in order to maintain the same benefits tomorrow that are enjoyed today. Basically net income tells us how much of today’s income we can spend while still enjoying exactly the same economic well being tomorrow. Note that under this definition capital consumption is not synonymous with depreciation or obsolescence. Depreciation is a change in an assets value due to supply and demand for the asset. Obsolescence reflects technological improvement, and technological improvement leaves us better off in the future, not equally well off. I think this distinction is critical. It’s one that I have to work with everyday. For example, an M109A6 self-propelled howitzer incurs capital consumption costs with use (e.g., gun barrels erode, breech loaders develop cracks, etc.). If you want to recapitalize an M109A6 to its original value, then you overcome capital consumption costs and charge the program to a specific account. If you want to upgrade to the new M109A7 configuration, then you are making a technological improvement and the program must be paid for using a different color of money. Failure to understand the difference between capital consumption and obsolescence will earn you free room and board at Ft Leavenworth…ill fitting orange jump suit at no extra cost. So with that out of the way, let me suggest what I thought might be an obvious example of an important asset that is immune from capital consumption. About 20 years ago you wrote an important book on time series analysis. The owner of the printing press incurs capital consumption costs; but the owner of the copyright does not. No matter how many editions are published, the value of the copyright is not consumed with use. Yes, if the publisher prints too many copies the value of the copyright might diminish due to supply and demand, but that is inherently no different than the value of an HD television declining if too many are produced. We don’t score asset losses due to supply and demand as capital consumption losses. Basically all intellectual property rights are immune from capital consumption. The copyright might also lose value due to obsolescence (e.g., new advances in time series analysis and software), but again, that is not capital consumption properly understood. Basically all intellectual property is immune from capital consumption costs.

          I would also point out that one obvious way r>g is if there is a wedge in the returns between domestic and overseas investments. Since Piketty would include those returns in his definition of net income, and “g” would be domestic growth, it’s fairly easy to see how r>g. Not forever, but for a very, very long time.

          One of the things that bothers me about looking at these issues through the lens of homogeneous aggregate production functions is that It treats the owners of capital as homogeneous. This completely misses the most important action. The struggle isn’t just between capital and labor, but between capital owners. My understanding of Piketty’s argument is that he calls for a wealth tax because big capitalists eat smaller capitalists. Income inequality isn’t just between the 99% and the 1%, it’s also between the less fortunate plutocrats near the bottom of the top 1% and those superplutocrats in the top 0.1% and 0.01%. That is completely missed when you frame things in terms of homogeneous aggregate production functions. And here I think Paul Krugman got it completely wrong. Joan Robinson got the Cambridge Controversy right. And I think getting this right matters a lot in terms of Piketty’s thesis.

          Finally, you’re probably already aware of this, but Brad DeLong has an interesting response to the “s / (g + d)” issue.

  23. Rick Stryker


    I’m not sure why you think my quantitative comment on Piketty’s model is bloated. It’s quite succinct I would think. If you looked at it carefully, you could learn the details about how Piketty’s model works since I’ve written out explicit solutions to the equations.

    For example, you can verify that for g >0, the growth rate of net income goes to g as t goes to infinity, consistent with Piketty’s model.

    You can also verify that the ratio of consumption to output Y goes to (1-s)*g/(g+s*d) as t goes to infinity. That implies that as g goes to 0, the ratio of consumption to Y goes to zero. In Piketty’s bizarre world, as g becomes small, consumers consume less and less and save more and more.

    You can also verify that ratio of capital K to output Y goes to s/(g + s*d) as t goes to infinity. When g = 0, it’s 1/d, which is also what you get when you solve the difference equation for the case g = 0.

    The second implication, that the ratio of consumption to income goes to zero as g goes to zero, i.e., the economy saves more as the growth of output declines, is the crazy implication of Piketty’s second “law” that discredits the whole argument.

  24. Rick Styker


    When I saw Delong’s defense of Piketty, I had to put that into the department of “huh” myself.

    Delong makes 2 points. First, d is not 10% but is rather something like 3%. And second, PIketty did mention the mainstream model with implication that Y/K = s/(d + g) but Krusell and Smith imply that Piketty missed that point. Delong is making a couple of trivial points that don’t in anyway address the serious criticisms that JDH and Krusell and Smith have made.

    Let’s suppose that d really is 3% rather than 10%. Does that change anything fundamental? Asymptotically, when g = 0, Piketty’s second law implies that K/Y goes to 1/d, which is 33.3 while in the mainstream model K/Y goes to s/d. If s = 30%, then you get a ratio of 10 for the mainstream model. Which is more plausible?

    But the real problem is the differences between how the models get to the limit as g goes to 0. I mentioned to Hans that asymptotically the ratio of consumption to output Y goes to (1-s)*g/(g+s*d) in Piketty’s model. Thus, as g goes to zero, the consumption rate goes to 0 and the savings rate goes to 1. As JDH points out, the economy starves itself to keep accumulating capital in Piketty’s bizarre economy. However, in the mainstream model, the consumption to output ratio converges to the more sensible 1 – s. Delong has not addressed these points.

    The other point that Delong makes is ridiculous. He’s saying that Krusell and Smith are asserting that Piketty missed the point that the ratio of K/Y goes to s/(g +d) but that in fact Piketty is aware of it. But that’s not Krusell and Smith’s point. Their point is that given the Piketty and everybody else is aware of the implications of the mainstream model, why is Piketty asserting a bizarro model in its stead? Krusell and Smith are asking rhetorically whether they and everyone else has missed something fundamental that only Piketty has seen. Of course, their conclusion is that they haven’t missed it and PIketty is wrong.

    Delong should read past the introduction of a paper that he’s criticizing.

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