Debraj Ray on Piketty’s Capital

As mentioned by Sandeep Baliga over at Cheap Talk, Debraj Ray has a particularly interesting new essay on Piketty’s Capital in the 21st Century. If you are theoretically inclined, you will find Ray’s comments to be one of the few reviews of Piketty that proves insightful.

I have little to add to Ray, but here are four comments about Piketty’s book:

1) The data collection effort on inequality by Piketty and coauthors is incredible and supremely interesting; not for nothing does Saez-Piketty 2003 have almost 2000 citations. Much of this data can be found in previous articles, of course, but it is useful to have it all in one place. Why it took so long for this data to become public, compared to things like GDP measures, is an interesting one which sociology Dan Hirschman is currently working on. Incidentally, the data quality complaints by the Financial Times seem to me of rather limited importance to the overall story.

2) The idea that Piketty is some sort of outsider, as many in the media want to make him out to be, is very strange. His first job was at literally the best mainstream economics department in the entire world, he won the prize given to the best young economist in Europe, he has published a paper in a Top 5 economics journal every other year since 1995, his most frequent coauthor is at another top mainstream department, and that coauthor himself won the prize for the best young economist in the US. It is also simply not true that economists only started caring about inequality after the 2008 financial crisis; rather, Autor and others were writing on inequality well before date in response to clearer evidence that the “Great Compression” of the income distribution in the developed world during the middle of the 20th century had begun to reverse itself sometime in the 1970s. Even I coauthored a review of income inequality data in late 2006/early 2007!

3) As Ray points out quite clearly, the famous “r>g” of Piketty’s book is not an explanation for rising inequality. There are lots of standard growth models – indeed, all standard growth models that satisfy dynamic efficiency – where r>g holds with no impact on the income distribution. Ray gives the Harrod model: let output be produced solely by capital, and let the capital-output ratio be constant. Then Y=r*K, where r is the return to capital net of depreciation, or the capital-output ratio K/Y=1/r. Now savings in excess of that necessary to replace depreciated assets is K(t+1)-K(t), or

Y(t+1)[K(t+1)/Y(t+1)] – Y(t)[K(t)/Y(t)]

Holding the capital-output ratio constant, we have that savings s=[Y(t+1)-Y(t)]K/Y=g[K/Y], where g is the growth rate of the economy. Finally, since K/Y=1/r in the Harrod model, we have that s=g/r, and hence r>g will hold in a Harrod model whenever the savings rate is less than 100% of current income. This model, however, has nothing to do with the distribution of income. Ray notes that the Phelps-Koopmans theorem implies that a similar r>g result will hold along any dynamically efficient growth path in much more general models.

You may wonder, then, how we can have r>g and yet not have exploding income held by the capital-owning class. Two reasons: first, as Piketty has pointed out, r in these economic models (the return to capital, full stop) and r in the sense important to growing inequality, are not the same concept, since wars and taxes lower the r received by savers. Second, individuals presumably also dissave according to some maximization concept. Imagine an individual has $1 billion, the risk-free market return after taxes is 4%, and the economy-wide growth rate is 2%, with both numbers exogenously holding forever. It is of course true true that this individual could increase their share of the economy’s wealth without bound. Even with the caveat that as the capital-owning class owns more and more, surely the portion of r due to time preference, and hence r itself, will decline, we still oughtn’t conclude that income inequality will become worse or that capital income will increase. If this representative rich individual simply consumes 1.92% of their income each year – a savings rate of over 98 percent! – the ratio of income among the idle rich to national income will remain constant. What’s worse, if some of the savings is directed to human capital rather than physical capital, as is clearly true for the children of the rich in the US, the ratio of capital income to overall income will be even less likely to grow.

These last couple paragraphs are simply an extended argument that r>g is not a “Law” that says something about inequality, but rather a starting point for theoretical investigation. I am not sure why Piketty does not want to do this type of investigation himself, but the book would have been better had he done so.

4) What, then, does all this mean about the nature of inequality in the future? Ray suggests an additional law: that there is a long-run tendency for capital to replace labor. This is certainly true, particularly if human capital is counted as a form of “capital”. I disagree with Ray about the implication of this fact, however. He suggests that “to avoid the ever widening capital-labor inequality as we lurch towards an automated world, all its inhabitants must ultimately own shares of physical capital.” Consider the 19th century as a counterexample. There was enormous technical progress in agriculture. If you wanted a dynasty that would be rich in 2014, ought you have invested in agricultural land? Surely not. There has been enormous technical progress in RAM chips and hard drives in the last couple decades. Is the capital related to those industries where you ought to have invested? No. With rapid technical progress in a given sector, the share of total income generated by that sector tends to fall (see Baumol). Even when the share of total income is high, the social surplus of technical progress is shared among various groups according to the old Ricardian rule: rents accrue to the (relatively) fixed factor! Human capital which is complementary to automation, or goods which can maintain a partial monopoly in an industry complementary to those affected by automation, are much likelier sources of riches than owning a bunch of robots, since robots and the like are replicable and hence the rents accrued to their owners, regardless of the social import, will be small.

There is still a lot of work to be done concerning the drivers of long-run inequality, by economists and by those more concerned with political economy and sociology. Piketty’s data, no question, is wonderful. Ray is correct that the so-called Laws in Piketty’s book, and the predictions about the next few decades that they generate, are of less interest.

A Comment on Thomas Piketty, inclusive of appendix, is in pdf form, or a modified version in html can be read here.

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4 thoughts on “Debraj Ray on Piketty’s Capital

  1. Karsten says:

    “If this representative rich individual simply consumes 1.92% of their income each year – a savings rate of over 98 percent! – the ratio of income among the idle rich to national income will remain constant.”

    You mean 1.92% of their *wealth*, or 50% of their income (continuously). I.e. a savings ratio of 50%. Positively spendthrift for a billionaire…

    • afinetheorem says:

      – Indeed I meant income. It might be spendthrift for a billionaire (perhaps), but spending less than half of your interest income is fairly unusual empirically, even for the rich…consider the recommended drawdowns of retirement savings and the like.

  2. First, thanks for the shout-out!

    Second, in line with my research, I think it’s worth remembering that while economists (and sociologists!) were very interested in inequality in the 1980s-1990s, they were not very interested in top inequality. That Autor can begin his recent Science piece with frustration about “The singular focus of public debate on the “top 1 percent” of households”” is very new to the past 10 years (and in no small part a result of Piketty’s research, and the network of scholars that have promoted it, especially Krugman). This nuance – which doesn’t seem that complicated to me* – seems to be lost in much of the current discussion about Piketty and his role.

    Third, a question. How does the emergence of new forms of financial diversification affect predictions of the growth of a patrimonial elite? It seems to me that the various waves of destruction (described by Ray with the phrase Kuznets cycles, though Schumpeter seems a more natural pick!) might have disrupted a 19th century elite that invested in a small class of assets, but seems unlikely to disturb the dominance of the 21st century wealth who benefit from all manner of diversified instruments (including the simple market index fund!). In this sense, I buy Ray’s point that the way to combat inequality in the future would be to make sure that everyone owned capital (with the assumption that such ownership would be diversified). Or, y’know, to implement a much more progressive system of wealth and income taxes, and perhaps a guaranteed basic income. It’s worth remembering that for all of Piketty’s economic fatalism, the book is meant as a political call to action which clearly asserts that policies have and can in the future prevent the rise of inequality and the growth of a class of inherited elites.

    * Though the nitty-gritty details are, of course worth remembering. For example, though Autor claims the discussion has been about the “‘top 1 percent’ of households”, Piketty’s data actually refer to the top 1% of tax units, which are not the same at all (a point which drew substantial criticism, mostly from conservative think tanks, in the mid-2000s, and which also seems to have been lost in the noise).

    • afinetheorem says:

      Fair point on the 1% focus (though, this is no surprise; 50-10 income inequality was actually growing in the 80s!) I wonder whether you consider things like Lazear’s tournaments model and the followups there to be about “1% compensation”?

      I think GBI is great, but am not sure it would help with asset concentration.

      Certainly financial diversification affects wealth accumulation; I was going to mention this in the original post, but an expected return of 4%, with nonzero bankruptcy probability, requires less than 100% assets to be invested if behaving optimally hence r>g is even less meaningful. I don’t know of any theory that has fully worked things out on your point, though.

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