Reviews of Thomas Piketty’s Capital in the Twenty-First Century continue to roll out, many by professional economists. Yet I continue to be frustrated by the fact that almost none of the  economists’ reactions to Piketty that I have read display any close familiarity with chapters 7 through 12 of the book, where all of the actual analysis of the structure of inequality is contained. Most of these reviews seem to go no further than Chapter 6, with Piketty’s now-famous inequality r > g then tossed into the salad for good measure, on the basis of which the reviewer then attributes to Piketty large claims about the dynamics of inequality based entirely on r > g and the contents of those introductory chapters. But everything in Chapters 1 through 6 is prefatory to the analysis of the structure and dynamics of inequality that follows.

The economists’ reviews and responses are also riddled with confusion over Piketty’s Second Fundamental Law of Capitalism. I have dealt with most of those confusions already in three posts:  Nothing Magical about Piketty’s Mathematics; Summers’s Review of Piketty: Underestimating the Argument for the Forces Driving Inequality; and Let’s End the Confusion over Piketty’s “Second Fundamental Law”. But the confusions continue to appear in the work of very competent economists.

I can summarize the problem briefly. The reviewers have persistently read the second law as an outright equation, some kind of approximate identity or long-term equilibrium condition of the form β  = s/g (or equivalently K/Y = s/g) which they then fold into an equilibrium model framework, and from which they then proceed to deduce bizarre results that they attribute to Pikeety. For example, Per Krussell and Tony Smith argue that the 2nd Fundamental Law is implausible because “implies saving behavior that, as the growth rate approaches zero, requires the aggregate economy to save 100% of GDP each year.”  They also say that, together with the 1st Fundamental Law α = rβ, which is a genuine identity, the 2nd fundamental law:

delivers the central relationship of Piketty’s book: capital’s share of income is r x s/g. This formula is alarming because it suggests that were the economy’s growth rate to decline towards zero, as Piketty argues it will, capital’s share of income could increase explosively.

But these readings, I believe, are quite incorrect. To be fair, Piketty does abbreviate the law in the form of a strict equation when he introduces it. But in his ample discussion in the text of the book right after he introduces the 2nd law, and in his online technical appeandix, he makes it clear that the law is only an asymptotic and inherently dynamic law that could just as well have been abbreviated in the form “β → s/g”, and does not license to importation of k/y = s/g as a constraint on the computation of some kind of equilibrium condition.  Indeed, the very idea of equilibria seems foreign to Piketty’s open-ended, empirical and irreducibly dynamic perspective which emphasizes historical contingency and volatility.

We can in fact compute that, even in the presence of very low national income growth rates, the capital-to-income ratio would grow at the annual rate of (s/β – g)/(1+g) , where β is the capital-to-income ratio, g is the growth of national income and s is the savings rate. The rate of increase would decrease slightly each year in accordance with the capital-to-income ratio, and it would continue with this pattern for as long as s and g remained constant. So, for example, if growth dropped to 1/8th of one percent, the initial capital-to income ratio were 5/1, and national savings remained constant at 10%, then β would begin to grow at about 1.9% per year, and grow at continually decreasing rates after that. It would in fact take 33 years for β to exceed 8/1. If g dropped all the way to zero, then the initial growth rate is simply s/β, which in this case is 2%. And it would still take 33 years to exceed 8/1. There is no sudden “explosion” of the capital-to-income ratio, nor some kind of induced surge in the savings rate. Piketty’s 2nd Fundamental Law is an inherently dynamic growth rule, not an approximate measure of some quickly achieved equilibrium condition. The value s/g is only the limiting value toward which this growth would converge, if extended indefinitely, for constant s and g.

I have also dealt in several posts with several misunderstandings about Piketty’s account of the structure and dynamics of inequality, including Piketty on the Dynamics of Inequality: Four Useful Theorems; The Financial Times’s Lazy Reading of Piketty; and How Hassett Gets Piketty Wrong. As I said, Piketty’s analysis of inequality lies in Part Three of the book, comprised of Chapters 7 through 12. Since the central topic of the book is economic inequality, then these chapters form the core of the book and are the source of Piketty’s most important arguments. But it is abundantly obvious that many of the reviewers are not reading these sections. I say that is obvious, because there is no way these professionals could be making the basic interpretive errors they are making if they were reading those parts of the book with care.

If they did read those parts of the book, they would find that:

1. Piketty lays great stress on the fact that the rich save higher proportions of their income than others, and that the propensity to save increases the further one goes up the wealth ladder. This fact is absolutely essential to Piketty’s analysis of the way in which the initial inequality in the distribution of capital income results in increasing wealth and income concentration and the growing importance of inherited wealth. (Chs. 10 and 11)

2. Piketty also lays great stress on the fact that wealthier capital owners tend to earn significantly higher returns on their wealth than the average capital owner. This fact is absolutely fundamental to Piketty’s analysis of the growth of the highest salaries and the role of globalization in accelerating inequality at the top. (Ch. 12)

3. Piketty really draws no important consequences regarding equality and inequality from the mere fact that r is greater than g. Obviously, if capital were owned equally, then returns on capital would be distributed equally, at no matter what rate they were earned. In such circumstances, a high rate r of return to capital would be a force for wealth and income convergence, not divergence. Piketty’s deployment of r and g in the explanation of increasing inequality of wealth and income is based on (i) the already-mentioned fact that capital is always unequally distributed in the first place, and (ii) that r is often “significantly and persistently” higher than g. Piketty makes it quite clear, and highlights the point several times, that it is the size of the difference r – g that is most crucial.

4. Piketty has a whole chapter on the role of the inequality of labor income (Ch. 9) in which r, g and capital income play no important role whatsoever.

I am beginning to scratch my head a lot over just how bad many of the reviews are. These errors and ommissions are not hard to avoid with a careful reading of the book. So at this point, I would have to say that the bungled reception of Capital in the Twenty-First Century is turning into something of a scandal to the economics profession, and casts an unflattering light on either their reading comprehension or intellectual honesty. Frankly, I think we are getting a large number of reviews by people who are only pretending to have read the book, but are actually working from some kind of Spark notes summary that they have picked up from either Piketty’s own seven-page conclusion, the online blurb for Harvard University Press, or from other reviews. Or maybe they are just reading Chapter 6 – the chapter that seems to possess the greatest number of points of contact of standard macroeconomic material – along with a few formulas gleaned from the relatively few pages that contain them.

I don’t know quite what accounts for the poor readings. But I suspect it has something to do with the fact that Piketty writes almost entirely in natural language prose, and that economists are wont to assume, from force of professional habit, that the only substantive economic theory in Piketty’s book occurs on those few pages where there are formulas. They thus conclude that the rest is nothing but 500+ pages of filler for the general reader that can safely be skipped. If this is what is going on, then they are missing 90% of Piketty’s argument, which is complex and nuanced, and can’t be summed up as “r > g, therefore … disaster.”

In a recent, much-praised review pf Piketty, Debraj Ray correctly stresses the role of the fact that “the savings rate climbs with higher incomes.” But he presents this as though he were revealing a lacuna in Piketty’s argument, not explicating the arguments that Piketty himself gives. In fact, it becomes clear that Ray’s purported criticisms of Piketty are really mostly criticisms of what he calls the “Piketty faithful”, who have tended to put all the weight on r > g, rather than Piketty himself.

Piketty deserves some blame for perhaps putting too much rhetorical emphasis on “r > g” alone in the conclusion and some of the best known passages of the book. The truth of that formula is only a precondition for all of the wealth and income divergence phenomena he studies, a necessary condition for them to occur. It’s not a sufficient condition. But Piketty is an extremely clear and careful writer all in all, and the full argument is as lucid as it is involved. The occasional simplifications don’t absolve reviewers of the obligation to read the book and attempt to grok Piketty’s full argument before assessing it.

Addendum:

I want to be even more vivid about just how slow is the capital-to-income ratio convergence process under conditions of low growth. I’ll use the exact same numerical example, but bring in a reference to the convergence value s/g. If the current capital-to-income ratio is 5/1, and the savings rate is 10%, and the growth rate drops to 1/8th of one percent, then the new value of s/g is 8000%, or 80/1. But Piketty by no means thinks that the capital-to-income ratio would suddenly surge to some new “equilibrium” value near 80/1.

As I mentioned in the post, all that would happen is that β would begin to grow at an annual rate of (s/β – g)/(1+g). Again, that’s below 2% in this case, and the growth rate would decrease slightly each year as β rises. If this process continued indefinitely with s and g unchanged, then β would converge to 80/1. But it’s a very slow convergence: As mentioned in the post, it would take 33 years for β to rise even as high as 8/1. We can also note that β wouldn’t exceed 75/1 for 2168 years!

Obviously the 2nd law has nothing to do with comupting equilbrium model estimates of the capital-to-income ratio under conditions of low growth. Piketty explicitly warns the reader off of such an interpretation in the text.