Debraj Ray’s original review of Piketty’s book was, appropriately, called “Nit-Picketty.” His reply to my critique of his critique, published here, could be called Nit-Picketting II or nit-Picketting big time. It brings no new points and thus leads our discussion to a close. I would organize my own nit-Debrajing into two parts, substantive and stylistic.
Substantive. Debraj has identified a weakness in Piketty’s model on which he spends some nine pages, denying the importance of the key insight of the book, and that weakness is as follows. r>g is not sufficient to guarantee either an increasing share of capital in total income (over time), nor increasing inter-personal inequality (over time, too) because it does not take into account what capitalists do with the r which they receive as income. They can consume it all, or consume enough of it so that the portion which is reinvested (r*) becomes less than g. Never mind that historically in the literature r was used, as Piketty does in his book, to indicate both the rate of return on capital and the subsequent rate of increase of the capital stock (under the simplifying but sensible assumption that capitalists just turn around and reinvest all their capital income). Never mind that all empirical studies show that propensity to save increases with income and that capitalists tend to be rich, and hence save proportionately more, so that their consumption will be insufficient to overturn the r>g inequality. Debraj has found a small, even trivial, point, and yes, he insists r has to be written as r*=r-cc, where cc is capitalists’ consumption out of their return (all expressed in terms of capital stock), and if Piketty were to write r*>g then, yes, everything would be fine, but you see, just writing r>g is all wrong. Without cc, no going. r>g “implies nothing”, but r*>g would solve everything.
Why not go further? Do we really know what capitalists will do with their r? They might give away a fair share of it. Denote the portion of their capital return which they donate by dd, and then write a new relationship that should be even more satisfying: r-cc-dd>g. However absurd this game of adding additional ways capitalists can use not to reinvest their full capital income is, adding dd makes more sense than adding cc. At least it is empirically justified. While for consumption/income ratio we know that it goes down as income goes up, for charity we know that it behaves exactly in the way to reduce r* as it increases with income. So capitalists will indeed have a positive dd, while for most of the others dd will be zero. Here I have now discovered that Piketty’s conclusions need to be modified in a yet another important way.
Fundamentally, Debraj and I do not disagree. It is just that I think that his point is (yes, I must say so again: the 2nd time) trivial, and while logically correct, all empirical evidence about savings, and all our views about the essential features of capitalism, show that it is not valid. For it to be valid, either rich people should not be capitalists, or average propensity to save of the rich people should be less than of the poor. Manifestly, neither is true, and Debraj agrees with it. In other words, Debraj wants to drive his small logical point to an end which is in contradiction with everything which we know about the behavior of capitalists and the nature of capitalism.
Stylistic. I personally like Debraj and admire his work. I was extremely impressed by his presentations and writings. He is a brilliant economist. In addition, for those who do not know him, he looks like a Greek demi-God. His thinking is at the same level. But even demi-Gods should get used to mortals disagreeing with them, and even of having to repeat the same thing 97 (or was it 98?) times.