Pure Math Distorting Political Debate

Debraj RayAbout a week ago, Debraj Ray wrote a critical article on Thomas Piketty’s new book, Capital in the Twenty-First Centery, Nit-Piketty. The basis of Piketty’s argument is the inequality: r>g. What that means is that the rate of growth of return on capital is greater than the growth of the economy as a whole. As a result, more and more wealth will be concentrated with the owners of capital. Ray cries foul, saying that this doesn’t actually mean anything to inequality. And like the good theoretician that he is, Ray’s point is both true and meaningless.

Branko Milanovic then wrote a critical article about Ray’s article. He characterizes Ray’s argument as follows. Imagine you have a rich man who makes $100K per year from work and another $100K per year from his capital investments. And then imagine you have a poor man who makes $10K per year from work and another $10K per year from his capital investments. If r>g for a year, at the end of the year, the rich man and poor man will be in exactly the same place as far as inequality goes. Before and after, there will be a 10:1 ratio of incomes.

This is where many economists—especially the conservative ones (although I really don’t know anything about Ray specifically)—go wrong. They make their assumptions and then think that anything that follows from those assumptions must be true. That’s fine as long as the assumptions are true. But in this case, the (unstated) assumption is preposterous: poor people make as large a percentage of their income from capital investments as rich people.

The way it works in the real world is much more as follows. The rich man makes $200K per year from his capital investments. The poor man makes $20K per year from his work. Thus, if we assume that the rate of return on capital is 5% and the return on work (because the economy grows) is 3%, then after a year, the rich man is making $210K per year, and the poor man is making $20.6K per year. So before, there was a 10:1 ratio of rich man income to poor man income. After a year, there is a 10.2:1 ratio of rich man income to poor man income. And that compounds so it gets worse faster ever year.

Now I have something to add that neither of these economists discussed. The more inequality there is, the more the rich can manipulate the political and thus the economic system. As we have seen for almost four decades now, economic growth does not translate into higher wages. And that is particularly true of low wage earners. So at the end of the first year, the poor man would not be making $20.6K per year, but something less—maybe even exactly what he was making at the start of the year: $20K. In that case, the ratio would have changed to 10.5:1.

I don’t doubt that Debraj Ray is a very smart guy. And looking at the titles of some of his papers, he does the kind of pure mathematical research that I find really stimulating. But the great thing about people who do pure mathematics is that they don’t care about the practical world. When Ray starts making such theoretical complaints about Piketty’s incredibly practical econometric work, he is acting (hopefully unintentionally) as an apologist for the status quo. I suppose it is important for economics students to understand his point but for the general reader, all he is saying is, “You don’t need to worry about what Piketty is saying, because in a totally unrealistic mathematical model, inequality isn’t just not increasing it cannot increase.” And from a policy perspective, that’s just rubbish.

Given that there are a bunch of really rich and powerful people who are looking for any reason to ignore our unjust system, Ray’s work is counterproductive.


See Paul Krugman’s column today, On Inequality Denial.

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About Frank Moraes

Frank Moraes is a freelance writer and editor online and in print. He is educated as a scientist with a PhD in Atmospheric Physics. He has worked in climate science, remote sensing, throughout the computer industry, and as a college physics instructor. Find out more at About Frank Moraes.

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