Piketty, inequality, and open borders

A society in which the rich have a very high degree of economic, political, and sociocultural influence is an unpleasant society in many ways.
Read more at http://www.project-syndicate.org/commentary/j–bradford-delong-is-surprised-by-the-poverty-of-conservative-criticism-of-capital-in-the-twenty-first-century#OS2DZ3JavDCdtOT1.99

Thomas Piketty’s just-released Capital in the 21st Century has been much talked about, e.g. by Greg Mankiw, Brad DeLong , Reihan Salam, Megan McArdle and Tyler Cowen, for starters. Reviews aside, Bryan Caplan’s post about (the myth of) the “hollowing out” of the economy, or Scott Sumner’s (tentative) advocacy of 80% marginal tax rates on consumption (more here) seem to show how Piketty’s influence has steered the conversation towards more talk about inequality.

I’ve read only a little, but already Piketty has opened my eyes to a possibility I had never before seen. Let r be the return on capital, e.g., the 7% long-run average return on US stocks. Let g be the (per capita) growth rate of the economy as a whole, e.g., 2%. An abstract “capitalist” will see his wealth, and therefore income, grow at rate r, minus his consumption, which is perhaps small compared to his income. An abstract “worker” will see his income rise at (roughly) rate g. So what happens to inequality? As long as r>g, it keeps increasing. Without limit. While r>g seems to be true, there are a lot of reasons why r>g as a story of ever-increasing inequality probably isn’t a good description of the real world. But I’m indebted to Piketty for elucidating the conceptual possibility.

Is ever-increasing inequality driven by r>g disturbing? Maybe not. As long as g is positive, the workers are still getting better off. Moreover, for r>g to drive ever-increasing inequality, the capitalists have to be rather abstemious, which takes some of the sting out of increasing wealth inequality. Capitalists have more, but don’t live that differently. If, on the other hand, capitalists dissipate their wealth on luxury consumption, that seems more offensive, then r>g increasing inequality.

Much depends on one’s “social welfare function” (SWF), that is, on how much you value the welfare of different people, and how much you think the millionaire’s marginal dollar is worth, compared to the pauper’s. Suppose desirable outcomes for society are defined by V=a1*f(W1)+a2*f(W2)+…+an*f(Wn), where individuals 1… n are all the members of society, a1… aN are parameters that govern the importance we replace on the welfare of difference individuals (in a “democratic” SWF a1=a2=…=aN), W1… Wn represent (in a concession to Piketty’s preoccupations) the wealth of the individuals (though Scott Sumner would rightly stress that consumption inequality is what we should really care about), and f is some function, the shape of which is the crucial, defining feature of the entire SWF (assuming that we’re all “democrats” and value everyone’s welfare equally). Presumably the first derivative of f is positive (each marginal dollar is worth something) and the second derivative of f is negative (each marginal dollar is worth less than the last), but– this is the key– by how much does the marginal value of a dollar decrease as one gets richer? A SWF in which the second derivative of f is only slightly negative might be called “right-wing” or “conservative,” in the sense of being relatively indifferent to inequality, while a SWF in which the second derivative of f is more negative is “left-wing,” more sensitive to inequality.

Here John Rawls offered an implausibly extreme answer: that society should only maximize the welfare of the worst-off, and in effect, should be completely indifferent to whether the not-worst-off are only slightly above the minimum, or enjoy vast prosperity and affluence. This is very odd. The wealth of millionaires is doubtless less good than the same wealth would be spread out among the poor; but surely it is worth something. I would have called Rawls the “far left” of the plausible set of SWFs. Yet as far as I can tell, Piketty’s social welfare function is to the left of Rawls’! The (unsympathetic) Wall Street Journal writes that…

Mr. Piketty urges an 80% tax rate on incomes starting at “$500,000 or $1 million.” This is not to raise money for education or to increase unemployment benefits. Quite the contrary, he does not expect such a tax to bring in much revenue, because its purpose is simply “to put an end to such incomes.”

while the (sympathetic) Brad DeLong, summarizing Piketty’s argument, does not say that capitalists are in any way impoverishing the workers by their epic feats of accumulation, but rather, that “A society in which the rich have a very high degree of economic, political, and sociocultural influence is an unpleasant society in many ways.” If DeLong and the WSJ (as I read them) are correctly characterizing Piketty’s position, then in his SWF, the first derivative of f is negative at some point. We should not just want to burden the rich a bit in order to bring ourselves up a bit. We should actually want to pull the rich down, even if we hurt ourselves in the process. I’ll be on the lookout, when I get a chance to read the book through, for whether Piketty really believes this. It would be an intriguing oddity.

My response to what I’ve gleaned about Piketty’s argument so far is twofold:

1. Western society already has a sufficient response to excessive wealth accumulation in monogamy. I like Scott Sumner’s 80% MTR on consumption, in principle, though I think it would be hard to implement. But I think monogamy basically is an 80% MTR on consumption, or more. If an amoral rich man could buy a harem, he could really hit the poor where it hurts. But if he can’t, the joke is on him. It would take some ingenuity for a monogamous man to come up with a way to spend tens of millions of dollars without generating major positive spillovers. If he sends his mediocre kids to Yale, they might not learn that much, but he’ll be subsidizing scholarship and science, as well as cross-subsidizing the educations of other, brighter students on financial aid. Or, if he hires a scholar (e.g., Adam Smith) to accompany his kid on a Grand Tour of Europe, the scholar will probably use the time to write a magnum opus on the side (the Wealth of Nations). If he goes to the opera, the music his money buys will soon get recorded and show up on everybody’s iPod. If he buys great paintings, which he probably doesn’t have the capacity to appreciate that much, cheap prints of those paintings, almost as good as the originals, will get made and sold by the thousands to middle-income art lovers to decorate their walls with. And the paintings will end up in museums sooner or later, to edify the common man. If he buys a huge mansion or yacht, his small body can’t occupy most of its rooms. To get any use of it at all, he needs lots of guests. Spillovers again. And of course, he’d have to be an idiot not to see that he’ll get far more satisfaction from giving his money away to a chorus of praise and gratitude, than from attempting to “consume” far more he can use to satisfy his needs. And so the rich become the great philanthropists, and I think a marginal dollar in the hands of the Gates Foundation is worth about a hundred times as much as a marginal dollar in the hands of any democratic government on earth. The Rockefeller Foundation financed the Green Revolution while the US government pours most of its money into pampering the elderly. Again: inequality without monogamy– harems and eunuchs and child brides, etc.– really is horrible. But the West has achieved the inestimable triumph of caging the selfish genes even of the very rich.

2. To the extent that inequality is an evil worth worrying about, there is no justification for diverting our attention from any policy response other than that of opening borders to migration. Fortunately, Piketty is not one of those contemptible humbugs who profess to care about inequality, yet oppose or ignore immigration. He has a few pages on immigration reform late in the book, and is unabashed in his support for more freedom of migration, with essentially no qualifications. But the passage doesn’t suggest that he has anything like an adequate appreciation of its importance. A vast amount of inequality depends merely on the luck of what country one is born into. While global wealth taxes would presumably weaken incentives and reduce global GDP, even if they made it more equally distributed– and it would require a terrifyingly invasive state to enforce them– open borders would double world GDP and make it more equitably distributed. So, let’s open the borders first. We’ve got plenty of work to do to get there. Then, if inequality still seems like too much of a problem, we can talk about whether a more invasive state, and weaker incentives to work, save, innovate, trade, economize, etc., are a price worth paying for still more equality.

P.S. It’s a little off-topic, but if we’re worried about r>g, the real fix is Social Security privatization. Forcing up the savings rate would mean more capital, lowering its marginal product– lower r— and raising the growth of the economy– higher g.

UPDATE: Minor corrections were made after this was first posted.

A society in which the rich have a very high degree of economic, political, and sociocultural influence is an unpleasant society in many ways.
Read more at http://www.project-syndicate.org/commentary/j–bradford-delong-is-surprised-by-the-poverty-of-conservative-criticism-of-capital-in-the-twenty-first-century#OS2DZ3JavDCdtOT1.99
A society in which the rich have a very high degree of economic, political, and sociocultural influence is an unpleasant society in many ways.
Read more at http://www.project-syndicate.org/commentary/j–bradford-delong-is-surprised-by-the-poverty-of-conservative-criticism-of-capital-in-the-twenty-first-century#OS2DZ3JavDCdtOT1.99
A society in which the rich have a very high degree of economic, political, and sociocultural influence is an unpleasant society in many ways.
Read more at http://www.project-syndicate.org/commentary/j–bradford-delong-is-surprised-by-the-poverty-of-conservative-criticism-of-capital-in-the-twenty-first-century#OS2DZ3JavDCdtOT1.99
A society in which the rich have a very high degree of economic, political, and sociocultural influence is an unpleasant society in many ways.
Read more at http://www.project-syndicate.org/commentary/j–bradford-delong-is-surprised-by-the-poverty-of-conservative-criticism-of-capital-in-the-twenty-first-century#OS2DZ3JavDCdtOT1.99
Nathan Smith

Nathan Smith is an assistant professor of economics at Fresno Pacific University. He did his Ph.D. in economics from George Mason University and has also worked for the World Bank. Smith proposed Don’t Restrict Immigration, Tax It, one of the more comprehensive keyhole solution proposals to address concerns surrounding open borders.

See also:

Page about Nathan Smith on Open Borders
All blog posts by Nathan Smith

2 thoughts on “Piketty, inequality, and open borders”

  1. I believe Delong and Piketty would argue with your functional form assumption that f_i is a function of W_i and not the complete vector W. f_i could still be increasing in W_i but for large W_j decreasing in W_j. The justification for this would be that those with extreme wealth yield excessive political power or something similar. You may not agree with this argument but I think it is logically coherent.

    1. I like the way you think! You definitely grasped the most esoteric point in the argument. Fun, fun, fun.

      However, I’ll be even more pedantic by defending my own formulation. You seem to be assuming that f_i represents individual utility, which the SWF somehow adds up in order to give a measure of social utility.

      But I’m not assuming that f_i represents individual utility. My SWF directly attaches values to individual wealth, which are not necessarily the same as the values attached by the individuals.

      Substantively, I agree with you: DeLong and Piketty seem to think that extreme wealth has negative externalities, maybe because it’s bad for the world when the rich exercise too much political power. I don’t think that’s crazy, but I don’t think it’s particularly likely either. If anything, I think extreme wealth has positive externalities, by the channels suggested (patronizing the arts, luxury goods that later become affordable to everyman, etc.). I’d still rather that an economic pie of a given size be more equally distributed, because the marginal utility of a dollar is decreasing. But if the rich can get richer without impoverishing the rest of us, then let them do it. And under capitalism, you generally can’t get rich without creating a lot of spillover value for others.

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