# John Kennan’s “Open Borders”

This post is going to attempt to do something difficult, namely: bring a contribution to technical economic theory within reach of lay readers. The typical lay reader, or for that matter even an atypically intelligent reader who is not a specialist in economics, could understand little of Kennan’s paper, or for that matter most academic economics papers. I don’t totally understand the paper either, but I think I mostly understand it. I’m pretty sure I understand the main thrust. The work in question is “Open Borders” by John Kennan. If one had to pick one thing to stick in a newspaper headline, it would be Kennan’s prediction that

For the 40 countries in Figure 6 this gives an estimate of \$10,798, per worker (including nonmigrants), per year (in 2012 dollars, adjusted for purchasing power parity). This is a very large number: the average income per worker in these countries is \$8,633, so the gain in (net) income is 125%. For all of the countries in the Penn World Table that are not at the productivity frontier (as deﬁned above), using GDP data to estimate relative wages, the estimated gain is \$10,135, relative to an average income of \$9,079, so the gain is 112%. These are of course just rough estimates, relying on a number of strong simplifying assumptions. But unless these assumptions are extremely far off the mark, the results indicate that the gains from open borders would be enormous.

In other words, open borders could double the income of the world’s most disadvantaged people. Far from causing a “brain drain” effect, harming poor countries by poaching productive people, even nonmigrants would benefit from open borders. Furthermore:

These gains are associated with a relatively small reduction in the real wage in developed countries, and even this effect disappears as the capital-labor ratio adjusts over time; indeed if immigration restrictions are relaxed gradually, allowing time for investment in physical capital to keep pace, there is no implied reduction in real wages.

How does Kennan arrive at this conclusion? Via a theoretical model, calibrated to fit certain real world data. The approach is oversimplified and crude, yet at the same time, in some ways, painstakingly subtle… but that’s economic theory for you. The logic must be impeccable, but economists’ tolerance for departures from realism can be opaque at first, then, once understood, rather shocking. But one has to do it. A question like “what would happen if the world opened its borders?” involves such a large departure from current reality that common sense and experience fail us. Theory can, so to speak, see in the dark. It allows us to keep thinking clearly, at least, about very remote situations. But down to business.

After a short intro, Kennan’s first really substantive paragraph is:

Before proceeding to analyze a world economy with open borders, the ﬁrst question that must be answered is whether restrictions on factor mobility have any real effects. If product prices are the same across countries (because there is free trade and transportation is not costly, for example), and if there are two goods that are produced in two different countries, and if the production technologies (for these two goods) are the same across the two countries, then the factor price equalization theorem applies. That is, real wages and other factor prices are equalized across countries even though factors are immobile, because differences in factor prices are implicitly arbitraged through the product market. The theoretical argument is beautiful, but of course the facts are otherwise. For example, wages in the U.S. are about 2.5 times the Mexican wage, for comparable workers.

This will require some unpacking, especially “factor price equalization” and “differences in factor prices are implicitly arbitraged through the product market.” An important result in international economics is that in the “long run,” given certain fairly standard (albeit apparently unrealistic) assumptions, immigration will not reduce wages in the host country, because the mix of industries in the host country will shift to accommodate the new supply of workers to such an extent that wages will be exactly the same. (See the closely related Rybczynski theorem.) Thus, to use the example from the Feenstra and Taylor textbook that I teach this stuff out of, suppose there are two industries, computers and shoes. Computers are a capital-intensive industry, shoes a labor-intensive industry. If a lot of immigrants enter a country called, say, Home, then Home will start producing more shoes and fewer computers.

Fewer computers? Yes, fewer. Even though there are more workers? Not just proportionally fewer? No, fewer in absolute terms. Think of it this way. There’s the same amount of capital in Home as there was before. But there are now more workers. It’s not surprising that the shoe industry will take the lead in absorbing these workers, since its technology is the more labor-intensive of the two. But as it does so, it will lower the marginal product of labor and raise the marginal product of capital in the shoe industry. Or to try to express it without the jargon, the shoe industry will have trouble finding useful things for so many new workers to do without new machines, structures, and other capital goods for them to work with. Even if the shoe industry can’t increase its capital at all, it could find something for all the new workers to do. It will be able to make more shoes. But not that many more shoes. The greater supply of workers increases the shoe industry’s demand for capital. In fact, it implies that the shoe industry wants capital more, at the margin, than the computer industry does. As capital moves from the computer industry to the shoe industry, workers move too, since the scarcity of machines makes them less productive in computers. Importantly, the relative price of computers and shoes stays the same. This is because prices are pinned down by international trade: any deviation in the relative price would cause arbitrage. Wages don’t fall– again, this is in the long run– because relative prices don’t fall, and wages depend on relative prices. The growth of the shoe industry and the shrinkage of the computer industry raise the economy’s demand for labor relative to capital, exactly canceling out the tendency for a greater supply of labor to reduce its wage. This implies not only that wages shouldn’t be reduced by immigration, but also that wages should be the same in every country. Continue reading John Kennan’s “Open Borders”