Double World GDP? Another Economic Model of Open Borders

The claim that open borders would “double world GDP” is one of our side’s better talking points. Of course, it’s just a guess, based on theoretical models calibrated to the data, which amounts to a sophisticated, but still very fallible, form of extrapolation. These models are easy to mock if you understand them well enough to see their weak points. Yet, what alternative is there? The question of what the global economic impact of open borders would be is interesting enough to be worth answering tentatively. I’ve been working on my own, which has evolved somewhat since I wrote about it a few months ago. Meanwhile, I came across a new one, “The Global Welfare and Poverty Effects of Rich Nation Immigration Barriers,” by Scott Bradford (2012).

First, Bradford’s conclusions. Under open borders (with an exponential distribution of skills, more realistic than the uniform distribution that Bradford also considers), total world output would rise from $74 trillion to $130 trillion. Not quite “double world GDP,” but a more than 75% increase. Wages in rich countries would fall by 7.5%. Since Bradford, like John Kennan, does not model human capital as an independent factor of production, but simply interprets “skill” as multiplying a person’s labor power, this 7.5% wage drop would equally affect workers at all skill levels. There would be a 46% increase in wages for those who stayed in poor countries, and migrants to rich countries would see their wages rise by 157%.

Bradford chooses to focus on the poverty impact of open borders, but this turns out to be sensitive to an assumption about the inherent fixed cost of migration. If this cost is $10,000, the fraction in poverty would fall by 66%. Raise it to $20,000, and poverty is reduced by only 42%.

Now for the model’s Achilles heel:

[The model] implies that 94-97% of the poor region workforce, or about 2 billion workers plus their depends, would move to [the rich countries] if they could. That is unrealistic. As long as total factor productivity is higher in the rich region, and capital can move along with labor, our analysis implies that the great majority of poor region workers would be economically better off, and would increase world output, if they could move freely to the North. Even if the results in this paper are off by an order of magnitude due to elements not captured by our simple model, opening up migration has great potential to boost incomes around the world.

Where does this concession leave the model? If the author’s verdict on his own projections of migrant numbers is “That is unrealistic,” then what exactly is he claiming? He can’t be claiming that the prediction of 94-97% migrating won’t come to pass, but the prediction of raising world GDP by 75% will, since the latter depend logically on the former. What does the “even if the results in this paper are off by an order of magnitude…” sentence mean? It could be read as, “For some reason that I don’t really know, let’s assume ten times fewer people would migrate. If the effects are proportional, you’d still see a big increase in global incomes and a lot of poverty reduction.” But to conclude with such vague hand-waving as that seems to render pointless the paper’s effort to give a logically precise description of the world and assign precise, empirically-grounded values to certain parameters and variables. If the predicted migration flows are unrealistic, then the model is leaving out something important– or many things. If those things were understood and incorporated, we have little reason to think the model’s other results would be preserved, or scaled down in any predictable way.

Actually, given his other assumptions, Bradford’s estimates of the number of migrants are, if anything, indefensibly low. You might ask how 90%+ of the population could afford to migrate at all if migration costs are assumed to be $10,000 or $20,000. But Bradford’s migrants optimize an intertemporal utility function, and migration is a long-term investment in living in a better place. But it’s hardly plausible that the cost of migration would be $10,000, let alone $20,000. Bradford cites empirical evidence for this, but here, extrapolation is illegitimate. If only a skilled elite is migrating, they’ll do it in a relatively comfortable and expensive way. Under open borders, there’d be economies of scale in the migration process itself, and mass migration would find the cheapest ways to move. You would expect, for example, to see a revival of people traveling by ship. There’s no point in that now, because anyone who can hope to travel internationally values their time enough to prefer a plane ticket and a few hours’ journey to spending weeks on a boat. The market for international passenger travel by sea would be tiny. Under open borders, with billions of poor people on the move, ocean-going ships would offer international travel for a fraction of the cost of a plane ticket. So even the fig leaf of respectability that Bradford’s model derives from the 3% of people in poor countries that are predicted to stay put, we must take away. (I think a tiny number of poor people would still stay home without that, merely for the sake of the cheap land left behind by the mass exodus.)

I don’t want to come across as too negative, though, because I know by experience how difficult it is to do what he is attempting. You can’t project what the global distribution of income would be like under open borders without first having a fairly thorough explanation of what it is like now. You really need a theory of the wealth and poverty of nations even to get a model of the global economic impact of open borders off the ground. And economists haven’t exactly covered themselves in glory by their successes in explaining the wealth and poverty of nations.

Bradford (2012) could have followed Kennan (2012) by simply assuming that “strong attachment to home locations” will prevent everyone from wanting to move, and then adopting an arbitrary assumption, or an assumption with very weak empirical motivations, about what share of people would. I respect Bradford’s frankness about his model’s failure to predict realistic numbers of migrants as much as (not necessarily more than) I respect Kennan’s ad hoc measures to reduce the number of migrants his model predicts. The question which brings both of them to grief, in different ways, is: Given the opportunity to migrate to countries that are much more productive and have higher standards of living, why would anyone stay home? It’s not that answers to this question are difficult to propose. The trouble is that it’s very hard to quantify them, even in the loosest and most arbitrary way.

So, can I do better? I think so. My model will include human capital as an explicit factor of production; economies of scale at the city level; and differences in the cost of capital across countries due to country risk premiums. But what it will predict, I won’t know until I’m done calibrating it. Stay tuned!

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

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