My Draft Paper: A Bit of Elucidation in Q&A Format

The draft of my paper “The Global Economic Impact of Open Borders” already feels a bit obsolete after some great real-time peer review and the rethinking it has been provoking me to do. Sometime soon (I hope) I’ll do a rewrite, but it’s already reshaped my thinking about what a world of open borders is likely to look like. I thought a Q&A format might be a good way to explain my methods, highlight some key predictions, and give voice to some of the skepticism readers are likely to feel, responding to it with a mix of rebuttal and concession. “Q” represents my impression of an intrigued, but sometimes confused or skeptical, reader. “A” is me in my role as author of the paper.

Q: Does your paper confirm the well-known claim that open borders would “double world GDP?”

A: Basically, yes. “Double world GDP” was always a kind of very rough midpoint of disparate projections. I present two scenarios, with Scenario 1 predicting an 80% increase in world GDP, and Scenario 2 predicting a 69% increase in world GDP. That’s less than doubling, but it’s in the ballpark.

Q: How many people would migrate?

A: Very many. Scenario 1 predicts well over 5 billion, Scenario 2, a little over 3 billion. This is one of the respects in which I think Scenario 2 is more realistic. By this account, international mobility under open borders would actually be similar to current levels of mobility among US states. That might sound odd, since, policy aside, the cultural and linguistic barriers to international migration are obviously much larger than for migration among US states. But the economic incentives for international migration are also larger. Wages and the general level of economic development differ far more among nations than across US states.

Q: Would open borders end world poverty?

A: That’s a little complicated because “poverty” is not well-defined. Have we ended poverty in the USA? Probably almost any American would say no. A development economist might be tempted to say yes, because even Americans below the “poverty line” tend to have plenty to eat, electricity, shoes, indoor plumbing, and all sorts of other things that would be luxuries in sub-Saharan Africa. Granted, people in homeless shelters may not have even that, but (a) they’re a tiny proportion of the population, and (b) since other factors like mental illness or substance abuse, or mere lifestyle choice, often account for homelessness, it’s not clear that “poverty” is the right diagnosis of the problem. Still, it would be too odd to claim that poverty has been eliminated in rich countries, and the lesson one learns in being forced to concede that is that poverty isn’t just a matter of not having enough money or material resources. It’s partly a matter of relative living standards, of social status, of character and mentality.Refugee in Uganda who repairs cellphonesSo, I would not really want to claim that open borders would end poverty. I would almost want to say it would eliminate “world poverty” but not “poverty” because when we say “world poverty” we mean something more extreme than when we say “poverty”… but that seems like verbal hair-splitting. Let’s say that open borders seems likely to eliminate, or at least to render rare to the point of negligible, the kind of extreme poverty that development economists usually have in mind when they talk about poverty, e.g., in Paul Collier’s book The Bottom BillionUnder my “Scenario 2,” the living standards of unskilled workers would converge to 44% of the current US level. If by “poverty” we mean $1/day or $2/day, that’s pretty much the end of world poverty.

Q: What’s the deal with “sigma?” Does the model really assume that unskilled workers have to be paid 1,000 times more to live in a big metropolis, compared to a small village? Is that plausible?

Sometimes economists have to use unrealistic assumptions to make a model work. Milton Friedman argued that the value of an economic theory depends on the accuracy of its predictions and, in effect, that it doesn’t matter how unrealistic one’s assumptions are. Someone pointed out (I can’t find the citation) that by that standard, “giants paint the sky blue every morning” is a valid theory, because its prediction– that the sky turns blue in the morning– is true, and the falsity of the assumption that giants are painting it is irrelevant. So, Friedman can’t be quite right… yet the idea of “market equilibrium” does seem to help economists understand the world, even if it’s never quite a true statement to say “this market is in equilibrium.”

At present, I need the unrealistic assumption of a high “sigma” in order to avoid imputing highly compressed distributions of local TFP to settlements in rich countries. Highly compressed distributions of local TFP within countries, mean small overlaps of local TFP distributions across countries, leading to extremely high total migration under open borders. By making “sigma” more realistic, I would make the model’s other predictions wildly unrealistic. Doesn’t that show that there’s something wrong with the model? Well, yes… but, what’s the alternative? Build a better model? Easier said than done. Just guess, without a model. No thanks, I prefer a flawed model (used with good judgment) to mere verbal hand-waving.

That said, I’m working on changes that will hopefully eliminate the need for an implausibly high “sigma.” Currently, the model has two extreme assumptions about how population density affects the cost of living. On the one hand, the elasticity of the raw wage with respect to settlement size (i.e., sigma) is 0.6. On the other hand, the elasticity of the human capital premium with respect to settlement size is zero. These assumptions are unrealistic in opposite directions, and may even cancel each other out in some respects, but it would be better if both the raw wage and the human capital premium were higher in cities. The elasticity of the human capital premium with respect to settlement size probably should be lower than the elasticity of the raw wage, since a lot of what cities have to offer, over and above what the countryside can, is of a luxury character (e.g., fancy restaurants) and/or more enjoyable to people with high human capital (e.g., museums). But it makes sense that lawyers and doctors should want to spend some of their extra earnings on backyards, not just on manufactured goods or foreign vacations or fine wines.

The question is: will the math still work? It’s almost impossible for laymen to understand this aspect of the alchemy of economic modeling. A non-economist, or even a well-trained economist, will suggest a plausible modification, seemingly simple and realistic, and the modeler stubbornly refuses to incorporate it. Little does the friendly critic know that his tweak breaks the solvability of the model. The difference between being able to solve for equilibrium, and not being able to, is like the difference between gliding along a bike path and hacking one’s way through the forest. Solvable means you can derive nice elasticities, and see how your variables and parameters are affecting your results. Not solvable means exorbitant computations to check any tweak of a parameter or a variable, and causation is still opaque.

But, I’ve started to work through this, and I think the math will work. So, in the next version of this paper, I may be able to dispense with the need for a high “sigma,” and the weird assumption about unskilled workers earning 1,000 times more in the big city than in the village. If not, I’m not above publishing a model that has a few giants painting the sky blue, if it enables me to perform mighty feats of plausible extrapolation.

Q: What’s the deal with these “new settler societies?” Are they just data artifacts?

A: “Scenario 1” makes some odd predictions to which I give the appealing name “new settler societies.” Thus, East Timor ends up with 478 million people (from just over 1 million), Botswana with 212 million (from a little over 2 million), and Swaziland with 138 million (from a little over 1 million). Under “Scenario 2,” the phenomenon is much less dramatic, but it’s still there. East Timor’s population soars to 43 million, Botswana’s to 36 million, and Swaziland’s to 35 million. I classify Qatar differently, but it would also see a surge in population, to 391 million.

Doubtless, these results are partly artifactual, and specifically, they reflect anomalously high “TFP” that is really just natural resource extraction, not extensible over a greatly increased population. I need better ways to quantify natural resource extraction and subtract it from GDP. (Currently, I have patchy data about oil exports, which I deduct from GDP, but I need a more refined and comprehensive approach.) It’s possible that if I had better data on non-natural-resource-extraction GDP, the “new settler societies” would disappear. Then again, a lot of resource-rich places didn’t show anomalously high TFP.Young European immigrants in early 20th c. USMy tentative guess is that the specific “new settler societies” that show up in my predictions are largely artifactual, but that there would be such a phenomenon as new settler societies under open borders. In certain places, a happy combination of natural and political circumstances would give rise to a fashionable migrant mecca, and a cosmopolitan settler community, self-selected to prefer the kind of society chance and circumstance had thrown up, would reinforce it. A virtuous cycle would ensue, and soon, some spot hardly anyone has heard of would be an admired and thriving city, with suburbs spreading out and skyscrapers surging up. And without claiming the site is specially probable, I see no harm in imagining the place to be East Timor, with lots of coastline, a tropical climate, and mountains. Why shouldn’t a flood of Chinese and Indians settle there, and found a string of Singapores?

Q: And meanwhile, there would be quite a few “ghost nations?” Sounds spooky.

Yes, it sort of does. This is one of the predictions of Scenario 1 that goes away in Scenario 2. Still, it has a certain logic to it. Why would anyone live in a place like Zimbabwe, Afghanistan, the Democratic Republic of the Congo, or Burma, unless they had to? According to Scenario 1, almost no one would. There would be a nearly universal exodus, leaving behind only a few half-mad beggars wandering among the deserted shantytowns.

According to Scenario 2, there are no ghost nations. The worst-off places would see a major exodus, but at some point they would be “rescued” by their diasporas. I think this is more likely. Large diasporas could undermine bad regimes and foster better ones. Some would return with skills and/or savings, start businesses, run for office, teach school. Migration would plug these countries in to world civilization, and they would change.

Q: But anyway, wouldn’t the governments of these countries restrict emigration, if they were on their way to becoming ghost nations?

Maybe, but the game is to predict what would happen if migration restrictions were abolished. So that’s ruled out by assumption.

Q: What’s the deal with “Scenario 1” and “Scenario 2?”

Scenario 1 applies the model in a straightforward and literal way. The result is that the tail of TFP ends up wagging the dog of global migration. TFP, or “total factor productivity,” is a kind of residual or “pure place premium.” TFP is the differences in GDP per capita that can’t be explained by other systematically observable and quantifiable variables. Now, I actually argue that “factor endowments” can do most of the work in explaining GDP per capita, leaving a relatively small explanatory burden for TFP. I see the wealth of nations as arising mostly from (a) large international differences in average human capital and (b) substantial country risk premia affecting the risk of investment capital, with TFP varying across countries much less than average human capital. Still, under open borders, because everything else is mobile, a little bit of TFP can move a lot of people. Hence the new settler societies mentioned above.

For Scenario 2, I (a) assume that open borders promotes human capital development, with the average native of each country closing 20% of the human capital gap with the US; (b) assume that open borders facilitates international capital flows, cutting in half the risk premia faced by many countries; and (c) adjust TFP downward in receiving countries, so that it shifts in the direction of the TFP of source countries, and adjust TFP upward in sending countries, so that it shifts in the direction of the destination countries. Migrants affect TFP both where they come from, and where they go to, albeit with one-fifth the weight of non-migrants in each case, reflecting the greater influence on institutions of those who stay put. All these modifications are very plausible qualitatively, but theory and evidence don’t pin down how they should be quantitatively implemented. Still, for the moment, Scenario 2 represents my “best guess” about what a world with open borders would “really” look like, partly just because the TFP adjustment mechanism reduces the probably distorting effect of apparent high TFP outliers.

I could generate many more of these “scenarios.”  Scenario 1 is to some extent unique, representing “the” result of global market clearing in the labor market, albeit I had some discretion in how to describe the status quo. But for Scenario 2, I had plenty of room to choose the rules differently. In future drafts, I plan to have more “robustness checks” showing how results depend on how some of these discretionary elements are chosen.

Q: Would rich countries by “swamped” by immigrants under open borders?

What do you mean by “swamped?” In Scenario 2, the population of the West (the EU and the Anglosphere) rises from 872 million to over 3 billion. But assimilation would still mostly prevail, at least as far as TFP indicates. Revolutionary English stock a small proportion of the current US population? If the answer is “no, because those immigrants assimilated and didn’t fundamentally alter American society,” then that answer may apply to open borders, too. There isn’t a formal theory of institutions undergirding these results, however, and if you think 3 billion people in the West would lead to complete societal collapse, this paper doesn’t refute that, it just starts with more optimistic assumptions.

I don’t find predictions of 3 billion people living in the West either surprising or alarming. Life is good here. Why shouldn’t almost half the human race want to come? Admittedly, international polls show much lower demand for migration than my model, or, say, John Kennan’s, predict. But that’s just diaspora dynamics. Migration would snowball as early migrants wrote home that the grass really was greener on the other side.

Q: Scenario 2 predicts huge gains in labor income for people in many poor countries? How exactly would that happen?

Open borders would enrich the world’s poorest in several different ways. First, many would move to more productive places. Second, open borders would increase both the incentive and the opportunity for people from poor countries to acquire human capital. Since unskilled workers are far more likely than skilled ones to be stuck in unproductive places under the status quo, open borders would increase the effective global supply of raw labor, relative to the effective supply of human capital. Human capital would become relatively scarcer and see its marginal product rise, giving people an incentive to study. At the same time, higher wages would give poor people more money to invest in their children’s education. And the experience of migration itself– permanent or temporary– would broaden the horizons of many and make them smarter and more modern. And people would get access to better schools in the West. Third, the poorest countries would benefit from having large diasporas abroad, becoming acquainted with better ways of doing things practiced in the rich world. Fourth, remittances from abroad would finance capital formation. Fifth, in some countries it would be important that emigration would raise the per capita value of extractible natural resources. People in the world’s most benighted countries would mostly improve their lot in life by moving abroad. In less desperate cases, such as India and China, around half the population would emigrate, but life would improve a lot for those who stayed behind, as well as for emigrants.

Q: Would Americans really see their incomes fall by 10% under open borders? Why?

Well, real estate would appreciate in value dramatically, so homeowners would see their net worth rise, and maybe their dollar incomes, too, if they went into business as landlords. There would also be a lot more capital in the world, so to the extent that Americans own a substantial share of that, that might also offset a drop in labor incomes. Finally, the US government would enjoy a much larger tax base, so depending on what it did with that, it might contribute something to natives’ disposable income through transfers and/or tax cuts. Also, I’ve left out of account the effect of open borders on technological change, but there are all sorts of reasons to expect open borders to accelerate that, which would bend all the model’s predictions in an appealing direction.

But yes, under Scenario 2, the average labor income of US natives would fall by 10%. And this applies across the human capital spectrum. Unskilled workers would see their living standards (not money wages though) fall to 44% of the current level. But, surprisingly, the human capital premium would fall, too, because the US would be such a magnet for human capital that average human capital would rise in the US. If the only effect of open borders were to increase population while keeping average human capital the same, money incomes would stay the same, though living standards would fall somewhat due to congestion disutilities. What causes a loss of labor income for Americans is that TFP falls under Scenario 2.

Q: How does the spatial model here relate to your OB post about “The Great Land Value Windfall from Open Borders?”

It is somewhat more pessimistic. In that post, I drew two land supply curves, one for existing urban land, one for new urban land. I treated the supply of existing urban land as perfectly inelastic, and the supply of new urban land as perfectly elastic. I treated these as separate markets, on the ground that what one is really paying for in urban land is precisely proximity to other people and centrality of location, so as urban centers grow, new urban land developed at the edges will have the same value as urban land at the edges previously had, but previously developed land closer to the city center will appreciate as the city population grows. In that model, there are no congestion disutilities, and no inherent scarcity of land as such.

In “The Global Economic Impact of Open Borders,” a scarcity of good city sites is a fundamental and important feature of the world. Consequently, mass immigration to the USA would reduce the living standards afforded by a given money income, due to congestion disutilities. In “The Great Land Value Windfall from Open Borders,” mass immigration would not reduce the living standard afforded by a given money income, because newly developed urban land at the margins of cities would be just as good as the formerly marginal land was. The difference between these models is not really accounted for by any change in my views of how the world works. It is simply that different assumptions proved analytically convenient for different purposes.

Q: This model pertains to universal open borders, right? What if open borders were implemented by just one country, say, the USA?

Yes, this model is for universal open borders. I don’t know what would happen if just the USA did it. I’d need to make fundamental changes to the model to answer that question.

Q: What about DRITI?

The paper contains no estimates of how much revenue could be raised by migration taxes, or how a world of open borders would change if governments sought to hold natives harmless through tax-and-transfer schemes.

Q: Do you think this paper should persuade policymakers to adopt open borders policies?

Yes and no. Yes, I think that if my predictions are right, or in the ballpark of right, they would be a very strong reason for benevolent policymakers to open the world’s borders to migration. But no, I of course don’t think it would be sensible for any policymaker to adopt such a radical policy on the basis of such tentative and speculative predictions as my paper contains.

Q: Why is there no literature review, no bibliography, and few citations in the paper?

A: Because it’s just a draft. I like to have a good idea where I stand before I really plow into what others have said. Sometimes you don’t even know what’s relevant until you’ve done a lot of your own exploration. And compiling bibliographies is tedious work. But I have read a good deal, and am reading more, and future drafts will reflect that.

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

One thought on “My Draft Paper: A Bit of Elucidation in Q&A Format”

  1. I have four thoughts on this.
    1)What do you think the actual time scale of this shift will be; will the mass migration happen in 30 years? 50? do you have no idea?
    2) Do you think there could be a threshold level of capital (human or otherwise) needed to migrate? I.e someone who is completely illiterate with no education and almost no assets may have a very hard time setting up in the U.S, even without any legal restrictions
    3) I think there would be a lot of important human capital that can’t be formally measured. Imagine a chef with minimal formal education. He may earn a low wage in his home nation, but his skills may be more marketable in the U.S.
    4) Countries receiving the immigrants would probably want to intensely invest in basic education among the new population. The effects of a developed nation like the U.S receiving a large population without education would be disruptive .

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