Upward and downward biases in the "double world GDP" estimates of the gains of open borders

Summary: I discuss recent estimates that open borders could double gross world product through increases to migrant productivity. Such a doubling would be extreme, but not out of the range of our experience: it would be equivalent to raising world per capita income to the level of Greece (U.S. levels would quadruple world product), or a couple decades of continued economic growth. However, it would require the great majority of the developing world to migrate. I discuss the migration levels required for the estimates, polling and historical data bearing on migration levels, and population and economic growth trends that affect the estimates. Over several decades, the impact estimates seem too high, requiring implausible quantities and rates of migration, although potential effects remain large. Over the longer term, boosts such as population growth in poor countries and increased education for second generation migrants increase the maximum potential of migration beyond doubling world output, but development in poor countries, changes in place premium, and other changes may reduce gains over time.

Recently, I had a conversation with Vipul Naik of the Open Borders blog about sources of uncertainty regarding estimates that open borders would double world GDP, and he mentioned that it would be good if the methods of the papers could be compared side by side with estimates of how many people would migrate. I am interested in better characterizing this promising cause, so I volunteered to look over the literature he had collected and write up my thoughts.

Below, in addition to discussing a number of factors influencing migrant flows, I also discuss some factors that could adjust the economic gains produced by migrants.

Getting a sense of scale: what would doubling world GDP mean?
The CIA world factbook gives a 2012 gross world product (GWP) of $84.97 trillion (PPP), and per capita PPP GWP of ~$12,400 (the table below uses a different source).

One way of thinking about doubling GWP is in terms of the per capita income of different countries today. Doubling GWP per capita would bring the world average close to that of economically depressed Greece. Bringing the world average to British or Japanese standards would triple GWP, while global American or Hong Kong per capita incomes would quadruple GWP.

Rank	Country	Int$	Year
6	United States	51,704	2012
—	Hong Kong	50,936	2012
21	United Kingdom	36,569	2012
22	Japan	35,855	2012
—	European Union	31,571	2012
42	Greece	24,260	2012
67	Mexico	15,363	2012
—	World[4]	11,964	2012
93	China	9,055	2012
133	India	3,843	2012
171	Haiti	1,229	2012
173	Mozambique	1,155	2012
186	Zimbabwe	552	2012
187	Congo, Dem. Rep.	365	2012

A different comparison is to the time it takes GWP to double at different growth rates. In recent years GWP has been growing at 3-4% per annum (note this is total GWP, not per capita GWP, so it includes the effect of population growth).

Region	2006	2007	2008	2009	2010	2011	2012	2013 (est.)	2014 (est.)
World	5.1	5.2	3.0	-0.5	5.3	3.9	3.2	2.9	3.6
Advanced economies	3.0	2.7	0.6	-3.4	3.2	1.7	1.5	1.2	2.0
Eurozone	2.9	2.7	0.7	-4.1	1.9	1.5	-0.6	-0.4	1.0
USA	2.7	2.1	0.4	-2.6	3.0	1.8	2.8	1.6	2.6
Developing countries	7.9	8.3	6.0	2.8	7.5	6.2	4.9	4.5	5.1

A 3% growth rates corresponds to GWP doubling ever 23.45 years, and a 4% rates gives a doubling time of 17.67 years.

So, an effect that doubled total world GDP would be amazing, but not wildly beyond the kind of variation we see across space today and across time in recent history.

John Kennan's "Open Borders"
At the Open Borders blog page, on "Double World GDP", the most recent paper listed is Open Borders by the economist John Kennnan. Kennan's basic approach relies on empirical data, provided by Michael Clemens, on the "place premium"for migrants from various countries to the United States, i.e. the degree to which wages are higher for migrant workers in the U.S. than similar-seeming counterparts in home countries. Kennan guesstimates a quantity of workers who would migrate to rich countries under open borders, assumes that their contribution to global labor supply would increase by the U.S. place premium, and then estimates economic impacts.

Since Clemens only provided place premium data for a limited set of countries, Kennan extrapolates estimated place premium values for other countries by regressing place premium against home country GDP. Absent any particularly principled account of how many would migrate under open borders, he assumes that for a place premium of X, then only 1/X will stay in the home country. Since place premiums for the countries containing most of the world population range from 2-10, this means Kennan is talking about the migration of billions of people, the bulk of the population of the developing world.

Economist and Open Borders blogger Nathan Smith has a post discussing the paper, and trying to determine the predicted economic gain:

Counting one US worker as an efficiency unit, the effective world supply today is estimated at 764.1 million workers. Open borders, using Kennan’s procedure for forecasting migration, would raise this 1,507.7 million. Thus open borders would more than double the world’s effectively labor supply. If all the migration occurred instantaneously, this would lead to a 20% drop in wages. A couple of further estimates derived from the model put the gain for people in developing countries at about $10,000 per worker. That’s an average over all workers, not just migrants...
He doesn’t tell us how world GDP would rise under open borders, in the short or the long run. He doesn’t tell us how many people would move, or where they would come from. I think Kennan’s model implies a short-run increase in world GDP of about 65%, and I’m pretty sure in the long run world GDP would double. [As investments in capital increased capital per effective worker to pre-open borders levels over time.]

For the rest of this post, I will look at some of the assumptions going into this estimate, and for questionable ones, whether they bias the estimates upward or downward.

The descendants of migrants from very poor countries will have more education and other human capital
The place premium estimates match workers by education levels, so if the education levels or other skills of workers systematically changed, it would throw off the impact estimates. In particular, levels of education, host country language skills, and health would be higher in later generations after a massive wave of low-skill migration.

Education levels in many developing countries are far below those in developed countries, and migrants close most of the extreme gaps in a single generation (or leapfrog the native population, in some cases).

In the longer term, taking this into account should boost GWP impacts, but with a number of decades of lag for migration, childbearing, and propagation through the work force.

Migration counts: labor force vs population

To estimate migrants from a country Kennan multiplies an estimate of a country's national labor force by 1 minus 1/(the relevant place premium). Some oddities of the labor force definition call this into question.

From a World Bank labor force page:

Total labor force comprises people ages 15 and older who meet the International Labour Organization definition of the economically active population: all people who supply labor for the production of goods and services during a specified period. It includes both the employed and the unemployed. While national practices vary in the treatment of such groups as the armed forces and seasonal or part-time workers, in general the labor force includes the armed forces, the unemployed, and first-time job-seekers, but excludes homemakers and other unpaid caregivers and workers in the informal sector.

As a result, less than 2/3 of the relevant age group in India are part of the measured labor force, while over 4/5 are in China, reflecting differing degrees of informal sector work and female labor force participation. However, in richer countries work tends to be formal and women are drawn into the work force, particularly in the second generation. Accounting for this would tend to push GWP estimates upward, as migrant workers are accompanied by nonworking spouses, children, and other family members.

Migrant counts: willingness to migrate

In the appendix of his paper, Kennan lists relative wages, labor forces, and other information on 40 less-developed migrant source countries. This leaves out many other countries, but since the world's most populous ones are included the group would still account for most migrants. Below are the number of migrants predicted from Kennan's data and migration decision function:

Country	2010 Relative wage	Workers (millions)	Migrants (millions, not including children and non-workers)
Argentina	0.431	18.8	10.6972
Bangladesh	0.224	75.9	58.8984
Brazil	0.274	104.8	76.0848
Belize	0.403	0.1	0.0597
Cameroon	0.15	8.1	6.885
China	0.238	794.9	605.7138
Dominican Republic	0.556	4.4	1.9536
Ethiopia	0.234	43.3	33.1678
Ghana	0.155	10.3	8.7035
Guatemala	0.329	5.4	3.6234
Guyana	0.287	0.3	0.2139
Haiti	0.093	4	3.628
Indonesia	0.168	119.5	99.424
Cambodia	0.144	8.1	6.9336
Nigeria	0.083	48.3	44.2911
Nicaragua	0.276	2.3	1.6652
Nepal	0.211	15.5	12.2295
Pakistan	0.153	63.4	53.6998
Sierra Leone	0.145	2	1.71
Thailand	0.492	37.8	19.2024
Turkey	0.498	24.1	12.0982
Uganda	0.235	13.4	10.251
Bolivia	0.2	4.6	3.68
Chile	0.297	7.9	5.5537
Colombia	0.359	21.1	13.5251
Costa Rica	0.493	2.1	1.0647
Ecuador	0.211	7	5.523
India	0.2	452.7	362.16
Jamaica	0.257	1.3	0.9659
Jordan	0.209	1.6	1.2656
Sri Lanka	0.235	8.7	6.6555
Morocco	0.525	11.3	5.3675
Mexico	0.364	48.6	30.9096
Panama	0.359	1.6	1.0256
Peru	0.296	15.4	10.8416
Philippines	0.275	41.5	30.0875
Paraguay	0.353	3.1	2.0057
Uruguay	0.351	1.7	1.1033
Vietnam	0.173	52.7	43.5829
South Africa	0.393	17.8	10.8046
Total (40 countries)		2105.4	1607.2557

From this sample over 75% of the labor force are predicted to migrate. As noted above, this leaves out many countries, children, and women not in the labor force, among others. If we included family members and other countries the implied number of migrants looks like it would exceed 3 billion.

These numbers are much larger than those suggested by Gallup international polls. The 2011 poll found that in India and China only 6% of adults say they would like to move  permanently to another country. For the rest of developing Asia only 13% said they wanted to move permanently. Gallup also asked about temporary migration for work, finding that 19% of Asian adults said they were willing, including 19% of Chinese and 8% of Indians.

Since Asia accounts for the bulk of the potential gains of migration in the model, such low numbers would slash the expected benefits of open borders. The idea of over 75% of the Chinese workforce migrating is further called into question by the possibility that the Chinese government might not permit its citizenry to depart en masse.

In sub-Saharan Africa percentages willing to migrate permanently rise to the 30s, and for temporary work almost 50%, but the survey numbers still fall far short of what is needed to match Kennan's predictions. People are often bad at predicting their future actions (although this cuts both ways: in the Gallup data often people who intend to move fail to do so), and under open borders early migrants could pave the way for others. Successful migrants would tell or transport friends and family to join in their success, and as diasporas build in rich countries new migrants might find conditions more congenial (migration follows patterns of language and religion to a substantial degree today).

Kennan mentions data about U.S. migration from Puerto Rico (which has open borders with the mainland) and Mexico (from which illegal immigration is relatively easy):

But it is consistent with the data on migration between Puerto Rico and the U.S. According to Clemens, Montenegro, and Pritchett (2008), the relative wage in Puerto Rico is approximately 2/3 of the U.S. wage, and according to the 2000 Census, the proportion of adults born in Puerto Rico who were living in Puerto Rico is also approximately 2/3. Moreover, Lessem (2011) estimates that a 10% increase in the Mexican/U.S wage ratio would decrease migration by 11.6%, which is roughly consistent with the unit elasticity of the migration rate predicted by the simple model.

The official Mexican-American community makes up nearly 22% of the Mexican origin population of the world, plus an extra several percent for undocumented migrants. 10-20% of the population in Mexico say they would like to permanently migrate, with another similar chunk expressing interest in temporary work. This suggests that polls might be accurate, but doesn't involve true open borders, as have obtained with respect to Puerto Rico since 1917.

The share of people of Puerto Rican background worldwide in the United States is larger than the share of adults born in Puerto Rico in the United States because of the cumulative effects of generations of migration. There are about 3.7 million people in Puerto Rico, about 1.5 million people born in Puerto Rico who have migrated to the United States, and another 3.5 million stateside Puerto Ricans. This puts the share of Puerto Ricans in the U.S. at closer to 2/3 than 1/3 but only after generations of migration:

Year	Population of Puerto Rico	Puerto Rican descendants in United States	Increase in stateside population (by decade)	Total population	Share of Puerto Rican descendants in U.S.
1920	1,299,809	11,811	10,298	1,311,620	0.90%
1930	1,543,913	52,774	42,476	1,596,687	3.31%
1940	1,869,255	69,967	27,491	1,939,222	3.61%
1950	2,210,703	226,110	198,619	2,436,813	9.28%
1960	2,349,544	892,513	693,894	3,242,057	27.53%
1970	2,712,033	1,391,463	697,569	4,103,496	33.91%
1980	3,196,520	2,014,000	1,316,431	5,210,520	38.65%
1990	3,522,037	2,728,000	1,411,569	6,250,037	43.65%
2000	3,808,610	3,406,178	1,994,609	7,214,788	47.21%
2010	3,725,789	4,623,716	2,629,107	8,349,505	55.38%

Note that despite open borders with the U.S. birth rates have mostly been able to outpace immigration over time. A sustained high migration rate over generations will eventually result in most of the migrating population living in the destination country, but a centuries-long delay would dramatically curtail the expected value of an open borders shift (as it might be rendered moot by other factors, and alternative investments could greatly compound over the period).

The polling data are consistent with this level of migration: 45% of people still in Puerto Rico say they have considered moving, and 25% have taken concrete steps (this after a third of people alive today born on the island have already moved). This supports the idea that migration totals would be in line with polls. 

However, the polls might change dramatically once migration is a live option (although the sharp distinction between, e.g. sub-Saharan Africa and South Asia in polled intentions still requires an explanation and account from that perspective). The place premium for a migrant from Puerto Rico coming to the United States is only on the order of 1.5, whereas for many populous poor countries it is in the 4-10 range, and it is intuitively plausible that demonstration effects of early migrants would be strong.. 

Non-wage factors in migration destination choice

In the migration polls many people from Muslim countries wish to move to Saudi Arabia, people from French-speaking countries often wish to move to France, and so forth. Less than a quarter of those expressing a desire to move permanently indicate the U.S. as their preferred destination. So open borders in just one country would attract even fewer total migrants.

The Clemens estimates are for the United States, and many other destinations have lower incomes, and perhaps less of a place premium (and often regulations less favorable to low-skill workers). If many rich countries opened their borders, then the additional migrants would often enjoy less in the way of income gains.

Non-border regulatory barriers to immigration

Even if current border controls were removed, a variety of policies might substantially hinder migration. For example, Singapore has one of the world's most open immigration policies, and admits many less skilled foreign workers from poor countries. However wages for these workers are very low by rich country standards (although high for the workers), and would run afoul of minimum wage laws in much of the world (Singapore has no minimum wage). Regulations which mandate costs for employers such as health insurance, labor unions, overtime rules, and other measures may disproportionately harm poor unskilled migrants' employment prospects (as can be seen in parts of Europe).

Restrictions on the construction of housing, and its use for high-density living accommodations in cities may drive the cost of living above what is practical for would-be migrants with lower skill levels who would otherwise greatly benefit from access to rich cities and regions.

If migrants are denied access to welfare state services in destination countries (while having them at home), this may also discourage migration (as with China's hukou system) and make it harder to reach the levels required to double GWP. [Chris Hendrix adds that welfare programs adapted to rich country incomes may produce higher disincentives for work for poor migrants, as with minimum wages and labor regulations.]

Population growth in poor countries

On the other hand, there is still rapid population growth in poor countries (more rapid than expected in Africa). Recent UN projections suggests several billion people will be added to the world population by 2050, mostly in Africa, currently the poorest continent. Billions of potential migrants in the regions with the highest willingness to move in polls and the largest wage gaps with developed countries could substantially increase GWP gains.

Migration might also have effects on population growth, which would have other potentially large effects on GWP.

Place premium decline: rising wages and development at home

If it takes decades, even more than a century, for migration flows to take their course, there will be plenty of time for economic development in poor countries to reduce wage gaps and place premium. Real per capita GDP growth in poor countries has been tremendous in recent decades, especially in the ultra-populous India and China. At recent rates real wage gaps between the United States and the latter countries would be cut in half in perhaps 10-15 years. Reversion to slower growth is likely, but growth may take off elsewhere, e.g. in sub-Saharan Africa (it has already picked up, even if not at Chinese or Indian rates). Bill Gates recently predicted that by 2035 there will be almost no poor (as opposed to middle-income) countries.

A falling place premium would reduce migration rates, as well as the economic gains of movement (the latter is most true in terms of log income, since absolute income is dominated by the richer countries).

Place premium change in destination country

The open borders analysis assumes that the place premium is unaffected by the change in population (although with the assumed billions of migrants, they would have to make up a majority). However, it is possible that the observed place premium figures would decline with large migrant flows. This would depend on the cause of place premium differences.

For example, some resource-rich countries may have high wages because of limited labor supplies for the oil or mining industries (and the service industries catering to employees thereof). Open borders might not much increase the production of oil, and so this wage premium would be competed away.

A place premium caused by better economic policies and institutions could scale to cover very many migrants, but might decline if a fall in education levels, increase in inequality, or failure to assimilate migrants to local practices disrupt those institutions or the political forces that sustain them.

A place premium caused by cluster effects/economies of scale and dense markets could increase with population.

Possible errors in initial place premium estimation
Access to migration was not randomly assigned, and bias from harder-to-observe factors may be distorting the place premium estimates in a way that does not generalize to mass migrations under open borders. The estimates also differ for different observable worker characteristics, and could go awry in other ways.

Clemens notes in his paper that it uses local PPP adjustments that understated place premium for some countries, but that new PPP adjustments came in too late to use.

Global growth effects

The many changes caused by open borders, including increased education levels by migrants and their children, larger markets to fund R&D, and bigger rich country tax bases (although perhaps larger spending increases) could all affect the movement of the technological frontier and thus global growth, rather than simply bringing more of the world closer to the existing frontier.

Migration may also increase the rate of catch-up growth in migrant-sending countries via diasporas that make it easier for capital and knowledge to flow from rich to poor countries. Nathan Smith suggests that these effects would eventually constitute most of the GDP gains from border liberalization:

Tentative conclusion so far: My sense is that economic models predicting that open borders will “double world GDP” will continue to depend on extremely large movements of people. Again, I will not say that such predictions are unrealistic, upon reflection they seem plausible to me. But we should avoid breezily quoting “double world GDP” predictions while allaying or minimizing people’s fears about epic movements of peoples. It is possible that open borders will prove to be a good less radical in its impact than the available theories suggest. But in that case, it won’t double world GDP, or at least, not in the ways that models like Kennan’s suggest.
Some important benefits of open borders, especially the stimulus it would provide to idea generation and institutional export, are omitted from the extant models, including this one. These factors are difficult to incorporate into theoretical models because there is relatively little agreement about what determines the rate of idea generation, or the quality of institutions. I expect that open borders probably would double world GDP with a mere hundreds of millions, not billions, of people actually migrating, but that may be more than I can say with my economic theorist hat on.

Such effects are not included in the "double world GDP" papers, but there is some literature studying the disproportionate role of diasporas in providing FDI and acting as middlemen for trade between their new and ancestral homes.

[Thanks to Nick Beckstead, Chris Hendrix, Vipul Naik, Anna Salamon, and Brian Tomasik for comments.]