Would the world's GDP double or triple if border controls were lifted and migrants moved from lower-to-higher wage countries? Several studies have concluded the answer is yes, so that maintaining border controls is equivalent to leaving "trillion dollar bills on the sidewalk."

The economic reasoning behind projections of huge increases in global GDP with more migration rest on a simple proposition. Wages reflect the value of the marginal contributions of workers to what they help to produce. Since more capital and better infrastructure make workers more productive in richer countries, workers who move from poorer to richer countries earn higher wages.

From a global perspective, low-wage countries have too many workers for their available capital and infrastructure. Transferring them to high-wage countries benefits the migrants, the receiving countries under the assumption that all migrants find jobs and do not displace local workers, and sending countries via remittances.

Global GDP, about $70 trillion in 2011, would increase by $40 trillion if: (1) wages were on average four times higher in the industrial countries with 600 million workers than in the developing countries with 2.7 billion; and (2) 2.6 billion or 95 percent of the workers in developing countries moved to industrial countries. These gains to global GDP would occur each year, making their present value huge.

There are also costs. Wages would fall in industrial countries, by 40 percent, and rise in developing countries, by over 140 percent. Capital would gain about $12 trillion.

However, the trillion dollar bills on the sidewalk from lifting migration restrictions are probably fake. Mass influxes of migrants are not likely to be costless, as the models assume. Models assume that all migrants get jobs on arrival, no local workers are displaced even as wages fall, and there are no broader socio-economic impacts as billions of migrants move from one country to another.

If people in developing countries have lower wages because of poor infrastructure and socio-economic institutions, and some of these institutional features transfer to industrial countries with the migrants, productivity might fall as institutions change. Depending on assumptions about how much productivity falls, global GDP might fall rather than rise with more migration.

The example of Puerto Rico is instructive. Two-thirds of Puerto Ricans live on the island where production workers earned an average $22,600 in 2012, compared to $34,500 on the US mainland. The fact that an average island worker could increase her income by $12,000 a year, or $240,000 over a lifetime at a five percent discount rate, suggests that personal migration costs must be very high to keep most Puerto Ricans on the island.

If migration costs are significant, global gains from migration decrease and could turn negative. If there are negative externalities from congestion, social unrest, or other factors, global gains soon disappear. It may be that governments understand at least somewhat the externalities that accompany migration, and that their migration policies aim to minimize migration costs.