The paper looks at changes in economic conditions, border enforcement and demographics in the United States and Latin America to try to isolate the factors that encourage people to migrate. It finds a strong relationship between the number of people born in Latin American and Caribbean countries and the percent change in immigrants to the United States between 1980 and 2015.

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For decades, Latin America was still experiencing a baby boom when the United States was not. While the U.S. baby boom ended in the 1960s, Mexico and other Latin American countries continued to see a surge in population into the 1970s and 1980s. By the early 1980s, the supply of labor in the United States was beginning to slow as the baby boomers aged, but that same change didn’t occur in Latin America until two decades later.

During the 1980s, 1990s and 2000s, that created a dynamic where low-skilled people in Latin America could do better economically by avoiding tougher competition at home and seeking out work opportunities in the United States, say researchers Gordon Hanson, Chen Liu and Craig McIntosh.

Today, the populations of most Latin American countries have begun aging, just like in the United States. And America’s population of immigrations from Latin America and Asia are growing older as well. In 1980, the median age of a Mexican-born person in the United States was around 20. In 2015, it had doubled to 40. By 2040, the researchers predict it could be roughly 70, as the chart below shows.

The researchers argue that aging populations will give low-skilled workers from those countries less motivation to immigrate to the United States, even without a massive border wall, as there will be reduced competition for jobs in their homes. They calculate the number of young, low-skilled workers coming into the United States from Latin America will continue to slow in coming decades.

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As a result, much of the current debate about low-skilled immigration into the United States, including discussions about building a massive border wall, are aimed at a situation that has already largely changed, the researchers say.

“The current U.S. debate about immigration policy has a backward-looking feel to it,” they write.

The United States has seen a substantial change in the character of its immigrants in recent years. Estimates by Pew Research indicate that, since 2009, more Mexican immigrants have returned to Mexico from the United States than migrated here. The researchers point out that the number of immigrants with a high school education or less coming into the United States has largely plateaued, while the number of highly educated immigrants has continued to rise, as the chart below shows.

The paper acknowledges the role of other factors in lessening the flow of less-skilled immigrants into the United States, namely the tougher immigration enforcement that also occurred in the last few decades. The number of U.S. agents patrolling the border doubled between 2000 and 2010, and the United States devotes far more resources to controlling illegal immigration in the interior of the country as well.

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Yet the researchers argue that demographic factors are likely the most important — meaning that immigration trends may be largely beyond the control of the government. “Taking our results at face value, the analysis suggests that labor-supply shocks play a dominant role in driving low-skilled immigration flows in the United States,” they write.

They then turn to predictions. Using United Nations estimates for population growth in those countries, the researchers predict falling migration from all major Latin American destinations, with a particularly rapid drop-off in immigrants from Mexico in coming decades.

“Absent economic or political crises in the Western Hemisphere that reignite international migration, standard migration models predict that migration rates from major U.S. sending nations will drop sharply in coming decades,” they write.

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This trend could affect industries where low-skilled immigrants play a big role — like farming, restaurants and construction, where firms may end up having to pay higher wages or look more to automation.

If these estimates prove true, the United States may not need to spend heavily on a border wall to keep low-skilled immigrants out, the researchers say.

Instead, the bigger issue the government may need to address is the population of aging undocumented workers who could be left in the United States. Over the next decade and a half, the U.S. population of undocumented immigrants under 40 will shrink by 6 percent, while the population over 40 will expand 82 percent. Will these people go back to their home countries in search of cheap medical care, or end up in U.S. emergency rooms?

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The paper is not without criticism. Some economists point to the leveling off of low-skilled immigration into the United States around the time of the Great Recession as evidence that economic factors in the United States may have played a more decisive role than demographics did.

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If that’s true, immigration from Latin America might tick up again as the economy recovers. There are likely still strong economic incentives for people from poorer countries to migrate: The paper calculates that in 2000 a 28-to-32-year-old male with 9 to 11 years of education might earn $10,600 more in the United States than Mexico.

Others point out that, even if low-skilled immigrants from Latin America decline in the future, the United States has a seemingly infinite supply of low-skilled immigrants from elsewhere — including Asia, which is now the largest source of immigrants to the United States, and Africa, which has the youngest population in the world.