There are numerous ways to consider how many immigrants a country takes in. First, we have to decide whether we are considering immigrant inflows bounded by a time period or immigrants in totality. Immigrant inflows refer to how many immigrants move to a country in a given time frame.
This 2012 Forbes article looks at the inflow of immigrants by year. In terms of the annual inflow (how many immigrants come to a country each year) the US is #1 with about a million immigrants moving to the US each year.
However, the article points out that given the size of the US, it's not all that surprising that more immigrants should come to the US each year. If we consider annual immigrant inflows relative to the size of the population, the US ranks #22. That same million annual immigrants entering the US account for a mere 0.4% of the population.
The Forbes article goes on to consider the totality of immigrants (foreign-born) in the country relative to the size of the country. Using this metric, the US comes in #12 with 12.1% of the country made up of immigrants (remember that the Forbes article is from 2012).
Given the last two stats, it may seem that the US's cherished idea of itself as an immigrant-receiving country is not nearly as fact-based as one would think. However, there are still additional ways to consider immigrant statistics. For example, we could also consider the total number of international immigrants worldwide and ask what percentage of this group reside in the US. Using this metric, the US once again moves to the top according to the UN Population Division's Trends in International Migrant Stock: The 2015 Revision report. The number of international migrants reached 244 million worldwide and about 47 million reside in the US or about 19% of the world's international migrants; no other country has a larger percentage of the world's foreign-born population. Meanwhile, that 47 million makes up 14.49% of the US population (again, placing the US in the middle of the pack relative to the size of the country).
Which ones should we focus on? Of course, they're all important and give us different data and ways to think about immigration flows and stocks. Yes, the percentage of immigrants relative to the population means that the US is not at the top, but it also seems unrealistic to think that the US should take in a proportion similar to Luxembourg's 2.9%; Luxembourg had a population of 590,667 people in 2017; 2.9% of 590,667 is 17,129 people. In contrast, the US population in 2017 was 325.17 million, 2.9% of that number would be 9.4 million people! Similarly, it would be unrealistic to imagine any country taking in as many immigrants as the US given that some countries may be quite small. In the example of Luxembourg, the US' 1 million immigrants per year is larger than the entire population of Luxembourg!
One way of looking at these numbers is to go back to the UN Population Division report whereby an estimated 47 million of 244 million immigrants live in the US. It seems foolish to condemn the US for not taking in more international immigrants when it already has close to 20% of world's immigrant population.
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Referenced and for further reading:
MPI: Immigrant and Emigrant Populations by by Country interactive map
Forbes "Is the U.S. the most immigrant friendly country in the world?"
The Economist: "Border follies: Liberalising migration could deliver a huge boost to global output"
New Republic: "All the Immigrants in the World, in One Addictive Interactive Map" (contains many great graphics)
The Telegraph: "Mapped: Which country has the most immigrants?"
UN Population Division: Trends in International Migrant Stock: The 2015 Revision report
UN Population Division:Trends in International Migrant Stock: The 2015 Revision highlights
Pew: "Chapter 2: Immigration’s Impact on Past and Future U.S. Population Change"