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To hear Donald Trump tell it, waves of undocumented immigrants are entering the U.S. each year, smuggling in drugs, committing acts of rape and murder, and stealing Americans’ jobs. As I’ve written repeatedly, the numbers don’t back that up: Immigrants have lower rates of violent crime than native-born Americans, and the number of people entering the country illegally has dropped sharply in recent years. (The total population of undocumented immigrants has been pretty much flat since 2008.)

But what about Trump’s claim about immigrants taking jobs? A new report from the Pew Research Center suggests that isn’t true either. Using data from the American Community Survey, Pew found that the number of undocumented immigrants in the U.S. workforce has held steady at about 8 million since the recession ended in 2009. As a share of the workforce, the undocumented population has actually shrunk slightly, to 5 percent from 5.4 percent in 2007. (See our story from 2014 for more on how researchers compile these figures.)

But there’s a reason that Trump’s rhetoric has found an audience. The undocumented workforce may no longer be growing, but it is still high by historical standards. And some U.S. workers, particularly those without a college degree, really do face significant competition from undocumented labor. Undocumented immigrants make up 17 percent of agricultural workers and 13 percent of construction workers. Also, illegal immigration doesn’t hit all parts of the country evenly, as the map below makes clear. As I wrote on Monday, immigration is a key source of economic strength for the U.S., but that doesn’t mean it benefits everyone equally.

Further reading

Immigration Is Changing Much More Than The Immigration Debate

The Consequences: A Look Behind The Claims On Immigration

Undocumented Immigrants Aren’t Who You Think They Are

Immigration Isn’t Driving Hispanic Population Growth