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FiveThirtyEight

In an article Wednesday, I wrote that despite the unfolding “unaccompanied minors” crisis on the Mexican border, the total population of undocumented immigrants has been more or less flat in recent years. That led several readers to ask: How do we know that?

It’s a reasonable question. For obvious reasons, there’s no official count of undocumented immigrants, and people who are here illegally are understandably reluctant to disclose their status to pollsters.

The numbers I used in Wednesday’s article came from the Pew Research Center, which estimates there were 11.7 million unauthorized immigrants in the U.S. in 2012. When it released that figure last fall, Pew also published an interview with senior demographer Jeffrey S. Passel explaining his approach; for a more detailed explanation of the center’s methodology, see Passel and colleague D’Vera Cohn’s 2008 paper.

Pew’s basic approach is to take the total number of immigrants in the U.S. and subtract all the people who are here legally; whoever’s left is here illegally.

That’s simple enough in theory. In practice, of course, it’s more difficult. Counting legal immigrants is straightforward enough: The Department of Homeland Security provides a count of legal permanent residents, and other agencies have data on refugees and people in the U.S. on temporary visas. Those numbers aren’t perfect — we don’t know exactly how many people have died or left the country — but they’re pretty good.

The hard part is estimating the total immigrant population. Pew uses two sources: The American Community Survey (ACS) and the Current Population Survey (CPS), both conducted by the Census Bureau. (Specifically, Pew uses the Annual Social and Economic Supplement to the CPS, which is conducted every March.) Both surveys aim to count all immigrants, regardless of their status; in fact, they don’t even ask people whether they are here legally. But that doesn’t mean we can take their figures at face value.

The first problem is simply sampling error. The CPS is large (about 80,000 households in the March supplement), and the ACS is huge (about 3 million people). But even surveys that big have significant margins of error when measuring small subgroups. The errors are even bigger when trying to measure change from one year to the next.

The even bigger issue is that some groups, including immigrants, are hard to count for various reasons — they’re less likely to respond to surveys, less likely to speak English, more likely to have informal or temporary living arrangements, among others. Counting undocumented immigrants is particularly difficult, because many fear census takers will report them to the government (they won’t).

Pew tries to account for this so-called undercount by adjusting its figures upward. In 2012, Pew estimates the official data undercounts the overall immigrant population by 2 to 3 percent, and the unauthorized population by 5 to 7 percent. The adjustments used to be bigger: In the 1990s, before the Census Bureau took steps to reach more Mexican immigrants, in particular, Pew estimates the official data undercounted the unauthorized population by 10 to 20 percent.

Still, Pew’s numbers have significant margins of error. The 90 percent confidence interval for Pew’s 2012 count of unauthorized immigrants runs from 11.1 million to 12.2 million, meaning Pew can’t say with confidence whether the number has been rising or falling in recent years. The Department of Homeland Security, using a similar methodology to Pew’s, estimates there were 11.4 million unauthorized immigrants in the U.S. in 2012, solidly within Pew’s range.

Other groups, mostly those favoring tighter enforcement of immigration laws, have put the figure much higher – 20 million and up. But even some groups critical of U.S. immigration policy come up with estimates that are generally consistent with Pew’s.

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