Posted on September 21, 2018

Yale Study Finds Twice as Many Undocumented Immigrants as Previous Estimates

Mohammad Fazel-Zarandi, Jonathan S. Feinstein, Edward H. Kaplan, Yale Insights, September 21, 2018

Generally accepted estimates put the population of undocumented immigrants in the United States at approximately 11.3 million. A new study, using mathematical modeling on a range of demographic and immigration operations data, suggests that the actual undocumented immigrant population may be more than 22 million.

Immigration is the focus of fierce political and policy debate in the United States. Among the most contentious issues is how the country should address undocumented immigrants. Like a tornado that won’t dissipate, arguments have spun around and around for years. At the center lies a fairly stable and largely unquestioned number: 11.3 million undocumented immigrants residing in the U.S. But a paper by three Yale-affiliated researchers suggests all the perceptions and arguments based on that number may have a faulty foundation; the actual population of undocumented immigrants residing in the country is much larger than that, perhaps twice as high, and has been underestimated for decades.

Using mathematical modeling on a range of demographic and immigration operations data, the researchers estimate there are 22.1 million undocumented immigrants in the United States. Even using parameters intentionally aimed at producing an extremely conservative estimate, they found a population of 16.7 million undocumented immigrants.

The results, published in PLOS ONE, surprised the authors themselves. They started with the extremely conservative model and expected the results to be well below 11.3 million.


The 11.3 million number is extrapolated from the Census Bureau’s annual American Community Survey. “It’s been the only method used for the last three decades,” says Mohammad Fazel‐Zarandi, a senior lecturer at the MIT Sloan School of Management and formerly a postdoctoral associate and lecturer in operations at the Yale School of Management. {snip}

The approach in the new research was based on operational data, such as deportations and visa overstays, and demographic data, including death rates and immigration rates. “We combined these data using a demographic model that follows a very simple logic,” Kaplan says. “The population today is equal to the initial population plus everyone who came in minus everyone who went out. It’s that simple.”

While the logic is simple — tally the inflows and outflows over time — actually gathering, assessing, and inserting the data appropriately into a mathematical model isn’t at all simple. Because there is significant uncertainty, the results are presented as a range. After running 1,000,000 simulations of the model, the researchers’ 95% probability range is 16 million to 29 million, with 22.1 million as the mean.


There are key areas of agreement between this paper and the existing survey numbers. Both methods found that the greatest growth of the undocumented population happened in the 1990s and early 2000s. Both found that the population size has been relatively stable since 2008.


Kaplan and Feinstein have worked on this type of problem for many years. “The analysis we’ve done can be thought of as estimating the size of a hidden population,” Kaplan says. “People who are undocumented immigrants are not walking around with labels on their foreheads. Neither are populations of homeless people, neither are populations of drug users, and neither are populations of terrorists. Yet for policy, it is very important to know the size of these hidden populations because that sets the scale of the problem in each of these different policy areas.”


In fact, some of the relevant data sets have only recently become available, so this approach might not have been possible for this particular puzzle, even a few years ago. Fazel‐Zarandi notes that 2015 was the first time that data on visa overstays was collected by the Department of Homeland Security.

Bringing all the different sources of data together is arduous. “There’s a lot hidden under the hood, so to speak,” Feinstein says. The key components — inflows and outflows — are each made of numerous subcomponents. Each subcomponent must be aggregated from different sources, evaluated for its specific level of certainty, then incorporated into the mathematical model in a consistent way.


He continues, “How many people are actually being apprehended at the border? That’s hard data. That’s reported each year.” From there it’s possible to reverse engineer an estimate of how many people must have tried to cross the border. “This kind of ‘backwards logic’ is common in models of this form.” {snip}


Kaplan adds, “What we’re saying is the number has been higher all along.”


How might this research inform the debate around immigration? Some might argue that the presence of twice as many undocumented immigrants justifies tougher immigration enforcement.

“One of the most common arguments in favor of a tougher immigration policy is that undocumented immigrants are coming with a lot of criminality,” Kaplan notes. But paradoxically, the new findings may undercut that argument. He points out that previous studies, based on the widely accepted total of 11.3 million undocumented immigrants, found that the rate of serious crimes committed by these immigrants is lower than for U.S. citizens. The new findings suggest that the rate is even lower than previously believed: “You have the same number of crimes but now spread over twice as many people as was believed before, which right away means that the crime rate among undocumented immigrants is essentially half whatever was previously believed.”


[Editor’s Note: The authors’ study, “The number of undocumented immigrants in the United States: Estimates based on demographic modeling with data from 1990 to 2016,” is available (with charts and tables) as a PDF and as an HTML document here.]