The results, published in PLOS ONE, surprised the Yale researchers themselves. Admitting they expected the real number to be well below 11.3 million, the researchers began the project with the expectation that at completion they would be able to break the news that there are far less illegal aliens in the U.S. than people think.
But they couldn’t have been more wrong.
“Our original idea was just to do a sanity check on the existing number,” says Edward Kaplan, the William N. and Marie A. Beach Professor of Operations Research at the Yale School of Management. “Instead of a number which was smaller, we got a number that was 50% higher. That caused us to scratch our heads.”
Jonathan Feinstein, the John G. Searle Professor of Economics and Management at Yale SOM, adds, “There’s a number that everybody quotes, but when you actually dig down and say, ‘What is it based on?’ You find it’s based on one very specific survey and possibly an approach that has some difficulties. So we went in and just took a very different approach.”
Yale Insights reports: 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. That made the researchers curious—could they reproduce the number using a different methodology?
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.
Notably, the upper bound of the traditional survey approach, which also produces a range, doesn’t overlap with the lower bound of the new modeling method. “There really is some open water between these estimates,” Kaplan says. He believes that means the differences between the approaches can’t be explained by sampling variability or annual fluctuations.
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.
“The trajectory is the same. We see the same patterns happening, but they’re just understating the actual number of people who have made it here,” says Fazel‐Zarandi. In his view, that suggests the survey method doesn’t effectively reach a group with incentives to stay undetected. “They are capturing part of this population, but not the whole population.”
While the findings are startling, they aren’t describing a new situation. “We wouldn’t want people to walk away from this research thinking that suddenly there’s a large influx happening now,” says Feinstein. “It’s really something that happened in the past and maybe was not properly counted or documented.”
Kaplan adds, “What we’re saying is the number has been higher all along.”
While immigration is a hot button topic, the researchers are adamant that their aim is to provide information. “Of course, our findings will get pulled and tugged in many ways, but our purpose is just to provide better information,” Feinstein says.
“This paper is not oriented towards politics or policy. I want to be very clear: this paper is about coming up with a better estimate of an important number.”