Although building a wall on the Mexican border gets most of the headlines, U.S. Sen. Ted Cruz, R-Texas, says other steps also must be taken to keep illegal immigrants from settling in the United States.

"Forty percent of illegal immigration doesn’t come across the border; it’s people coming legally on visas and overstaying their visas," the presidential candidate said during a recent interview on "The John Fredericks Show," broadcast from Portsmouth.

Cruz pledged to develop a program to record and store biometric information on visas to help track the entry and departure of visitors to the United States. Biometrics refer to characteristics such as fingerprints, eye recognition and DNA.

We decided to examine Cruz’s statement that 40 percent of illegal immigrants are people who have overstayed their visas - a claim often cited by Republicans. Two of Cruz’s rivals for the GOP nomination, U.S. Sen. Marco Rubio of Florida and former Florida Gov. Jeb Bush , also have mentioned the statistic this year.

When we asked Cruz’s campaign for the source of the statistic, a spokesman referred us to PolitiFact Texas’ 2013 fact-check of a similar statement made by U.S. Rep. John Carter, R-Texas.

Carter’s statement was based on a 2006 report by the Pew Research Center that estimated "nearly half of all the unauthorized migrants now living in the United States entered the country legally through a port of entry such as an airport or a border crossing point where they were subject to inspection by immigration officials." While the source data gave an estimate that ranged from 33 percent to 50 percent, the report went middle-of-the-road and called it 45 percent.

Pew relied on a 1997 study by the Immigration and Naturalization Service . The INS report concluded that in 1996, 41 percent of illegal immigrants had entered the United States legally. The problem is that neither the INS nor its successor, the Department of Homeland Security, have provided updated statistics on overstayed visas since that aging study. Subsequent estimates have been based on taking that core 1996 data and adapting it to current trends.

In 2003, the INS reprocessed the data and estimated that 33 percent of the illegal immigrant population in the nation in 2000 had overstayed their visas. A 2004 report from the General Accounting Office , based on 2000 data, gave estimates on visa overstays ranging from 27 percent to 57 percent. The GAO cautioned that its methodology in reaching the figures was "complex, indirect and marked by weaknesses."

Robert Warren, a former INS demographer whose work was a part of that 1997 report, is among those who have published updated estimates based on the old data.

Warren, now a senior fellow at the nonpartisan Center for Migration Studies, theorized in a 2014 study that because it has gotten harder in recent years to enter the U.S. through its southern borders, the percentage of illegal immigrants overstaying their visas has increased and in 2012 may have been 58 percent.

But because there’s no new hard data, no one knows for sure. "They’re all ballpark estimates," said Marc Rosenblum, an analyst with the Migration Policy Institute.

Our ruling

Cruz said that 40 percent of illegal immigrants in the U.S. are "people coming legally on visas and overstaying their visas."

This widely cited statistic is based is an estimate based on research going back to the 1990s. The federal government hasn’t provided updated statistics on overstayed visas, and subsequent research has focused on adapting the old data to new trends. Estimates in those reports have ranged from 27 percent to 58 percent of illegal immigrants overstaying their visas.

So Cruz is using what research shows to be an acceptable middle figure. But he would be more accurate to refer to the 40 percent figure as an estimate rather than a fact.

We rate his statement Mostly True.