Fox & Friends ran a segment this morning touting a study that claims a border wall with Mexico could pay for itself by reducing crime and the flow of drugs into America. President Donald Trump saw fit to amplify the report:

"According to the Center for Immigration Studies, the $18 billion wall will pay for itself by curbing the importation of crime, drugs and illegal immigrants who tend to go on the federal dole…" https://t.co/NdLC6jZwWE — Donald J. Trump (@realDonaldTrump) March 13, 2018

Trump is wrong, because Fox & Friends is wrong, because the Center for Immigration Studies—an anti-immigration think tank that has been pushing the wall-will-pay-for-itself narrative pretty much since Trump took office—is wrong.

And the center is wrong mostly because it failed to account for the true cost of the border wall. The $18 billion figure relies on "unrealistically cheap construction costs and outrageous estimates of the number of illegal immigrants that it will deter," wrote Alex Nowrasteh and David Bier, a pair of immigration policy experts at the Cato Institute, in an analysis of the center's border wall projections last year.

As Nowrasteh and Biers point out, simply building the wall is likely to cost more than $18 billion. The Department of Homeland Security estimates that each mile of the border wall will cost about $17 million—including the cost of buying or seizing land along the border from private owners—and therefore a 1,900-mile wall would end up costing taxpayers around $28 billion.

And after you build a wall, you have to maintain it. Those maintenance costs will leave taxpayers with an additional $48.3 billion tab for the wall's first decade alone.

That's not all. The wall won't catch illegal immigrants by itself, and the Trump administration knows this. "If you build a wall, you would still have to back that wall up with patrolling by human beings," then–Secretary of Homeland Security John Kelly told Congress less than a week after Trump took office. In the executive order that authorized the construction of the border wall, Trump called for hiring 5,000 additional Border Patrol agents.

Each of those 5,000 agents will cost taxpayers more than $100,000 in annual pay and benefits, amounting to a decade-long personnel cost of over $6 billion. And that's still not a full summation of the costs involved, since it does not include the equipment border agents will use to apprehend immigrants, or the legal costs associated with convicting, jailing, or deporting those border-crossers.

Will the wall pay for itself? The Center for Immigration Studies claims that $18 billion price tag can be met by preventing 200,000 future crossings, a number that Steven Camarota, director of research at the center, has said represents only a modest reduction in illegal immigration.

According to the center, each illegal border-crosser represents a $74,000 drain on the American economy. Multiply that figure by 200,000 fewer border-crossers, and you'll reach the study's estimate that the wall will save about $18 billion. But that fails to account for the age and education level of the average border-crosser, argue Nowrasteh and Bier. They say the average illegal immigrant costs about $43,000 in public services, about half of what the center estimates.

And that doesn't account for economic growth that would be lost by reducing immigration as a whole. This is no small matter; immigrants, even illegal ones, boost wages, pay taxes, and increase long-term economic growth.

But let's set that aside, and accept for the sake of argument that each illegal immigrant imposes a net cost on the U.S. economy. In that case, after we adjust to a more realistic estimate of the wall's costs, it would still be theoretically possible for the wall to pay for itself. But it would be a lot harder.

"The wall would have to deter just over 1 million illegal immigrants who would have otherwise entered the United States," Nowrasteh and Bier conclude. In other words, it would have to stop about 60 percent of all illegal immigration into the country.

Can it do that? Not likely.

For starters, about a third of all illegal immigrants are people who came to the United States legally and simply overstayed their visa. A border wall would do nothing to stop them.

As for the rest, it might be only moderately useful. Take for example a 14-mile stretch of wall near San Diego that "did not have a discernible impact on the influx of unauthorized aliens coming across the border in San Diego" when it was built in the early 1990s, according to the Congressional Research Service. As Reason has previously detailed, efforts to make the San Diego border wall more robust increased the cost of the project but didn't do much to stop the flow of illegal immigrants.

So even if you accept the center's premises about the costs of immigration, the wall couldn't pay for itself unless it stops five times as many illegal immigrants as even staunchly pro-wall activists like Camarota say it will. That's completely unrealistic.