Republican vice presidential nominee Sen. JD Vance, R-Ohio, followed through on his promise to cite the source of a claim he made about immigration driving up U.S. housing costs during the CBS News Vice Presidential Debate on Tuesday night.

In the showdown with fellow vice presidential hopeful Minnesota Gov. Tim Walz, Vance blamed Vice President Kamala Harris' border policies for allowing "25 million illegal aliens" into the U.S. during her tenure in the Biden-Harris administration, saying the surge of migrants has contributed to higher housing prices.

"Competing with Americans for scarce homes is one of the most significant drivers of home prices in the country," Vance said. "It's why we have massive increases in home prices that have happened right alongside massive increases in illegal aliens, alien populations under Kamala Harris' leadership."

A moderator then asked Vance to cite the source of his claim, saying, "Senator, on that point, I'd like for you to clarify there are many contributing factors to high housing costs. What evidence do you have that migrants are part of this problem?"

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"Well, there's a Federal Reserve study that we're happy to share after the debate," Vance said. "We'll put it up on social media, actually, that really drills down on the connection between increased levels of migration, especially illegal immigration and higher housing prices."

Following the debate, Vance posted on X, "As promised earlier tonight, here is Michelle Bowman of the Federal Reserve Board of Governors: ‘Given the current low inventory of affordable housing, the inflow of new immigrants to some geographic areas could result in upward pressure on rents.’"

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Bowman's quote was from a speech the Fed governor made on May 3.

Vance also pointed to two studies supporting his claims. The first was from the Journal of Housing Economics from 2017, which found that "Immigration inflows into a particular Metropolitan statistical area (MSA) is associated with increases in rents and with house prices in that MSA while also seeming to drive up rents and prices in neighboring MSAs."

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The second study Vance cited was a July report from the Congressional Budget Office, which said that the "research literature has generally found that increases in immigration raise state and local governments’ spending — particularly on education, health care, and housing — more than their revenues."