Turns out Vance is full of shit. Vance said, “which does [emphasis added] drive up costs”. The quote he provided says, “There is a risk that strong consumer demand for services, increased immigration, and continued labor market tightness could lead to persistently high core services inflation. Given the current low inventory of affordable housing, the inflow of new immigrants to some geographic areas could result in upward pressure on rents, as additional housing supply may take time to materialize.” It’s clear from the wording in the quote that these pressures have not yet resulted in the higher prices, and that it’s a potential factor at some point in the future, rather than a current pressure.

Vance is, at best, being misleading.