The high mortgage rates that have prevented many people from buying homes may not fall quickly, even if President Donald Trump succeeds in appointing a new Federal Reserve chairman who shares his desire to slash the central bank’s target rate.

Trump has reportedly narrowed down the list of possible candidates for Fed Chairman Jerome Powell’s replacement to one person and has hinted that it might be National Economic Council Director Kevin Hassett. Hassett is seen as a candidate who would follow through on Trump’s desire for a lower Fed rate target, which the president has said would help spur homebuying and boost the overall economy.