Can higher federal funds rates control mortgage lending during periods of high inflation and high house prices?

The U.S. is facing higher inflation since December 2020 along with higher house prices. After a sharp increase, house prices have started to decline very recently even more drastically – reminding us of the global financial crisis 2007–08. Rather late, from December 2021 onwards, the Fed started to increase the Fed funds rate. However, it is unclear whether the Fed funds rate can control bank lending activities – especially, mortgage lending. Surprisingly, our results suggest that the Fed funds rate fails to control mortgage lending during high inflation and high house prices in the absence of bank reserve requirements.