The model also predicts a nonmonotonic relationship between the price-to-rent ratio on housing and nominal interest rates -- housing booms occur both when the nominal rate is especially low and when it is especially high.

http://web.stanford.edu/~piazzesi/illusion.pdf?hc_location=ufi

This paper considers asset pricing in a general equilibrium model in which some, but not all, agents suffer from inflation illusion. Illusionary investors mistake changes in nominal interest rates for changes in real rates, while smart investors understand the Fisher equation. The presence of smart investors ensures that the equilibrium nominal interest rate moves with expected inflation. The model also predicts a nonmonotonic relationship between the price-to-rent ratio on housing and nominal interest rates -- housing booms occur both when the nominal rate is especially low and when it is especially high.