However, the difference between the two neighbors is that the smart neighbor actually uses the expected inflation rate to compute the real cost of his mortgage.

http://web.stanford.edu/~piazzesi/illusion.pdf

For example, consider an illusionary investor who compares the utility he obtains from buying a home to the nominal cost of borrowing. This investor agrees with his smart neighbor about expected inflation. However, the difference between the two neighbors is that the smart neighbor actually uses the expected inflation rate to compute the real cost of his mortgage.