House price changes are strongly correlated in the data following monetary policy shocks. I build a New Keynesian model of the housing market where households choose the optimal amount of housing and mortgages. To accommodate realistic house price movements, I extend the housing market structure to include search frictions and house price rigidity so that the housing market clears through the relative fraction of successful buyers and sellers each period. I show that the house price momentum does not translate into slow movements of output and therefore it cannot explain the high degree of persistence found in the data following a contractionary monetary shock. I also highlight important redistributional effects between savers and borrowers in the economy. In particular, house price momentum coupled with the loan-to-value constraint forces the indebted households to cut their consumption for several quarters following a contractionary monetary shock.