A Matching Model of the Housing Market: Searching for a Motivated Partner

We construct a bilateral search model of the housing market in which agents differ in their flow rewards while searching. Buyers and sellers enter the market with high flow rewards, but move at a Poisson rate to a state with low flow rewards if they do not transact in the meantime. We characterize the equilibrium steady state matching pattern and compare this to the constrained efficient matching pattern. We also characterize the joint distribution of price and time to sale (for sellers). The expected price conditional on time to sale falls with time spent on the market, while the conditional variance of price first rises and then falls with time on the market