The Home Selling Problem: Theory and Evidence

Abstract

This paper formulates and solves the problem of a homeowner who wants to sell her house for the maximum possible price net of transactions costs (including real estate commissions). The optimal selling strategy consists of an initial list price with subsequent weekly decisions on how much to adjust the list price until the home is sold or withdrawn from the market. The solution also yields a sequence of reservation prices that determine whether the homeowner should accept offers from potential buyers who arrive stochastically over time with an expected arrival rate that is a decreasing function of the list price. We estimate the model using a rich data set of complete transaction histories for 780 residential properties in England introduced by Merlo and Ortalo-Magné (2004). For each home in the sample, the data include all listing price changes and all offers made on the home between initial listing and the final sale agreement. The estimated model fits observed list price dynamics and other key features of the data well. In particular, we show that a very small “menu cost” of changing the listing price (estimated to equal 10 thousandths of 1% of the house value, or approximately £10 for a home worth £100,000) is sufficient to explain the high degree of “stickiness” of listing prices observed in the data.

Keywords: housing, bargaining, sticky prices, optimal selling strategy, dynamic programming

JEL Classification: H5