Notes on collateral constraints in a simple model of housing

These notes provide the derivations of results stated without proof in Hornstein (2009). For a simple model of the demand for housing, it is shown that on a balanced growth path, the rate at which the relative price of housing changes over time is determined by the relative productivity growth rates of the housing sector and the rest of the economy. The model is then modified to include a collateral constrained consumer. We show that collateral constraints may affect the level of the housing price path, but they do not affect the growth rate of housing prices.