We describe a simple model of the demand for housing and show 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. A calibrated version of the model has only limited success in accounting for the increased rate of house price appreciation since the mid-1990s. We then extend the model to include a collateral constrained consumer. We show that the impact of collateral constraints is limited. Collateral constraints may affect the level of the housing price path, but they do not affect the growth rate of housing prices.

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