This paper presents a simple model of trade in the housing market. The crucial feature is that a minimum downpayment is required for the purchase of a new home. The model has direct implications for the volatility of house prices, as well as for the correlation between prices and trading volume. The model can also be extended to address the correlation between prices and time-to-sale, as well as certain aspects of the cyclical behavior of housing starts.
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Jeremy C. Stein (1995) studied this question.