The key stylized facts of the housing market are positive serial correlation of price changes at one year frequencies and mean reversion over longer periods, strong persistence in construction, and highly volatile prices and construction levels within markets. We calibrate a dynamic model of housing in the spatial equilibrium tradition of Rosen and Roback to see whether such a model can generate these facts. With reasonable parameter values, this model readily explains the mean reversion of prices over five year periods, but cannot explain the observed positive serial correlation at higher frequencies. The model predicts the positive serial correlation of new construction that we see in the data and the volatility of both prices and quantities in the typical market, but not the volatility of the nation's more extreme markets. The strong serial correlation in annual house price changes and the high volatility of prices in coastal markets are the two biggest housing market puzzles. More research is needed to determine whether measurement error-related data smoothing or market inefficiency can best account for the persistence of high frequency price changes. The best rational explanations of the volatility in high cost markets are shocks to interest rates and unobserved income shocks.