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We show that dynamic stochastic general equilibrium (DSGE) models with housing and collateralized borrowing predict a fall in house prices following positive government spending shocks. By contrast, we show that house prices in the United States rise persistently after identified positive government spending shocks. We clarify that the incorrect house price response is due to a general property of DSGE models—approximately constant shadow value of housing—and that modifying preferences and production structure cannot help in obtaining the correct house price response. Properly accounting for the empirical evidence on government spending shocks and house prices using a DSGE model therefore remains a significant challenge.