Most dynamic stochastic general equilibrium (DSGE) models with a housing market do not explicitly include a rental market and assume a tight mapping between house prices and rents over the business cycle. However, rents are much smoother than house prices in the data. We match this feature of the data by adding both an owner‐occupied housing market and a rental market in a standard DSGE model. The intertemporal preference shock accounts for more than half of the variation in house prices and contributes to residential investment fluctuations through the liquidity constraint, and nominal rigidity in rental contracts captures the variation in the price‐rent ratio.