Empirical evidence suggests that local jurisdictions are internally more heterogeneous than standard sorting models predict. We develop a dynamic multi-region model, with fluctuating regional house prices, where an owner-occupying household’s location choice depends on its current wealth and its current ‘match’ and involves both consumption and investment considerations. The relative weights of the consumption and investment motives in the location choice determine the equilibrium pattern of residential sorting, with a strong investment (consumption) motive implying sorting according to match (wealth). The model predicts a negative relation between size of house price fluctuations and residential sorting in the match dimension. Also movers should be more sorted than stayers. These predictions are consistent with evidence from US metropolitan areas when income, age and education are used as proxies for the match.