Empirical evidence indicates 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 strength of the consumption motive and the investment motive in the location choice determines the equilibrium pattern of residential sorting, with a strong investment (consumption) motive implying sorting according to the match (wealth). The model predicts a negative relation between the 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.