Estimation of a spatial simultaneous equation model of population migration and housing price dynamics

Identifying the local interactions between housing prices and population migration is complicated by their simultaneous and spatially interdependent relationship. Higher housing prices may repel households and push them into neighboring areas, suggesting that separately identifying interactions within versus across local neighborhoods is important. Aggregate data and standard econometric models are unable to address the multiple identification problems that may arise from the simultaneity, spatial interaction, and unobserved spatial autocorrelation. Such problems can generate biased estimates that run counter to economic theory. Using Michigan census tract-level data, we estimate a spatial simultaneous equations model that jointly considers population change and housing values, while also explicitly modeling interactions within neighborhoods, spatial interactions across neighborhoods, and controlling for unobserved spatial correlations. After controlling for simultaneity and spatial autocorrelation, the results show that neighborhoods are likely to experience an increase in their housing values if they gain population and they are more likely to lose population if they experience an increase in housing values. Our results are consistent with theory and underscore the importance of accounting for spatial interdependencies between population change and housing values.