A Spatiotemporal Equilibrium Model of Migration and Housing Interlinkages

This paper develops and solves a spatiotemporal equilibrium model in which regional wages and house prices are determined jointly with location-to-location migration flows. The agent's optimal location choice and the resultant migration process is shown to be Markovian with the transition probabilities across all location pairs given as non-linear functions of wage and housing cost differentials, endogenously responding to migration flows. The model is calibrated on a panel of states in the U.S. mainland, and is shown to fit the data well. It is then used to analyze the size and speed of spatial spill-over effects by computing spatiotemporal impulse responses of positive productivity and land-supply shocks to California, as an example. It is shown that such a positive productivity shock raises local wages and induces net migration inflows from other states to California, and reduces population and house prices in other U.S. states. Not surprisingly, the responses of population and house prices tend to be stronger and quicker for the nearby states. The responses of U.S. states to a positive land-supply shock in California also have qualitatively the same spatiotemporal patterns. Similar results are obtained for other major U.S. states.