A Spatiotemporal Equilibrium Model of Migration and Housing Interlinkages

Abstract

This paper develops and solves a spatiotemporal equilibrium model in which regional wages and house prices are jointly determined with location-to-location migration flows. The agent’s optimal location choice and the resultant migration process are 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 can be used for the analysis of spatial distribution of population, income, and house prices, as well as for spatiotemporal impulse response analysis. The model is estimated on a panel of 48 mainland U.S. states and the District of Columbia using the training sample (1976-1999), and shown to fit the data well over the evaluation sample (2000-2014). The estimated model 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, Texas, and Florida. Our simulation results show that states with a lower level of land-use regulation can benefit more from positive state-specific productivity shocks; and positive land-supply shocks are much more effective in states, such as California, that are subject to more stringent land-use regulations.