Housing Dynamics: Theory Behind Empirics

We extend the recent macro housing literature by including endogenous internal urban structure to better fit with important stylized facts. We construct a two-sector optimal growth model of housing where consumable housing is produced by land and housing structures, where within-city locational choice is explicitly modeled. Housing services derive positive utility but are decayed away from the city center. Our model enables a full characterization of the dynamic paths of housing and housing and land prices. The model is calibrated to fit part of the stylized facts: faster growth of housing structures than housing, faster growth of land prices than housing prices, and downward housing price and land rent gradients within a city. The calibrated model can then be used to predict the remaining untargeted part of stylized facts: a locationally steeper land rent gradient than the housing price gradient, relatively flatter housing quantity and price gradients in larger cities with flatter population gradients and moderate rise in the housing expenditure share. The calibrated model can further yield additional insights on housing dynamics and spatial distribution. The main punchline is: nonhomotheticities in housing preference and housing production are crucial for realistic model predictions particularly to account for internal urban features.