Housing affordability has become the main policy challenge for most large cities
in the world. Key policy levers are zoning, rent control, housing vouchers, and tax
credits. We build a new dynamic stochastic spatial equilibrium model to evaluate the
effect of these policies on house prices, rents, residential construction, labor supply,
output, income and wealth inequality, as well as the location decision of households
within the city. The analysis incorporates risk, wealth effects, and dynamic spatial
equilibrium. We calibrate the model to the New York MSA, incorporating current
zoning and rent control policies. Our model suggests sizable welfare gains from relaxing
zoning regulations in the city center, as well as from expanding rent control
and housing voucher programs. Housing affordability policies have a hitherto underappreciated
insurance value which needs to be traded off against potential efficiency
losses. The calibrated model implies gains in social welfare from reducing housing
inequality.