Several institutional frameworks were enacted by jurisdictions in Japan, which were intended to provide some type of economic aid (compensation) to households that are deprived of their dwellings by natural disaster and intend to reconstruct and/or rent a house in the damaged region. In this work a dynamic model is formulated to investigate house-owners and tenants' housing choice after their dwellings are destroyed by an earthquake as well as owners' insurance behavior before the earthquake. The study analyzes the effects of the subsidy for reconstruction and/or lease (compensation) on the housing market in the damaged region. It is found that the compensation motivates damaged households to reconstruct and/or rent a house in the damaged region and consequently prevents households from flowing out of its region, while insurance has neutral effect on housing choice.