A Model of Life-Cycle Housing Choices with Uninsurable Labor Income and House Price Risks

In this paper, we study a household’s optimal life-cycle housing choices by calibrating a model with uninsurable labor income and house price risks. In our setup, the household not only decides between renting and owning a house, but also chooses the size of its house. Borrowing is allowed but only through a fixed-rate mortgage. Adjusting the size of the existing house or mortgage incurs transaction costs. Our policy functions suggest that the household purchases a house when its wealth on hand is high relative to its permanent labor income. A homeowner who experiences a negative labor income shock may choose to convert illiquid home equity to liquid asset to finance non-housing consumption in the absence of lower borrowing rates. In keeping with stylized empirical facts, in our simulation homeownership rates and house values exhibit hump-shaped life-cycle patterns, while the holding of illiquid home equity exhibits a U-shape over a household’s age. Mortgage refinancing activities demonstrate a bi-modal pattern ― young homeowners refinance to ease liquidity concerns, while old homeowners refinance to defer house selling expenses and avoid higher renting costs. Comparative static analysis further reveals the importance of labor income and house price risks in housing decisions. In comparison to the benchmark case, a higher transitory income risk delays households’ home purchases, and leads to frequent refinancing activities among young, liquidity-constrained homeowners. By contrast, a higher permanent income risk induces households to save more. Although more of the savings are in liquid form, households also purchase their houses earlier, a result of households’ portfolio decision. Similar to the temporary labor income risk, a higher house price risk delays homeownership and increases the frequency of costly mortgage refinancing by young households who try gain access to illiquid home equity.