Discrete Housing Choices, Discontinuous Asset Allocations and Consumption

This dissertation studies households' housing choices in an incomplete market and explores the implications on the dynamic optimal housing allocations over time and the intertemporal consumption decisions. The first chapter studies the effects of increasing home values on consumption through discrete housing transactions. I utilize the dynamic consumption model including illiquid assets and show the housing wealth effect is positive because of both changing probabilities of housing transactions and the actual discrete changes in assets from down-payment constraints, trade frictions and changes in precautionary savings. Higher housing prices raise the probabilities of home purchases and upgrades while decreasing the probabilities of home sales and downgrades. This leads to positive consumption growth because households reduce current consumption and save more for payments of future transactions. I use households' survey data to test the predicted consumption growth conditional on housing choices in both panel and multinomial selection regressions. Controlling for endogenous housing decisions and households' characteristics, the estimations suggest the joint effects of housing prices on illiquid assets and consumption generate the comovement, and there is little evidence of a housing wealth effect for households who do not trade or who have very low probabilities to trade even though their home values also rise with aggregate prices. The second chapter studies the optimal discontinuous evolutions for housing and liquid assets. Consumption-maximizing consumers choose housing wealth to have the ratios of home value over liquid wealth stay within an optimal range, similar to the optimal stopping behaviors for durable goods. The thresholds for the optimal range are endogenously determined by the aggregate economy. Households make discrete changes to the optimal ratios once the boundaries of the optimal region are reached, which leads to discontinuous changes to households' portfolios. I empirically identify the thresholds and estimate both the jumps in the likelihoods of changing housing assets and the sizes of kinks in the optimal ratios at the thresholds. I find that: (1) the distances between the thresholds and current optimal ratios are indicative of expected future housing changes; (2) the likelihoods of discrete housing decisions are affected by not only the thresholds but also other households' covariates; and (3) the sizes of the kinks in optimal ratios only depend on the lagged values given a certain set of thresholds. The last chapter proposes a theoretical model to study households' dynamic discrete and continuous choices for housing assets over the life cycle. Consumers choose between liquid wealth and housing wealth for the optimal savings allocation to maximize and smooth total consumption in the presence of trading frictions. The model explains the increases and declines in the buying and selling probabilities over time, while considering the unobserved housing services provided by housing assets, which are modeled as complements to nondurable goods in the households' budget constraints. Through simulations, I show higher housing returns increase lifetime wealth, consumption and housing demand for larger houses and lower borrowing constraints encourage earlier homeownership with smaller houses, lower liquid savings and higher probabilities of home sales for liquidity constrained households.