This dissertation studies households' housing decision in the presence of income risks, and its implication on within-cohort income/consumption inequality and the nature of income risks facing households. It is composed of three chapters. The first chapter presents evidence from Panel Study of Income Dynamics (PSID) and Consumer Expenditure Survey (PSID) that housing consumption and housing investment are negatively affected by income risks. Within a household portfolio choice model, the negative effect can be attributed to the illiquidity of housing investment and the positive correlation between house price and income. The second chapter provides empirical evidence that the secular rise of income and consumption inequalities in the United States is age-dependent. It is more significant among younger households. With this feature, biasedness arises from the traditional methodology of decomposing inequality into age effect, year effect and cohort effect. A simple but effective remedy for the problem is proposed. The third chapter of the dissertation studies the age-profile of within-cohort income/consumption inequality, using the methodology proposed in the second chapter. It documents the age-profile of housing consumption inequality which is almost flat. This stands in contrast to the well-documented fact that within-cohort nonhousing consumption inequality rises with age, which has been argued to be evidence for persistent, uninsurable income shocks to households. This argument is challenged by the finding that housing consumption inequality has a flat age-profile. Within the framework of standard lifecycle model, the coexistence of rising nonhousing consumption inequality and flat housing consumption inequality constitutes a puzzle. A potential resolution lies in the negative effect of income uncertainty on housing decision which diminishes with age, as shown in the first chapter of the dissertation. / text