This Ph.D. thesis deals with questions related to the housing market, and answers the questions: "Does it matter if housing markets are underpriced?" and "How do the legal system and the loan contract affect those who default on their mortgage payments?

"When selling a home, a popular marketing strategy is to set the list price far below market value. The idea is that a low list price will attract loads of buyers, who will push up the sale price. This thesis finds that a voluntary reform can reduce underpricing in the short run. Further, underpriced housing markets do indeed require more attention from potential buyers during all stages — online, at open houses, and during the bidding. This extra search effort is costly to society. However, underpricing is found not to affect the sale price, the time to sell, who the buyers are, or how hard the real estate agent works.

The household's choice to default on a mortgage depends on the cost of the default (the legal system) and the mortgage contract. By studying a heterogeneous agent consumption/savings lifecycle model, this thesis finds that households prefer "lender friendly" laws that are costly for the homeowners upon default. This is because costly defaults yield fewer defaulters and thus lower interest rates, and thus are cheaper for non-defaulters. Households always prefer non-amortizing mortgages except when defaults do not have any cost associated with them, and they prefer adjustable rates over fixed rates. The benefits of costly defaults are particularly large for non-amortizing mortgages.

The thesis concludes with the development of a new mathematical method to solve a particular class of dynamic programming problems, using stochastic simulated grids and nearest-neighbour interpolation.​

We characterize the condition under which mortgage defaults occur and the welfare consequences of recourse versus non-recourse under different types of mortgage contracts. We build a model where household endogenously chooses to default on their mortgage and where bank endogenously set the risk premium tailored to the kind of mortgage contract and the current exemption level. We find that even moderate recourse, i.e. some garnishment of wages and assets upon default, provides a potent means for discouraging defaults. Furthermore, we find that households prefer strong recourse to weak recourse, as it implies a reduction of the risk premium. Under non-recourse, households prefer ARMs over IOs and FRMs, while under moderate recourse they prefer IOs over ARMs and FRMs. Our analysis suggests that the moral hazard effects on labor supply under strong recourse do not outweigh the benefits of the reduction in the risk premium. In no regime do households prefer FRMs over ARMs.

We propose two modications to the method of endogenous grid points that greatly decreases the computational time for life cycle models with many exogenous state variables. First, we use simulated stochastic grids on the exogenous state variables. Second, when we interpolate to nd the continuation value of the model, we split the interpolation step into two: We use nearest-neighbor interpolation over the exogenous state variables, and multilinear interpolation over the endogenous state variables. We evaluate the numerical accuracy and computational eciency of the algorithm by solving a standard consumption/savings life-cycle model with an arbitrary number of exogenous state variables. The model with eight exogenous state variables is solved in around eight minutes on a standard desktop computer. We then demonstrate the usefulness of the algorithm by solving a model which includes a more realistic income process estimated by Guvenen et al. (2015).