In Chapter 1 we study optimal mortgage design. A borrower (a household) with limited liability needs financial support from a lender (a big financial institution) to purchase a house. We characterize the optimal allocation in a continuous time setting in which (i) the borrower's income is volatile and its realization is unobservable to the lender, (ii) the lender has a right to costly foreclose the loan and seize the house, (iii) the borrower's intertemporal consumption preferences are represented by a constant discount factor, (iv) the lender discounts cash flows using a stochastic discount factor that depends on the market interest rate. We show that the optimal allocation can be implemented using either an option adjustable rate mortgage or a combination of an interest only mortgage with a home equity line of credit. Under the optimal contracts, mortgage payments and default rates are higher when the market interest rate is high. However, borrowers benefit from low mortgage payments and low default rates when the market interest rate is low. The gains from using the optimal contract relative to simpler mortgages are substantial and the biggest for those who buy pricey houses given their income level or make little or no downpayment. Thus, our analysis provides theoretical evidence that high concentration of the alternative mortgages among risky borrowers and in the higher-priced regional markets can be economically efficient.;In Chapter 2 we study the structure of optimal wedges and capital taxes in a Mirrlees economy with endogenous skills. Human capital is a private state variable that drives the skill process of each individual. Building on the findings of the labor literature, we assume that human capital investment is (a) risky, (b) made early in the life-cycle, and (c) hard to distinguish from consumption. These assumptions lead to the optimality of (a) a human capital premium, i.e., an excess return on human capital relative to physical capital, (b) a large intertemporal wedge early in the life-cycle stemming from the lack of Rogerson's [Econometrica, 1985] "inverse Euler" characterization of the optimal consumption process, and (c) an intra-temporal distortion of the effort/consumption margin even at the top of the skill distribution at all dates except the terminal date. The main implication for the structure of linear capital taxes is the necessity of deferred taxation of physical capital. In particular, deferred taxation of capital prevents the agents from making a joint deviation of under-investing in human capital ex ante and shirking from labor effort at some future date in the life-cycle, as the marginal deferred tax rate on physical capital held early in the life-cycle is history-dependent. The average marginal tax rate on physical capital held in every period is zero in present value. Thus, as in Kocherlakota [Econometrica, 2005], the government revenue from capital taxation is zero. However, since a portion of the capital tax must be deferred, expected capital tax payments cannot be zero in every period. Necessarily, agents face negative expected capital tax payments due early in the life-cycle and positive expected capital tax payments late in the life-cycle. Also, relative to economies with exogenous skills, the optimal marginal wealth tax rate is more volatile.
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