Essays on Market Incompleteness

Abstract

This thesis studies incomplete market economies. First from a normative perspective in Chapter 1, then from a positive one in Chapter 2. Chapter 1 studies optimal taxation in an environment where heterogeneous households face uninsurable idiosyncratic risk. To do this, we formulate a Ramsey problem in a standard infinite horizon incomplete markets model. We solve numerically for the optimal path of proportional capital and labor income taxes, (possibly negative) lump-sum transfers, and government debt. The solution maximizes welfare along the transition between an initial steady state, calibrated to replicate key features of the US economy, and an endogenously determined final steady state. We find that in the optimal (utilitarian) policy: (i) capital income taxes are front-loaded hitting the imposed upper bound of 100 percent for 33 years before decreasing to 45 percent in the long-run; (ii) labor income taxes are reduced to less than half of their initial level, from 28 percent to about 13 percent in the long-run; and (iii) the government accumulates assets over time reducing the debt-to-output ratio from 63 percent to -17 percent in the long-run. Relative to keeping fiscal instruments at their initial levels, this leads to an average welfare gain equivalent to a permanent 4.9 percent increase in consumption. Even though non-distortive lump-sum taxes are available, the optimal plan has positive capital and labor taxes. Such taxes reduce the proportions of uncertain and unequal labor and capital incomes in total income, increasing welfare by providing insurance and redistribution. We are able to quantify these welfare effects. We also show that calculating the entire transition path (as opposed to considering steady states only) is quantitatively important. Implementing the policy that maximizes welfare in steady state leads to a welfare loss of 6.4 percent once transitory effects are accounted for. The main determinants of credit limits are the rules that govern the ability of households to default on their loans and the risks that they are exposed to. Chapter 2 investigates the quantitative relevance of these determinants using a version of the incomplete markets life cycle model in which agents are allowed to default on their debt holdings by declaring bankruptcy. I document that credit limits are positively correlated with households' income levels. I then show that the introduction of profile heterogeneity in the households' income processes increases the correlation between income and credit limits. This fact is consistent with the theoretical results established in a simple example. I also show that proportional income punishments or a threshold level of income, such that agents are only allowed to declare bankruptcy only for income levels bellow that threshold, can also be used to generate such a positive correlation. Finally, the main calibration results suggest an important qualification about heterogeneous income profile models: the lower levels of uncertainty implied by these models lead to a severe underestimation of the number of bankruptcy filings.