This paper shows that numerical solutions to models with incomplete markets and aggregate uncertainty obtained using the Krusell and Smith (1998) algorithm are sensitive to the parameterization of the grid in the aggregate asset holdings direction. Higher moments of the cross-sectional...

We study the dynamic Ramsey problem of finding optimal public debt and linear taxes on capital and labor income within a tractable infinite horizon model with incomplete markets. With zero public expenditure and debt, it is optimal to tax the risky labor income and subsidize capital, while a...

In this paper, we prove an existence theorem for approximated equilibria in a class of discontinuous economies. The existence result is a direct consequence of a discontinuous extension of Brouwer’s fixed point Theorem (1912), and is a refinement of several classical results in the standard...

We consider an economy where individuals face uninsurable risks to their human capital accumulation, and analyze the optimal level of linear taxes on capital and labor income together with the optimal path of government debt. We show that in the presence of such risks it is beneficial to tax...

In this chapter we study dynamic incentive models in which risk sharing is endogenously limited by the presence of informational or enforcement frictions. We comprehensively overview one of the most important tools for the analysis such problems—the theory of recursive contracts. Recursive...

Although almost nonexistent 15 years ago, there are now numerous papers that analyze models with both aggregate uncertainty and a large number—typically a continuum—of heterogeneous agents. These models make it possible to study whether macroeconomic fluctuations affect different agents...

In this paper, we document that households’ consumption expenditures depend on their expected earnings - even after controlling for realized earnings and wealth. To explain this evidence, we develop and structurally estimate a standard-incomplete markets model in which rational households...

While it is common knowledge that portfolio separation in a continuous-time lognormal market is due to the basic properties of the Gaussian distribution, the usual textbook exposition relies on dynamic programming and thus Itô stochastic calculus and the appropriate regularity conditions. This...

In this paper we study the effects of financial integration on risk-sharing. Conventional macroeconomic theory suggests that the integration of financial markets improves welfare. In contrast to the literature we assume that households have heterogeneous beliefs. Because of the differences in...

We study consumption-portfolio and asset pricing frameworks with recursive preferences and unspanned risk. We show that in both cases, portfolio choice and asset pricing, the value function of the investor/representative agent can be characterized by a specific semilinear partial differential...