This paper is part of a project to model the interaction between heterogeneous agents in intertemporal stochastic models and to develop numerical algorithms to solve these kind of models. It is well-known that solving dynamic heterogeneous agent models is a challenging problem, since in these models the distribution of wealth and other characteristics evolve endogenously over time. Existing dynamic models in the literature contain therefore just two agents or other simplifying assumptions to limit the heterogeneity.

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This paper investigates the optimal tax structure in an overlapping generations model in which individuals face idiosyncratic income risk, borrowing constraints and lifetime uncertainty. The calibrated model economy produces some quantitative results that differ significantly from the findings of the previous research. The main finding in this imperfect insurance setup is that moving away from capital income taxation toward higher labor income taxation yields a (steady-state) welfare benefit of 1% of aggregate consumption compared with the 6% figure Lucas (1990) finds in an infinite-horizon, complete markets model. This is because replacing the tax on capital income with a higher tax on labor income redistributes resources away from the young working years during which borrowing constraints are more likely to bind. Furthermore, when the individuals have access to a private annuity market to insure against uncertain lifetimes, it becomes optimal to tax capital. When a consumption tax is made available, it is optimal to switch to consumption taxation. The welfare benefit from implementing this optimal plan is on the order of 1.5-3.2% of GNP.

This paper considers the unobserved endowment economy of Green (1987) with a restriction that agents can walk away from insurance contracts at the beginning of any period and contract with another insurer (one-sided commitment). An equilibrium is derived characterized by a unique, market determined insurance contract with the property that agents never want to walk away from it. I show that trade (or insurance) still occurs and that a non-degenerate long-ran distribution of consumption exists.