Conclusion
Previous studies show that private information is important for determining the extent to which agents can get together and pool idiosyncratic risk. The analysis in this paper suggests that insurance capabilities improve as a consequence of the introduction of capital accumulation. Under certain conditions, we show that (i) when an agent’s Pareto weight is sufficiently large, her incentives to cheat under the full information allocation disappear; (ii) the full information allocation may be incentive compatible when both agents have equal Pareto weights; and (iii) in the long run, either one of the agents is driven to immiseration, or both agents’ lifetime utilities are approximately equal. Throughout a series of extensions and generalizations, we have learned that there are two key ingredients needed for Proposition 1 to hold. First, the economy must have a technology to transfer resources across time. In the benchmark model, we assume capital accumulation with decreasing returns to scale. The advantage is that we can solve the infinite horizon model and challenge the celebrated immiseration result. In a supplemental note, we consider a model with a linear storage technology and show that a result similar to Proposition 1 also holds in that environment. The second ingredient is that marginal utilities of consumption are private information. As is standard in the literature, e.g., Atkeson and Lucas (1992), we assume that agents face privately observed liquidity needs. In a supplemental note, we show that a similar result to Proposition 1 holds if agents have privately observed endowment shocks, as in Thomas and Worral (1990). What matters is that the shocks affect the marginal utility of consumption. When θ = 1, private and aggregate marginal costs of operating the saving technology coincide and there are no incentives to cheat.
