Optimal social insurance, private information, and non-exclusive contracting

This thesis studies the optimal provision of social insurance in the presence of asymmetric information. Agents are subject to idiosyncratic shocks and sign contracts to insure against them. The main friction present in all the environments studied in this thesis is that these shocks are privately observed by agents. Each chapter of the thesis considers a particular environment with asymmetric information and for each case we characterize the optimal contract and study its quantitative implications.;The focus of chapter 2 is to study the quantitative properties of constrained efficient allocations in an environment where risk sharing is limited by the presence of private information. We consider a life cycle version of a standard Mirrlees economy where shocks to labor oroductivity have a component that is public information and one that is private information. agents sign an exclusive contract with a planner that prescribes the consumption and output allocations. The presence of private shocks has important implications for the age profiles of consumption and income implied by the optimal contract. First, they introduce an endogenous dispersion of continuation utilities. As a result, consumption inequality rises with age even if the variance of the shocks does not. Second, they introduce an endogenous rise of the distortion on the marginal rate of substitution between consumption and leisure over the life cycle. This is because, as agents age, the ability to properly provide incentives for work must become less and less tied to promises of benefits (through either increased leisure or consumption) in future periods. Both of these features are also present in the US survey data. We look at the data through the lens of our model and estimate the fraction of labor productivity that is private information. We find that for the model and data to be consistent, a large fraction of shocks to labor productivity must be private information.;In chapter 3 we study how the presence of non-exclusive contracts limits the amount of insurance provided in a decentralized economy. We consider a dynamic Mirrleesian economy in which agents are privately informed about idiosyncratic labor productivity shocks. Agents sign privately observable insurance contracts with multiple firms (i.e., they are non-exclusive), which include both labor supply and savings aspects. Firms have no restriction on the contracts they can offer, interact strategically. In equilibrium, contrary to the case with exclusive contracts, a standard Euler equation holds, the marginal rate of substitution between consumption and leisure is equated to the worker's marginal productivity. Also, each agent receives zero net present value of transfers. To sustain this equilibrium, more than one firm must be active and must also offer latent contracts to deter deviations to more profitable contingent contracts. In this environment, the non-observability of contracts removes the possibility of additional insurance beyond self-insurance. To test the model, we allow firms to observe contracts at a cost. The model endogenously divides the population into agents that are not monitored and have access to non-exclusive contracts and agents that have access to exclusive contracts. We use US survey data and find that high school graduates satisfy the optimality conditions implied by the non-exclusive contracts while college graduates behave according to the second group.;Chapter 4 considers the Rothschild and Stiglitz (1976) insurance environment relaxing the assumption of exclusivity of insurance contracts. Agents are privately informed about the probability of their income realization, which is publicly observed. Agents can engage in multiple insurance contract simultaneously and the terms of these contracts are not observed by other firms. Insurance providers behave non-cooperatively and compete offering menus of insurance contracts from an unrestricted contract space. We derive conditions under which a separating equilibrium exists and fully characterize it. The equilibrium allocation consists of agents with a lower probability of accident purchasing no insurance and agents with higher accident probability buying the actuarially fair competitive level of insurance. The equilibrium allocation also constitutes a linear price schedule for insurance. To sustain this allocation firms must offer latent contracts. We show that latent menus can prevent cream-skimming strategies, however pooling equilibrium still fails to exists.