Non-Exclusive Dynamic Contracts, Competition, and the Limits of Insurance

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.