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 insurance contracts with multiple firms (i.e., they are non-exclusive), which include both labor supply and savings aspects. These contract arrangements are private information. Firms have no restriction on the contracts they can offer, interact strategically, and, as in common agency problems, might offer latent contracts to sustain equilibrium allocations. In equilibrium, contrary to the case with exclusive contracts, a standard Euler equation holds, and the marginal rate of substitution between consumption and leisure is equated to the worker’s marginal productivity. Finally, each agent receives zero net present value of transfers from insurance providers. To sustain this equilibrium, more than one firm must be active in offering the equilibrium allocation. Each active firm 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 household 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. ∗We are grateful to Larry Jones, Patrick Kehoe, and V.V. Chari for their continuous help and support. We thank Fabrizio Perri and Dirk Krueger for providing the CEX data. We thank Arpad Abraham, Andy Atkeson, Kim-Sau Chung, Roozbeh Hosseini, Narayana Kocherlakota, Ellen McGrattan, Lee Ohanian, Fabrizio Perri, Chris Sleet, Aleh Tsyvinski, Pierre Yared, and Sevin Yeltekin for comments and suggestions. Remaining mistakes are ours. The views expressed in this paper are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. †Contact Maziero: Department of Economics, University of Minnesota, 4-101 Hanson Hall, 1925 Fourth Street South, Minneapolis, MN 55455. Email: [email protected]