Work In Progress:
(joint with Laurence Ales)
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 costly observe contracts. 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.
(joint with Laurence Ales)
We 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 lifecycle version of a standard Mirrlees economy where shocks to labor productivities have a component which is public information and one which is private information. The presence of private shocks has important implications for the age profiles of consumption and income. First, they introduce an endogenous dispersion of continuation utilities. As a result consumption inequality rises with age even though the variance of the shocks does not. Second, they introduce an endogenous rise in the covariance between consumption and income over the lifecycle. 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 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 productivities must be private information.
Skill, luck and information: private information as a source of lifetime inequality
(joint with Laurence Ales)
Data on consumption inequality is inconsistent with models with full risk sharing. Recent literature has addressed this fact by introducing market incompleteness or limited commitment. In this paper we focus on an alternative channel to generate consumption inequality. We consider an environment in which private information is the main friction. We focus on two sources of private information, one permanent and one temporary. The first is learning ability which is draw once and for all before entering the labor market. We assume that learning ability affects the workers' productivity only through the accumulation of human capital. Labor productivity is also affected by a temporary shock which is the second source of private information. We solve for the information constrained optimal allocation for this environment and compare it with the distributions of consumption, income and hours in the US data. This approach allows us to study the joint determination of income and consumption and to look at the implication for conditional moments of these two variables. The private information nature of the productivity shock allows us to match the overall change in consumption variability over the lifecycle while also being consistent with the decline of conditional income variance with age. Models with incomplete markets that specify an exogenous income process cannot match this feature of the data. In our environment differences in learning abilities generate permanent consumption inequality early in life. The increase in inequality over the lifecycle is necessary to provide incentives to reveal the idiosyncratic productivity shock. Preliminary results indicate that differences in learning ability are more important when accounting for consumption inequality.
Efficient Allocations with Limited Commitment
(joint with Roozbeh Hosseini)
We study the social insurance problem in an environment where agents have private information about their taste shocks and the insurance provider (or government) cannot commit to the ex ante optimal allocation rules. With no commitment, the government is tempted to use updated beliefs about agents’ types and offer a new insurance plan each period. Given this lack of commitment, we allow the government to use a general communication mechanism (as opposed to direct communication). In this communication system, agents report their type to a mediator, and the mediator sends a (possibly random) signal of the types to the government. We show that in this setup the revelation principal holds and agents’ behavior can be summarized by a set of incentive compatibility constraints. This allows us to write the problem of finding the efficient allocation as a maximization problem subject to a set of incentive and feasibility constraints and a series of time consistency constraints. In general, the optimal allocation rules in environments with noisy communication (with mediator) might be different from the ones with direct communication. Every optimal allocation under direct communication can be implemented by a noisy communication system, however, the converse is not always true. We use this set up to investigate this issue and provide a simple example in which the optimal allocation is indeed different under both communication system.
Adverse Selection and Non-exclusive Contracts
(joint with Laurence Ales)
This paper studies the Rothschild and Stiglitz (1976) insurance environment relaxing the assumption of exclusivity of insurance contracts. Agents can engage in multiple insurance contract simultaneously and the terms of these contracts are not observed by other firms. Insurance providers behave non-cooperativelly and compete offering menus of insurance contracts from an unrestricted contract space. We show that the Rothschild and Stiglitz equilibrium allocation is not an equilibrium in the presence of non-exclusive contracting, since firms will offer latent contracts to prevent deviation by other firms that prevent separation of the agents. This possibility also implies that latent menus can prevent cream-skimming strategies, however pooling equilibrium still fails to exists. We derive the 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 actuarilly fair competitive level of insurance. To sustain the equilibrium allocation firms must offer latent contracts. The equilibrium allocation also constitute a linear price schedule for insurance.
Journal of Economic Theory, vol. 142, Issue 1, September 2008, pg. 5-27
Prior to 1863, United States banks issued notes---dollar-denominated promises to pay specie on demand. Banknotes circulated at par locally but at a discount outside the local area. Discounts varied by bank location and the location of the discount quote and were asymmetric across locations. Discounts increased when banks suspended payments. In this paper we construct a random matching model to qualitatively match these facts. The model has nonbankers and bankers in each of two locations. Bankers issue and redeem notes that serve as media of exchange. The model delivers predictions consistent with the discount facts.