Endogenous Insurance and Informal Relationships
A rich literature seeks to explain the distinctive features of equilibrium institutions arising in risky environments which lack formal insurance and credit markets. I develop a theory of endogenous matching between heterogeneously risk-averse individuals who, once matched, choose both the riskiness of the income stream they face (ex ante risk management) as well as how to share that risk (ex post risk management). I find a clean condition on the fundamentals of the model for unique positive-assortative and negative-assortative matching in risk attitudes. From this, I derive an intuitive falsifiability condition, discuss support for the theory in existing empirical work, and propose an experimental design to test the theory. Finally, I demonstrate the policy importance of understanding informal insurance as the risk-sharing achieved within the equilibrium network of partnerships, rather than within a single, isolated partnership. A hypothetical policy which reduces aggregate risk is a strict Pareto improvement if the matching is unchanged, but can be seen to harm the most risk-averse individuals and to exacerbate inequality when the endogenous network response is taken into account: the least risk-averse individuals abandon their roles as informal insurers in favor of entrepreneurial partnerships. This results in an increase in the risk borne by the most risk-averse agents, who must now match with each other on low-return investments.
Risk, Incentives, and Contracting Relationships
The aim of this paper is to understand the impact of optimal provision of both risk and incentives on the choice of contracting partners. I study a risky setting where heterogeneously risk-averse employers and employees must match to be productive. They face a standard one-sided moral hazard problem: mean output increases in the noncontractible input of the employee. Better insurance comes at the cost of weaker incentives, and this tradeoff differs across partnerships of different risk compositions. I show that this heterogeneous tradeoff determines the equilibrium matching pattern, and focus on environments in which assortative matching is the unique equilibrium. This endogenous matching framework enables a concrete and rigorous analysis of the interaction between formal and informal insurance. In particular, I show that the introduction of formal insurance crowds out informal insurance, and may leave those individuals acting as informal insurers in the status quo strictly worse off.
A Note on Moral Hazard and Linear Compensation Schemes
This note identifies a moral hazard environment in which a piecewise linear compensation scheme is optimal. Both the principal and the agent have CARA utility, mean output is increasing in the agent's noncontractible input, and output is distributed according to a Laplace distribution, which resembles a normal distribution (e.g. it is symmetric about the mean), but has fatter tails. The key property of the Laplace distribution is that the likelihood ratio is a piecewise constant, where the discontinuity occurs at the mean.
The value of this approach is twofold: first, a tractable, empirically-observed wage scheme emerges as the equilibrium in a simple static contracting model. Second, the optimal piecewise linear scheme cleanly separates insurance and incentive provision. The linearity at output levels away from the mean captures insurance, while the jump at the mean captures incentive provision. Hence, this model is ideal for studying a wide variety of principal-agent problems in risky environments subject to moral hazard, such as the effect of risk and moral hazard constraints on employment relationships in developing economies.
Interdependent Utility and Truthtelling in Two-sided Matching
Mechanisms which implement stable matchings are often observed to work well in practice, even in environments where the stable outcome is not unique, information is complete, and the number of players is small. Why might individuals refrain from strategic manipulation, even when the complexity cost of manipulation is low? I study a two-sided, one-to-one matching problem with no side transfers, where utility is interdependent in the following intuitive sense: an individual’s utility from a match depends not only on her preference ranking of her assigned partner, but also on that partner’s ranking of her. I show that, in a world of complete information and linear interdependence, a unique stable matching emerges, and is attained by a modified Gale-Shapley deferred acceptance algorithm. As a result, a stable rule supports truthtelling as an equilibrium strategy. Hence, these results offer a new intuition for why stable matching mechanisms seem to work well in practice, despite their theoretic manipulability: individuals may value being liked.