Working Paper: NBER ID: w13894
Authors: Noah Williams
Abstract: This paper studies the design of optimal contracts in dynamic environments where agents have private information that is persistent. In particular, I focus on a continuous time version of a benchmark insurance problem where a risk averse agent would like to borrow from a risk neutral lender to stabilize his income stream. The income stream is private information to the borrower and is persistent. I find that the optimal contract conditions on the agent's reported endowment as well as two additional state variables: the agent's utility and marginal utility under the contract. I show how persistence alters the nature of the contract, and consider an exponential utility example which can be solved in closed form. Unlike the previous discrete time models with i.i.d. private information, the agent's consumption under the contract may grow over time. Furthermore, in my setting the efficiency losses due to private information increase with the persistence of the endowment, and the distortions vanish as I approximate an i.i.d. endowment.
Keywords: Optimal Contracts; Private Information; Dynamic Contracting
JEL Codes: D82; D86; E21
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| persistence of private information (D89) | optimal contract conditions (D86) |
| persistence of endowment (D14) | efficiency losses due to private information (D82) |
| optimal contract conditions (D86) | efficiency of contracts (D86) |
| structure of the contract (L14) | growth of agent's consumption over time (E20) |