Persistent Private Information


  • Noah Williams

    1. Dept. of Economics, University of Wisconsin–Madison, William H. Sewell Social Science Building, 1180 Observatory Drive, Madison, WI 53706-1393, U.S.A.;
    Search for more papers by this author
    • I thank Dilip Abreu, Katsuhiko Aiba, Narayana Kocherlakota, Rui Li, Chris Sleet, and Ted Temzelides for helpful comments. I also especially thank the co-editor and two anonymous referees for comments that greatly improved the paper. Financial support from the National Science Foundation is gratefully acknowledged.


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 utility. The agent privately observes a persistent state variable, typically either income or a taste shock, and he makes reports to the principal. I give verifiable sufficient conditions showing that incentive-compatible contracts can be written recursively, conditioning on the report and two additional state variables: the agent's promised utility and promised marginal utility of the private state. I then study two examples where the optimal contracts can be solved in closed form, showing how persistence alters the nature of the contract. Unlike the previous discrete-time models with independent and identically distributed (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 private information, and the distortions vanish as I approximate an i.i.d. environment.