Working Paper: CEPR ID: DP4455
Authors: Matthias Doepke; Robert M. Townsend
Abstract: We develop general recursive methods to solve for optimal contracts in dynamic principal-agent environments with hidden states and hidden actions. In our baseline model, the principal observes nothing other than transfers. Nevertheless, optimal incentive-constrained insurance can be attained. We show that the optimal contract can be implemented as a recursive direct mechanism with a vector of utility promises as the state variable. The standard recursive formulation suffers from a curse of dimensionality that arises from the interaction of hidden income and hidden actions; this curse can be overcome by introducing judiciously chosen utility bounds for deviation behaviour off the equilibrium path. Our methods generalize to environments with multiple actions and additional states. The key to implementing these extensions is to introduce multiple layers of off-path utility bounds.
Keywords: Dynamic Contracts; Mechanism Design; Recursive Contracts
JEL Codes: C63; C73; D82
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| hidden actions (Y50) | optimal contract (D86) |
| utility bounds (L97) | optimal contract (D86) |
| hidden actions (Y50) | intertemporal rate of substitution (D15) |
| intertemporal rate of substitution (D15) | optimal contract (D86) |
| hidden actions (Y50) | future income realizations (G19) |
| optimal information-constrained insurance (G52) | borrowing-lending solutions (F34) |