Working Paper: CEPR ID: DP7578
Authors: Alex Edmans; Xavier Gabaix
Abstract: This paper identifies a class of multiperiod agency problems in which the optimal contract is tractable (attainable in closed form). By modeling the noise before the action in each period, we force the contract to provide sufficient incentives state-by-state, rather than merely on average. This tightly constrains the set of admissible contracts and allows for a simple solution to the contracting problem. Our results continue to hold in continuous time, where noise and actions are simultaneous. We thus extend the tractable contracts of Holmstrom and Milgrom (1987) to settings that do not require exponential utility, a pecuniary cost of effort, Gaussian noise or continuous time. The contract's functional form is independent of the noise distribution. Moreover, if the cost of effort is pecuniary (multiplicative), the contract is linear (log-linear) in output and its slope is independent of the noise distribution, utility function and reservation utility. In a two-stage contracting game, the optimal target action depends on the costs and benefits of the environment, but is independent of the noise realization.
Keywords: Closed forms; Contract theory; Dispersive order; Executive compensation; Incentives; Principal-agent problem; Subderivative
JEL Codes: D2; D3; G34; J3
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| timing of noise (C58) | contract tractability (D86) |
| modeling noise before action (C58) | incentive compatibility must hold state-by-state (H73) |
| incentive compatibility must hold state-by-state (H73) | simpler solution for contracting problem (D86) |
| cost of effort is pecuniary (D61) | optimal contract is linear in output (D86) |
| marginal benefit of effort > marginal cost (D61) | maximum effort is optimal (D29) |
| structure of contracts (L14) | incentives faced by agents (D82) |
| incentives faced by agents (D82) | effort levels and overall outcomes (D29) |
| specific features of the environment (Q56) | form of the optimal contract (D86) |