Indicator Choice in Pay-for-Performance

TL;DR

This paper analyzes how the choice of information signals by agents affects optimal contracts in principal-agent models, revealing that simple binary or threshold signals often suffice for efficiency and surplus extraction.

Contribution

It characterizes the optimal information structure in moral hazard settings with endogenous signal choice, showing the sufficiency of coarse signals like binary or threshold signals.

Findings

Binary signals can achieve the agent's best outcome.

Conditions identified for full surplus extraction and first-best efficiency.

Threshold signals are optimal in one-dimensional effort-performance models.

Abstract

We study the classic principal-agent model when the signal observed by the principal is chosen by the agent. We fully characterize the optimal information structure from an agent's perspective in a general moral hazard setting with limited liability. Due to endogeneity of the contract chosen by the principal, the agent's choice of information is non-trivial. We show that the agent's problem can be mapped into a geometrical game between the principal and the agent in the space of likelihood ratios. We use this representation result to show that coarse contracts are sufficient: The agent can achieve her best with binary signals. Additionally, we can characterize conditions under which the agent is able to extract the entire surplus and implement the first-best efficient allocation. Finally, we show that when effort and performance are one-dimensional, under a general class of models, threshold signals are optimal. Our theory can thus provide a rationale for coarseness of contracts based on the bargaining power of the agent in negotiations.