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Robust Contracts: A Revealed Preference Approach

The Review of Economics and Statistics 2024
We study an agency model in which the principal knows the agent-optimal actions in response to K “known” contracts but is unaware of other actions available or their costs, and seeks a contract to maximize worst-case profits. The optimal contract is a mixture of the known contracts and output. Moreover, when K = 1, the single known contract maximizes the principal's profit guarantee, whereas with two known contracts, the optimal mixture puts positive weight on one of the known contracts. Our methodology is straightforward to implement, a point that we demonstrate using data from an experimental study of different incentive schemes.

Optimal Monitoring Design

Econometrica 2020 88(5), 2075-2107 open access
This paper considers a Principal–Agent model with hidden action in which the Principal can monitor the Agent by acquiring independent signals conditional on effort at a constant marginal cost. The Principal aims to implement a target effort level at minimal cost. The main result of the paper is that the optimal information‐acquisition strategy is a two‐threshold policy and, consequently, the equilibrium contract specifies two possible wages for the Agent. This result provides a rationale for the frequently observed single‐bonus wage contracts .

A/B Contracts

American Economic Review 2022 112(1), 267-303
This paper aims to improve the practical applicability of the classic theory of incentive contracts under moral hazard. We establish conditions under which the information provided by an A/B test of incentive contracts is sufficient for answering the question of how best to improve a status quo incentive contract, given a priori knowledge of the agent’s monetary preferences. We assess the empirical relevance of this result using data from DellaVigna and Pope’s (2018) study of a variety of incentive contracts. Finally, we discuss how our framework can be extended to incorporate additional considerations beyond those in the classic theory. (JEL D82, D86, D91)

Flexible Moral Hazard Problems

Econometrica 2024 92(2), 387-409
This paper considers a moral hazard problem where the agent can choose any output distribution with a support in a given compact set. The agent's effort‐cost is smooth and increasing in first‐order stochastic dominance. To analyze this model, we develop a generalized notion of the first‐order approach applicable to optimization problems over measures. We demonstrate each output distribution can be implemented and identify those contracts that implement that distribution. These contracts are characterized by a simple first‐order condition for each output that equates the agent's marginal cost of changing the implemented distribution around that output with its marginal benefit. Furthermore, the agent's wage is shown to be increasing in output. Finally, we consider the problem of a profit‐maximizing principal and provide a first‐order characterization of principal‐optimal distributions.

Feedback Design in Dynamic Moral Hazard

Econometrica 2025 93(2), 597-621
We study the joint design of dynamic incentives and performance feedback for an environment with a coarse (all‐or‐nothing) measure of performance, and show that hiding information from the agent can be an optimal way to motivate effort. Using a novel approach to incentive compatibility, we derive a two‐phase solution that begins with a “silent phase” where the agent is given no feedback and is asked to work non‐stop, and ends with a “full‐transparency phase” where the agent stops working as soon as a performance threshold is met. Hiding information leads to greater effort, but an ignorant agent is also more expensive to motivate. The two‐phase solution—where the agent's ignorance is fully frontloaded—stems from a “backward compounding effect” that raises the cost of hiding information as time passes.

Optimal Feedback in Contests

Review of Economic Studies 2023 90(5), 2370-2394
We obtain optimal dynamic contests for environments where the designer monitors effort through coarse, binary signals—Poisson successes—and aims to elicit maximum effort, ideally in the least amount of time possible, given a fixed prize. The designer has a vast set of contests to choose from, featuring termination and prize-allocation rules together with real-time feedback for the contestants. Every effort-maximizing contest (which also maximizes total expected successes) has a history-dependent termination rule, a feedback policy that keeps agents fully apprised of their own success, and a prize-allocation rule that grants them, in expectation, a time-invariant share of the prize if they succeed. Any contest that achieves this effort in the shortest possible time must in addition be what we call second chance: once a pre-specified number of successes arrive, the contest enters a countdown phase where contestants are given one last chance to succeed.