We consider moral hazard problems where a principal has access to rich monitoring data about an agent's action. Rather than focusing on optimal contracts (which are known to in general be complicated), we characterize the optimal rate at which the principal's payoffs can converge to the first-best payoff as the amount of data grows large. Our main result suggests a novel rationale for the widely observed binary wage schemes, by showing that such simple contracts achieve the optimal convergence rate. Notably, in order to attain the optimal convergence rate, the principal must set a lenient cutoff for when the agent receives a high vs. low wage. In contrast, we find that other common contracts where wages vary more finely with observed data (e.g., linear contracts) approximate the first-best at a highly suboptimal rate. Finally, we show that the optimal convergence rate depends only on a simple summary statistic of the monitoring technology. This yields a detail-free ranking over monitoring technologies that quantifies their value for incentive provision in data-rich settings and applies regardless of the agent's specific utility or cost functions.

翻译：本文研究委托代理问题中的道德风险情境，其中委托人能够获取关于代理人行为的丰富监督数据。与聚焦于最优契约设计（已知此类契约通常具有高度复杂性）的传统思路不同，我们刻画了当数据量趋于无穷时，委托人收益向最优收益收敛的理论速率上限。主要结论为广泛存在的二元薪酬方案提供了新的理论依据：研究表明此类简单契约能够达到最优收敛速率。值得注意的是，为实现最优收敛速率，委托人必须设定宽松的临界值以区分代理人获得高薪与低薪的阈值。相比之下，其他常见的薪酬与观测数据精细挂钩的契约形式（如线性契约）只能以次优速率逼近最优收益。最后，我们证明最优收敛速率仅取决于监督技术的一个简单统计量。这一发现构建了与细节无关的监督技术排序体系，该体系能够量化数据丰富环境下不同监督技术对激励设计的贡献价值，且其适用性独立于代理人具体的效用函数或成本函数。