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：本文研究委托人能够获取代理人行为的丰富监控数据时的道德风险问题。不同于聚焦最优合约（已知通常较为复杂），我们刻画了随着数据量增大，委托人收益收敛至最优收益的最优速率。主要结论为普遍存在的二元工资方案提供了新颖解释：此类简单合约恰好能达到最优收敛速率。值得注意的是，为实现最优收敛速度，委托人必须对代理人获取高/低工资设定宽松阈值。与之对比，其他常见合约（如线性合约）中工资随观测数据更精细变化时，其近似最优收益的速率远低于最优水平。最后，我们证明最优收敛速率仅依赖于监控技术的简单汇总统计量。这给出了监控技术的无需细节的排序，量化了数据丰富环境下监控技术对激励提供的价值，且该排序不受代理人具体效用函数或成本函数的影响。