Monitoring with Rich Data

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.