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.

A consumer can acquire information from different review platforms before buying a product, a graduate student often seeks advice from multiple faculty members when pursuing a new project, and an investor often solicits the recommendations of different financial consultants. In all these settings, different sources of information are potentially correlated: different review platforms may include reviews from the same reviewer, opinions of faculty members in the same department are rarely independent, and different financial consultants themselves often collect information from the same data provider such as Bloomberg. However, knowledge about these underlying correlations is often very limited. In such circumstances, how can one combine and make use of multiple information sources while being robust to the hidden correlations? We study a model where an agent confronts a binary state decision problem after observing signals generated from distinct information sources (Blackwell experiments). The agent fully understands each information source in isolation but has no knowledge about the correlations between different information sources, and thus chooses a decision plan that maximizes the expected payoff with respect to the worst possible correlation. We call such a decision plan, the robustly optimal strategy.