  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.
