Machine learning has become increasingly popular in informing data-driven policy-making. Policies influence behavior in individuals or populations, and ideally, through observational signals, policy-makers learn which policies are effective. However, in many settings, individual actions cannot be perfectly observed. This issue, known in economics as moral hazard, poses a significant challenge. In this work, we study the foundational multitasking principal-agent contract design problem and demonstrate how instrumental regression and the generalized method of moments (GMM) estimator can be used to estimate or learn a good contract. As a bonus result, we also give a uniformity characterization of the shape of the optimal contract.