This dissertation contains two essays on econometric methods for policy choice. The first essay develops a method for designing experiments with the objective of choosing optimal policies. An experimenter wants to choose a policy to maximize welfare subject to budget or other policy constraints. The effects of counterfactual policies are described by a structural econometric model governed by an unknown parameter. The experimenter has some pilot data, and has the opportunity to collect another wave of experimental data. The joint experimental design and policy choice problem is a dynamic optimization problem with a very high-dimensional state space. I propose a low-dimensional approximation and show it is asymptotically optimal under Bayes expected welfare. The method accommodates discrete as well as continuous treatments, such as cash transfers, prices, or tax credits, and allows targeting based on covariates. I demonstrate the method using the conditional cash transfer program Progresa, showing how to design an experiment to help choose a policy aimed at increasing graduation rates and reducing gender disparities in education. Compared to the original Progresa experiment, the optimal experiment requires only one quarter as many observations to obtain equally effective policies. The second essay studies how to choose a policy to allocate treatment to a heterogeneous population on the basis of experimental data that includes only a subset of possible treatment values. The effects of new treatments are partially identified through shape restrictions on treatment response. I propose solving an empirical minimax regret problem to estimate the policy and show it has a linear- and integer-programming formulation. I prove the maximum regret of the estimator converges to the lowest possible maximum regret at the slower of $N^{-1/2}$ or the rate at which heterogeneous treatment effects can be estimated. In an application to designing targeted subsidies for electrical grid connections in rural Kenya, I estimate that nearly the entire population should be given a treatment not implemented in the experiment, reducing maximum regret by over 60\% relative to the policy that restricts to the original set of treatments.