We discuss using Wasserstein Generative Adversarial Networks (WGANs) as a method for systematically generating artificial data that mimic closely any given real data set without the researcher having many degrees of freedom. We apply the methods to compare in three different settings twelve different estimators for average treatment effects under unconfoundedness.

We propose using a Bayesian hierarchical latent class model to summarize and interpret observed heterogeneity in categorical expectations data. We show that the statistical model corresponds to an economic structural model of information acquisition, which guides interpretation and estimation of the model parameters.

There is increasing interest in allocating treatments based on observed individual characteristics: examples include targeted marketing, individualized credit offers, and heterogenous pricing. Treatment personalization introduces incentives for individuals to modify their behavior to obtain a better treatment. This shifts the distribution of covariates, which means the Conditional Average Treatment Effect (CATE) now depends on how treatments are targeted. The optimal rule without strategic behavior allocates treatments only to those with a positive CATE. With strategic behavior, we show that the optimal rule can involve randomization, allocating treatments with less than 100\% probability even to those with a positive CATE induced by that rule. We propose a sequential experiment based on Bayesian Optimization that converges to the optimal treatment rule without parametric assumptions on individual strategic behavior.

We introduce a stochastic model of potential outcomes in market equilibrium, where the market price is an exposure mapping. We prove that average direct and indirect treatment effects converge to interpretable mean-field treatment effects, and provide estimators for these effects through a unit-level randomized experiment augmented with randomization in prices. We also provide a central limit theorem for the estimators.

We consider the problem of learning how to optimally allocate treatments whose cost is uncertain and can vary with pre-treatment covariates. This setting may arise in medicine if we need to prioritize access to a scarce resource that different patients would use for different amounts of time, or in marketing if we want to target discounts whose cost to the company depends on how much the discounts are used. Here, we show that the optimal treatment allocation rule under budget constraints is a thresholding rule based on priority scores, and we propose a number of practical methods for learning these priority scores using data from a randomized trial. Our formal results leverage a statistical connection between our problem and that of learning heterogeneous treatment effects under endogeneity using an instrumental variable. We find our method to perform well in a number of empirical evaluations.

We study the problem of a planner who wants to reduce inequality by awarding prizes to the worst contestants in a tournament without incentivizing shirking. We design an approximately optimal, incentive-compatible mechanism that targets low-ranked contestants based on the tournament's history up to an endogenous stopping time. We describe applications to eligibility for remedial education, retraining benefits for the unemployed, and draft lotteries in sports.