Essays in Policy Design and Statistical Inference
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Essays in Policy Design and Statistical Inference


This thesis is devoted to designing and analyzing statistical decision rules to improve public policy. The first three chapters study the estimation and inference of welfare-maximizing treatment rules in the context of experimental design, spillover effects, and algorithmic fairness. The last chapter focuses on statistical inference in experiments with multiple policy effects (either of different interventions or on different outcomes).

Specifically, Chapter 1 proposes an experimental design for estimation and inference of welfare-maximizing policies with spillover effects. As a first contribution, we introduce a single-wave experiment to estimate the marginaleffect of a change in treatment probabilities, taking spillover effects into account. Using the marginal effect, we propose a practical test for welfare-maximizing policy. As a second contribution, we design a multiple-wave experiment to estimate treatment rules and maximize welfare. We provide asymptotic and small-sample guarantees of the procedure and study its numerical properties in simulations calibrated to existing experiments.

Chapter 2 studies how to allocate treatments on a network, using information from an existing (quasi)-experiment. We introduce a method that maximizes the sample analog of social welfare whenspillovers occur. We construct semi-parametric welfare estimators and cast the optimization problem into a mixed-integer linear program. We derive guarantees on the regret and illustrate the method's advantage when targeting information on social networks.

Chapter 3 studies the problem of allocating treatments when policymakers have preferences for non-discriminatory actions. We adopt the non-maleficence perspective of ``first do no harm": we select the fairest allocation withinthe Pareto frontier. We derive off-the-shelf optimization procedures and regret bounds on the unfairness of the estimated policy function. We illustrate our method using an application from education economics.

Chapter 4 focuses on inference in the presence of multiple hypothesis testing. The use of multiple hypothesis testing adjustments varies widely in applied economic research, without consensus on when and how it should be done. We provide a game-theoretic foundation for this practice. We show that adjustments with many interventions must depend on the nature of scale economies in the research production function and on economic interactions between policy decisions. When research examines multiple outcomes, our framework motivates aggregating outcomes into sufficient statistics for policy-making.

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