Chapter 1 studies the optimal allocation of subsidies based on individual characteristics. We show that the marginal treatment effect is a “sufficient statistics” for the counterfactual welfares and develop identification results based on marginal treatment effects. We also show that subsidy rules, which assigns subsidy for treatment take-up, weakly dominate treatment rules, which assigns treatment directly, in terms of the social welfare achieved.

Chapter 2 establishes that the assumptions of conditional local average treatment effect (CLATE) has a selection model representation in which a specific form of separability needs to hold. Based on the representation results, we develop several testable implications of the CLATE model that are sharper than the existing ones in the literature.

Chapter 3 proposes a new empirical Bayes method that utilizes a decision tree to improve the statistical accuracy of the estimates while maintaining the interpretability of the result. Instead of the “shrinking toward the grand mean” that is employed by conventional empirical Bayes methods, the proposed method will group similar effects and make the shrinkage to be group-specific. We also provide a method to select the best decision tree that minimizes the estimation errors.