Economics research often addresses questions with an implicit or explicit policy goal. When such a goal involves an active intervention, such as the assignment of a particular treatment variable to participants, the analysis of its effects requires the tools of causal inference. In such settings, the opportunity to use experimental or observational data to tease out policy parameters of interest requires a combination of statistical and causal assumptions. In reduced form work, where an explicit economic theory is not laid out to allow identification of policy parameters from data, the investigation of the causal assumptions becomes a critical exercise for the credibility of the results. Many robustness exercises evaluate the effect that relaxing and/or modifying assumptions produces on the results of the study. The scope of these exercises is very broad, reflecting the need to tailor specific robustness exercises to whichever assumptions are most likely to be violated in a given domain. This dissertation is a collection of three essays on robust causal inference that share a unifying theme: preserving the nonparametric nature of the robustness exercise. This aspect has both a theoretical and practical relevance. First, causal assumptions are usually nonparametric: robustness exercises that restrict to parametric cases might lead to misleading insights. Further, economics research has started to incorporate more flexible nonparametric and semi-parametric techniques which may call for robustness exercises that are readily applicable to these approaches.

Because robustness exercises are context specific, each of these essays addresses a separate aspect of it. Chapter 1 investigates how changes in the distribution of covariates may invalidate given experimental results, with implications for evidence based policy-making. It proposes an explicit metric of robustness that measures the distance of the closest distribution of covariates for which experimental results are violated. Chapter 2 analyses the practice of robustness checks as a way to validate a researcher's identification strategy. It details out the limitations of these exercises in detecting failure of identification and proposes a non-parametric robustness test that bypasses functional form assumptions.Finally, Chapter 3 focuses on the robustness of Marginal Treatment Effect identification when the instrumental variables fail to incentivize treatment for a subset of the population. It provides two alternative identification results which can be relevant in practice.

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.