Three Essays in Robust Causal Inference

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