Essays in causal inference

This dissertation explores the estimation of causal effects in settings with non-standard data. In the first chapter, the treatments are not directly assigned to outcome units but instead occur in the same geographic space. In the second chapter, responses to hypothetical questions describing both the treated and control state are used to learn about the effects of a treatment on real behavior (outcomes). In the third chapter, treatments are assigned according to a randomized experiment but outcomes are heavy-tailed, such that semiparametric approaches are useful to improve efficiency and robustness. The first chapter considers settings where the treatments causing the effects of interest are not directly associated with specific units for which we measure outcomes, but rather occur in the same geographic space. Many events and policies (treatments), such as opening of businesses, building of hospitals, and sources of pollution, occur at specific spatial locations, with researchers interested in their effects on nearby individuals or businesses (outcome units). However, the existing treatment effects literature primarily considers treatments that could experimentally be assigned directly at the level of the outcome units, potentially with spillover effects. I approach the spatial treatment setting from a similar experimental perspective: What ideal experiment would we design to estimate the causal effects of spatial treatments? This perspective motivates a comparison between individuals near realized treatment locations and individuals near counterfactual (unrealized) candidate locations, which is distinct from current empirical practice. I derive standard errors based on this design-based perspective that are straightforward to compute irrespective of spatial correlations in outcomes. Furthermore, I propose machine learning methods to find counterfactual candidate locations and show how to apply the proposed methods on observational data. I study the causal effects of grocery stores on foot traffic to nearby businesses during COVID-19 shelter-in-place policies. I find a substantial positive effect at a very short distance. Correctly accounting for possible effect "interference" between grocery stores located close to one another is of first order importance when calculating standard errors in this application. The second chapter is co-authored with B. Douglas Bernheim, Daniel Björkegren, and Jeffrey Naecker. We explore methods for inferring the causal effects of treatments on choices by combining data on real choices with hypothetical evaluations. We propose a class of estimators, identify conditions under which they yield consistent estimates, and derive their asymptotic distributions. The approach is applicable in settings where standard methods cannot be used (e.g., due to the absence of helpful instruments, or because the treatment has not been implemented). It can recover heterogeneous treatment effects more comprehensively, and can improve precision. We provide proof of concept using data generated in a laboratory experiment and through a field application. The final chapter is co-authored with Susan Athey, Peter J. Bickel, Aiyou Chen, and Guido W. Imbens. We develop new semiparametric methods for estimating treatment effects. We focus on a setting where the outcome distributions may be heavy-tailed, where treatment effects are small, where sample sizes are large and where assignment is completely random. This setting is of particular interest in recent experimentation in tech companies. We propose using parametric models for the treatment effects, as opposed to parametric models for the full outcome distributions. This leads to semiparametric models for the outcome distributions. We derive the semiparametric efficiency bound for this setting, and propose efficient estimators. In the case with a constant treatment effect one of the proposed estimators has an interesting interpretation as a weighted average of quantile treatment effects, with the weights proportional to (minus) the second derivative of the log of the density of the potential outcomes. Our analysis also results in an extension of Huber's model and trimmed mean to include asymmetry and a simplified condition on linear combinations of order statistics, which may be of independent interest

Keywords: Economics.
Advisor: Imbens Guido
Bernheim B. Douglas
Spiess Jann