Essays in Econometrics

Abstract

This dissertation consists of three essays in econometrics. A common throughline is decision theory, defined here broadly as the formal considerations justifying, informing, or undermining choices of statistical procedures. The first chapter proposes a new interpretation of synthetic control methods as instances of online convex optimization algorithms. Viewed in a certain way, synthetic control methods implement an algorithm called Follow-The-Leader. Mathematical guarantees of Follow-The-Leader then translate into new guarantees for synthetic control. Specifically, over long time horizons, synthetic control methods predict almost as well as the best weighted average of untreated units chosen ex post. The second chapter proposes new empirical Bayes methods that improve statistical decision- making. It shows that conventional empirical Bayes methods embed an assumption called prior independence; this assumption frequently fails to hold; and imposing this assumption incorrectly can harm the performance of standard empirical Bayes methods. Motivated by these observations, the chapter proposes new empirical Bayes methods and proves some new decision-theoretic guarantees. The third chapter is a paper co-authored with Jonathan Roth. Empirical researchers frequently want to estimate some causal effect in terms of the log transformation of their outcome variables. However, when the outcome variable can take the value zero, its log is not well-defined. In such situations, empirical researchers often resort to certain “logarithm-like” transformations that are defined at zero and continue to interpret results as approximate log or percentage effects. We show that such interpretations are inappropriate. We also show that there exists no estimand satisfying certain desirable properties simultaneously, and one has to forgo at least one of these properties.