Topics in Causal Inference and the Law

Abstract

Randomized experiments are a fundamental tool for estimating the causal effects of proposed interventions. While analysis of some experiments can be quite straightforward, other experiments may present difficult analytical choices. For a variety of reasons, causal inference problems may call for complex modeling of the potential outcomes by, for example, posing a likelihood function and a prior distribution on a parameter vector. Additionally, analytical challenges might arise when the randomized treatment assignments are not obeyed (i.e. when there is "noncompliance"), particularly when there is substantial missing data about whether the units complied with their assignments. After a brief introduction in Chapter 1, Chapter 2 investigates the consequences of model misspecification in model-based Bayesian causal inference settings via a full factorial simulation experiment. We use Bayesian evaluation criteria for evaluating the severity of the misspecification. We find that posterior inferences are particularly sensitive to a failure to adequately transform the outcome variable, especially in conjunction with a poor choice of prior distribution. Chapter 3 develops a methodology for analyzing experiments with two-way noncompliance when there is substantial missing data about whether units took the treatment to which they were assigned. We validate this methodology with simulation studies and apply it to a randomized evaluation of Philadelphia divorce court. The results of this analysis, we argue, suggest that Philadelphia divorce court procedures are unconstitutional under the Due Process Clause of the Fourteenth Amendment.