Causal Inference with Longitudinal Data: Moving Beyond Difference-in-Difference

Difference-in-Difference is a widely used method in health policy and health services research for estimating a causal effect. Unfortunately, the validity of difference-in-difference is difficult to evaluate without a tool to directly assess the parallel trends assumption. For example, existing tools indirectly examine the parallel trends assumption using pre-treatment observations. Developments in the methodological literature have given rise to an alternative class of estimators -- Synthetic Controls -- that do not make the parallel trends assumption and to sensitivity analysis tools that provide a novel approach for directly evaluating the parallel trends assumptionThe first chapter of this dissertation develops guidelines for the use of synthetic control methods alongside difference-in-difference. Synthetic control methods are a valuable tool because they don't assume parallel trends; however, they are not without assumptions of their own. This chapter provides guidance for the utilization of synthetic controls and difference-in-difference and proposes several post-estimation validity analyses to further evaluate the assumptions made by each method.The second chapter examines the effect of Medicaid Expansion on State Medicaid spending. The analysis is done using a subset of states among which the parallel trends assumptions is tenuous. Using a kernel-balanced synthetic control, and the post-estimation analyses introduced in the first chapter, this paper shows no evidence for Medicaid Expansion increasing or decreasing State Medicaid spending over a three-year period.The third chapter extends a suite of sensitivity tools for estimating the sensitivity of difference-in-difference to unobserved time-varying confounders -- parallel trends violations. The tools utilize the explanatory power of observed covariates to estimate how strong unobserved confounders must be to change the conclusions. They not only relax the strict binary nature of classic indirect parallel trends tests but also utilize the post-period outcome data to directly examine the parallel trends assumption