Primary Submission Category: Difference in Differences
Marginal Structural Nested Mean Models Under Parallel Trends
Authors: Zach Shahn, Oliver Dukes, James Robins, Andrea Rotnitzky,
Presenting Author: Zach Shahn*
Suppose an investigator conducting a DiD analysis is interested in modeling effect heterogeneity as a function of only a subset of the adjustment variables required to satisfy conditional parallel trends. Abadie (2005) proposed an estimator for the parameter of such a marginal effect heterogeneity model in the point exposure setting. Using marginal Structural Nested Mean Models (mSNMMs), we provide a doubly robust and efficient estimator of this parameter under the same assumptions, and also generalize the problem to the time-varying setting. We thus enable DiD practitioners to model heterogeneity of time-varying treatment effects as a function of a low dimensional time-varying covariate even when the adjustment set is large. For example, we use mSNMMs to estimate how effects of Medicaid expansion vary with eligibility thresholds at time of expansion, while adjusting for demographic variables. Modeling lower dimensional effect modification reduces the risk of serious model misspecification and can improve interpretability. In the special case when the effect modifiers of interest are the empty set, mSNMMs target similar estimands to the host of other recently developed and widely used time-varying DiD methods, but with certain advantages. For example, under conditional parallel trends assumptions for dynamic regimes, mSNMMs can identify effects of sustained treatment regimes even when treatment switches on and off in the data, a source of consternation in the DiD literature.