Primary Submission Category: Difference in Differences
Structural Nested Mean Models Under Parallel Trends Assumptions
Authors: Zach Shahn, Oliver Dukes, David Richardson, Eric Tchetgen Tchetgen,
Presenting Author: James Robins*
We link and extend two approaches to estimating time-varying treatment effects on repeated outcomes–time-varying Difference in Differences (DiD) and Structural Nested Mean Models (SNMMs). In particular, we show that SNMMs, which were previously only known to be nonparametrically identified under a no unobserved confounding assumption, are also identified under a generalized version of the parallel trends assumption typically used to justify time-varying DiD methods. Because SNMMs model a broader set of causal estimands, our results allow practitioners of existing time-varying DiD approaches to address additional
substantive questions (such as characterization of time-varying effect heterogeneity, estimation of the lasting effects of a blip of treatment at a single time point, controlled direct effects, and others) under similar assumptions. Further, while some common time-varying DiD approaches are restricted to staggered adoption settings in which a binary treatment is permanently sustained once initiated, SNMMs straightforwardly accommodate potentially multivariate treatments with continuous and discrete components and arbitrary treatment patterns. We also identify optimal dynamic treatment regimes under parallel trends plus the extra assumption that unobserved confounders are not effect modifiers. Finally, using SNMMs to estimate the same effects under alternative identifying conditions can potentially enable triangulation of evidence.