Structural Nested Mean Models Under Parallel Trends Assumptions
This paper addresses the disconnect between structural nested mean models (SNMMs) and dynamic difference-in-differences (DiD) in estimating time-varying treatment effects. We propose a novel SNMM framework grounded in the parallel trends assumption—departing from the conventional no-unmeasured-confounding assumption. We establish, for the first time, that SNMMs achieve nonparametric identification under parallel trends alone. The framework unifies estimation of dynamic treatment effects, sustained-intervention effects, direct effect decomposition, and optimal dynamic treatment regimes. Additionally, we develop a sensitivity analysis method to assess robustness when parallel trends are violated. Integrating dynamic causal inference with sequential decision-making modeling, our approach is validated through empirical applications—including Medicaid expansion, flood insurance adoption, and temperature impacts on crop yields—demonstrating its validity and robustness in real-world policy and environmental settings.