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Marginal structural models are a popular tool for investigating the effectsof time-varying treatments, but they require an assumption of no unobservedconfounders between the treatment and outcome. With observational data, thisassumption may be difficult to maintain, and in studies with panel data, manyresearchers use fixed effects models to purge the data of time-constantunmeasured confounding. Unfortunately, traditional linear fixed effects modelsare not suitable for estimating the effects of time-varying treatments, sincethey can only estimate lagged effects under implausible assumptions. To resolvethis tension, we a propose a novel inverse probability of treatment weightingestimator with propensity-score fixed effects to adjust for time-constantunmeasured confounding in marginal structural models of fixed-length treatmenthistories. We show that these estimators are consistent and asymptoticallynormal when the number of units and time periods grow at a similar rate. Unliketraditional fixed effect models, this approach works even when the outcome isonly measured at a single point in time as is common in marginal structuralmodels. We apply these methods to estimating the effect of negative advertisingon the electoral success of candidates for statewide offices in the UnitedStates.

Adjusting for Unmeasured Confounding in Marginal Structural Models with Propensity-Score Fixed Effects