  Marginal structural models are a popular tool for investigating the effects
of time-varying treatments, but they require an assumption of no unobserved
confounders between the treatment and outcome. With observational data, this
assumption may be difficult to maintain, and in studies with panel data, many
researchers use fixed effects models to purge the data of time-constant
unmeasured confounding. Unfortunately, traditional linear fixed effects models
are not suitable for estimating the effects of time-varying treatments, since
they can only estimate lagged effects under implausible assumptions. To resolve
this tension, we a propose a novel inverse probability of treatment weighting
estimator with propensity-score fixed effects to adjust for time-constant
unmeasured confounding in marginal structural models of fixed-length treatment
histories. We show that these estimators are consistent and asymptotically
normal when the number of units and time periods grow at a similar rate. Unlike
traditional fixed effect models, this approach works even when the outcome is
only measured at a single point in time as is common in marginal structural
models. We apply these methods to estimating the effect of negative advertising
on the electoral success of candidates for statewide offices in the United
States.
