The effect of political advertising after Citizens United : adjusting for unmeasured confounding in marginal structural models

Corporations, unions, and other interest groups have become key sponsors of television advertising in US elections after the Supreme Court’s decision in Citizens United v. FEC that eliminated restrictions on such spending. This paper estimates the partisan effects of ads sponsored by these groups to obtain a more complete picture of voter behaviour and electoral politics. Advertising strategies vary over the course of the campaign, making marginal structural models a natural tool for this setting. Unfortunately, this approach requires an assumption of no unobserved confounders between the treatment and outcome, which may not be plausible with observational electoral data. We propose a novel weighting estimator with propensity-score fixed effects to adjust for time-constant unmeasured confounding in marginal structural models of fixed-length treatment histories. This estimator is 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 in our setting. Against conventional wisdom, we find interest group ads are only effective when run by Democratic groups, and these effects are most prominent after Donald Trump became a presidential candidate in 2015.