Telescope Matching for Reducing Model Dependence in the Estimation of the Effects of Time-Varying Treatments: An Application to Negative Advertising
提出一种两步匹配方法（望远镜匹配），用于估计两期时变处理的效应，减少模型依赖性，并以美国选举中负面广告对投票率和得票率的影响为例进行说明。
Abstract Time-varying treatments are prevalent in the social sciences. For example, a political campaign might decide to air attack ads against an opponent, but this decision to go negative will impact polling and, thus, future campaign strategy. If an analyst naively applies methods for point exposures to estimate the effect of earlier treatments, this would lead to post-treatment bias. Several existing methods can adjust for this type of time-varying confounding, but they typically rely on strong modelling assumptions. In this paper, we propose a novel two-step matching procedure for estimating the effect of two-period treatments. This method, telescope matching, reduces model dependence without inducing post-treatment bias by using matching with replacement to impute missing counterfactual outcomes. It then employs flexible regression models to correct for bias induced by imperfect matches. We derive the asymptotic properties of the telescope matching estimator and provide a consistent estimator for its variance. We illustrate telescope matching by investigating the effect of negative campaigning in US Senate and gubernatorial elections. Using the method, we uncover a positive effect on turnout of negative ads early in a campaign and a negative effect of early negativity on vote shares.