Telescope Matching: Reducing Model Dependence in the Estimation of Controlled Direct Effects

Matching methods are widely used to reduce the dependence of causal inferences on modeling assumptions, but their application has been mostly limited to the overall effect of a single treatment. The controlled direct effect, which is the effect of a treatment fixing some mediator, has become an increasingly popular estimand in the social and biomedical sciences. Standard matching analyses, however, are not directly applicable to the estimation of this quantity because of their tendency to induce post-treatment bias, and so almost all applications that estimate these effects are dependent on the correct specification of several models. In this paper, we propose a novel two-step matching approach to estimating direct effects, telescope matching, that reduces model dependence without inducing post-treatment bias. This method uses matching with replacement to impute missing counterfactual outcomes and then employs flexible regression models to correct for bias induced by imperfect matches. We derive the asymptotic properties of this estimator and provide a consistent estimator for its variance. We apply this approach to estimate the effectiveness of a job training program on health fixing the value of post-training employment. *Thanks toAlberto Abadie, Paul Kellstedt, Gary King, Jamie Robins, Jann Spiess, and Yiqing Xu for valuable feedback and discussions. Any remaining errors are our own. Software to implement the methods in this paper will be found in the DirectEffects R package on CRAN. †Department of Government and Institute for Quantitative Social Science, Harvard University, 1737 Cambridge St, ma 02138. web: http://www.mattblackwell.org email: mblackwell@gov.harvard.edu ‡New York University, 60 5th Ave, New York, NY 10011, web: https://www.antonstrezhnev.com/ email: as6672@nyu.edu

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