Telescope Matching : Reducing Model Dependence in the Estimation of 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. Direct effect analyses, which estimate the effect of a treatment not due to some mediator, have become increasingly popular in the social sciences for a wide variety of inferential targets, including understanding the causalmechanisms of a treatment. Standardmatching analyses, however, are not directly applicable to direct effect analyses because of their tendency to induce post-treatment bias, and so almost all applications 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 in a flexible manner and relies on regression models to correct for bias induced by imperfect matches. We show in simulations that our approach is more robust to misspecification of these regression models than non-matching estimators. We derive the asymptotic properties of this estimator and provide a consistent estimator for its variance. Finally, we apply this approach to estimating the direct effect of a job training program on long-term mental health not due to employment and show that it can generate substantively different inferences than standard approaches. *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 ‡University of Pennsylvania Law School, 3501 Sansom Street, Philadelphia, PA 19104, web: https://www.antonstrezhnev.com/ email: astrezhn@law.upenn.edu

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