Conditioning on Post-treatment Quantities with Structural Mean Models∗

In this paper, I demonstrate how structural mean models (SMMs) can be used to estimate quantities based on post-treatment variables. SMMs are semiparametric models where the parameters of the model or models correspond to meaningful functions of expected potential outcomes for subjects actually exposed to the treatment. SMMs provide a flexible framework for estimating causal effects with noncompliance even with binary outcomes. More widely used methods such as two-stage least square impose stronger distributional assumptions on the data. Next, I show how SMMs can be used to estimate treatment effect modification by a post-treatment variable. Often an intermediate variable between treatment and outcome may alter the causal effect. Effect modification of the type can be easily accommodated in the SMM framework. I demonstrate the utility of SMMs with applications to the get-out-the-vote literature.