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There are various matching procedures in the causal inference literature, from exact matching to propensity score matching and more. The goal is usually to find the Average Treatment Effect (ATE). Most literature seem to encourage the researcher to add as many covariates as they can that they think would influence the outcomes. This is to reduce the confounding bias.

However, I am wondering if there are cases where matching on more covariates would result in more bias. In other words, are there scenarios where removing covariates to match on gives a better estimate of the ATE? Thanks.

user321627
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1 Answers1

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I am wondering if there are cases where matching on more covariates would result in more bias.

Yes, there are several cases where matching on more covariates can result in more bias. First let's consider the cases where the covariates you are matching on are not confounders, as in the examples given here.

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In all these examples, matching on those covariates ($Z$ in the first and second cases, and $M$ in the third case) would induce bias where none existed.

But even when the matching covariates are in fact confounders, this can still increase bias. One case is the following: imagine you have measured some confounders, but there are still unmeasured confounders you did not account for. If the measured confounders and unmeasured confounders are acting in different directions (and perhaps attenuating each other), matching on the observed confounders may increase bias.

Carlos Cinelli
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