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Suppose I use propensity score matching to select a sample of treatment and control subjects from a larger population for a follow-up survey. Assuming I matched subjects using the full range of p-scores, and assuming I matched on all observables and that unobservables were not a problem: would my estimates of impact be equivalent to an Average Treatment Effect or an Average Treatment Effect on the Treated?

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Typical K:1 matching in which K control units are matched to a single treated unit each estimates the ATT. This is because the distribution of covariates in the matched sample is similar to that of the treated group.

There are ways of estimating the ATE using matching, but they differ somewhat from the method I described. You can perform matching imputation, which is what the R package Matching and Stata teffects psmatch do, which involves imputing the missing potential outcomes for members of both groups based on matching close units from the other group. You can also perform full matching on the propensity score, after which you can compute matching weights that target the ATE. This can be done in the MatchIt package.

Also note that if calipers are used or if a common support or exact matching constraint causes you to discard treated units, the estimand is neither the ATE nor ATT but rather an undefined estimand.

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  • $\begingroup$ thanks so much for your reply. I have read all your posts closely, and greatly value your insights! Just to clarify: if treated units are "discarded" in the process of sampling using PSM, but the final sample (treated and control) appear to be representative of the overall population (based on pre-treatment covariates) - then is it not possible that we are estimating the ATE? $\endgroup$
    – Tanya99
    Commented Dec 7, 2020 at 9:53
  • $\begingroup$ Thank you for the kind words! It is possible, and that is exactly the motivation for template matching as described by Bennett et al. (2020). It is just quite unlikely with PS matching. $\endgroup$
    – Noah
    Commented Dec 7, 2020 at 21:47
  • $\begingroup$ thanks for the reference! $\endgroup$
    – Tanya99
    Commented Dec 8, 2020 at 11:11

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