I was using full matching (using MatchIt, method = "full") to estimate the ATE. Now I want to extend this to examine a moderation effect by a categorical variable. I am fitting separate propensity score models within each moderator subgroup, and setting the estimand to ATE as well. I am getting quite high weights in separate groups (maximum of 22 in 1 group and 15 in the other - which as I understand is a way high), as well as relatively low ESS. I tried to apply calipers, which did help to improve the max weights (subgroup 1: 22.4 → 13.2; subgroup 2: 14.8 → 8.0) and ESS (subgroup 1: 74 → 111; subgroup 2: 93 → 156), balance was also mainly improved. It led to discarding 20 out of 275 observations in one subgroup and 6 out of 251 in the other. As I understand the result may not anymore correspond to the ATE. After applying the calipers I am targeting slightly different populations, correct? How reasonable it is then to compare these subgroup estimates in order to draw conclusions about moderation in this case? any additional diagnostics I should try? should I avoid calipers in moderation at all?

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