What matching method for Propensity Score Matching

Dear Statalister,

This if my first post so please forgive any etiquette mistakes...

I'm trying to figure what matching method to use for my study.

I'm using Stata/IC 14.0, and the user-written program psmatch2

I have a large dataset (68 000 treated, 1 500 000 untreated). For the characteristics I'm controlling for, there is not much bias (age, gender, geographical distribution, month...).

I would prefer matching without replacement (easier to explain the procedure and calculations to an average audience). When I do that, my untreated group has the exact same characteristics as my treated group, which is nice.

But I still feel it's a shame to loose the information from all these other untreated observations.

I understand psmatch2 cannot perform matching without replacement with multiples neighbors.

Would you rather oversample the untreated group with replacement, or perform a 1:1 matching without replacement ?

Thanks in advance,

Léon-Paul Schwab