Effect estimation after exact matching in MatchIt I am performing exact matching on a set of continuous and categorical covariates. Once the matched (via MatchIt) is performed, I use logistic regression to estimate the effect of my treatment variable on a binary outcome. At this stage, I include all the covariates used in the matching procedure, as I want to isolate the underlying effect of the treatment as much as possible even when perfect balance has been achieved (please correct me if this is a wrong choice).
However, I have a doubt regarding the estimation procedure.
Do I mandatorily need to include weights estimated in the matching step, as weights in the glm model? When I do so, the estimates change a bit compared to the models without weights.
Thanks in advance for your help!

If you use glm estimation that uses all the relevant covariates, you don't "have to" use matching at all, let alone include the weights in the model estimation.
But if you do, you can make your results more robust against possible misspecification of the model (your glm model might not be perfectly adequate). This is the whole point of the paper:

Ho, Daniel E., Kosuke Imai, Gary King, and Elizabeth A. Stuart. 2007. “Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference.” Political Analysis 15 (3): 199–236.

Furthermore, including the weights from the matching into the regression can reduce the variance and bias of the estimate.
