I am running Coarsened Exact Matching (CEM) on a highly unbalanced panel data (with 26 periods: 13 pre-shock and 13 post-shock), for a diff-in-diff analysis with fixed effect.
1. Is it flawed if I match treated and control groups in *both* pre & post shock periods (rather than just pre-shock periods) with a set of covariates?
2. In general, I force Stata to use the non-coarsened version of period *period(#0)* in my CEM command, so the matching occurs exactly within each period of the panel. Obviously, individual A may be matched with B in t1, but with C in t2. Does it sound fine?
3. After dropping unmatched observations, may I use my diff-in-diff analysis without using the weights. Meaning, I use CEM just to make the control and treated groups comparable (reducing the noise).

Many thanks