How to combine difference in difference with propensity score matching and NN matching

[Stefano Scibilia]

Dear Statalisters,

I am running a difference in difference and I was wondering what should I code in order to do a DID on a matched sample
I have 1000 observation recorded for 3 years, 2 pre-treatment and 1 post-treatment.
Production is my outcome treatgroup my treatment, this is my standard DID:

 xtreg prod treatgroup##i.year capital_per_worker graduates lprod if year==2014 | year==2015, fe

in order to match it, I am using change_prod that stands for the change in production between 2014 and 2015 with lagged covariates from 2014. Should I use a similar change variable for time variant covariates as well? is the following code doing DID matching?

teffects nnmatch (change_prod lagged_age lagged_capital lagged_graduates industry) (treatgroup) if year==2015, ematch(industry lagged_age) biasadj(lagged_capital lagged_graduates) atet nneighbor(1) vce(iid)

I am quite perplexed since the results is very different from the non-matched DID and the Screened DID (more than double in magnitude).
meanwhile if I code

teffects nnmatch (change_prod lagged_age lagged_capital lagged_graduates industry) ( treatgroup ), ematch (industry lagged_age) biasadj (lagged_capital lagged_graduates) atet nneighbor (1) vce (iid)

without year==2015 I get more reasonable results, but in this way, I am using 2013 data also! and what about PSM? is it correct to perform it like this?

teffects psmatch (change_p) (treatg lage lcap lgrad industry, logit) if year==2015, atet nneighbor(1)

I am quite lost, thank you for your attention.