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I am facing some challenges using the DID.I have around 500 Items off which 100 are test and its very difficult to find a control group for DID, so I used PSM to find control group using nearest method. Now there are chances that the control group may not follow parallel trend assumption then how am I supposed to do post(by implementing DID). Am I doing it right? And what variable should i use for post, should it be propensity score?

Thanks you

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You can do a standard DID in your propensity score-matched group. The point of matching is to provide robustness against the potential violation of the parallel trends assumption. Once you've done the matching, the propensity score is irrelevant. There may be additional doubly robust approaches to further provide robustness to violations of the parallel trends assumption, but I think matching with DID is standard practice.

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  • $\begingroup$ Thanks for your comment Noah. The post treatment in DID is all about comparing the changes in outcomes over time between a population that is enrolled in a program (the intervention group) and a population that is not (the control group). And if the control group which I found using propensity score doesn't follow parallel trend or if it's not even close enough to test, then how can i do the post. mailman.columbia.edu/research/population-health-methods/…. $\endgroup$
    – Nivas
    Commented Mar 14, 2019 at 20:26
  • $\begingroup$ Are you assessing the parallel trends assumption by using several pre-intervention time periods and seeing that the pre-intervention trends are not parallel? If so, then your matching has failed and you should try another method of matching or otherwise equating the groups to ensure the pre-intervention trends looks the same. Entropy balancing is a good and simple way to do this. $\endgroup$
    – Noah
    Commented Mar 14, 2019 at 23:24
  • $\begingroup$ Yes, you are correct. I am trying to see if my control group satisfies the parallel trend of treatment group for pre-intervention so that I can use DID in post . Thanks for your suggestion Noah , I will try to use Entropy balancing . So do you think, Entropy balancing can be used to find better control group which will most likely satisfy/match with treatment group in pre-intervention time periods. $\endgroup$
    – Nivas
    Commented Mar 15, 2019 at 0:28
  • $\begingroup$ Yes, entropy balancing guarantees exact balance on all the covariates you request balance on. The problems with it are that it will fail if the problem is infeasible (i.e., it's impossible to achieve exact balance) and in some cases, the effective sample size of the balanced samples is very small and your standard errors become huge. One solution is approximate balancing, such as by using the R package optweight (which I wrote), but there hasn't been much written about this method and none of it in the context of DID. $\endgroup$
    – Noah
    Commented Mar 16, 2019 at 4:47

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