It seems that in economics, matching techniques (such as pscore, covariate matching, regression adjustment) are not as popular as selection-on-unobservables techniques (such as DiD, IV).
Indeed I recently had a paper rejected by one referee on the basis that "no-one uses matching these days".
If that's true then, why? In some case it's not possible to come up with a natural experiment or perfect instrument to tease out treatment effects, and so matching strikes me as attractive.
It's not true that "no-one uses matching these days". It's a bit too definitive. For example, see Bilicka (2019) who recently published in the American Economic Review. I am sure it's possible to find other recent examples.
It's true however that the matching estimator is much less popular than the DiD or IV. This is because the results are not always consistent and robust across estimators. They sometimes differ depending on the estimator used (propensity score matching, PSM, or nearest neighbor matching, NNM) and the way in which the treatment and control groups are matched. It is also sometimes difficult to obtain matched samples that are as comparable as those in Bilicka's paper (see her Table 1).
As an example, there is a well know controversy in the Journal of Econometrics, involving Rajeev Dehejia, Jeffrey Smith and Petra Todd.
My recommendations would be
Good luck with your resubmission!
