Hi

I'm writing a paper evaluation a public school reform in Denmark.
Since all the students got the reform, my control group is other european counties using PISA-data (standardized test).

To analyse the reform effect i use Difference in difference, estimation difference in developments before and after the reform. Since some students i Denmark has left the public school (to go to private school), and other students have joined (due to law of inclusion) the population is changed from before and after treatment.

I want to correct for this by matching the danish pretreatment with the post treatment both in Denmark and europe.
I've found a paper using Difference in Difference with matching, that shows two steps. The idea is to match the people from the treated group, pretreatment with respondents form three other groups (1:Treated group after treatment, 2: untreated group before AND 3: after)

1: Run two propensity scores (treatment and time, respectively) on X.

2: Match individuals with a variant of nearrest neighbors caliper matching with replacement bt pairring each treated respondent with a respondent in each comparison group. The respondents in each comparison group is chosen to minimiaze the euclidean distance from the treated individuals two estimated propensity scores, given the restrictions on the maximum allowable distance (the caliper) as well as common support.

And here comes my question. How can i matching on two propensity scores in three different groups?