Objective: I want to test the effect of a regulatory change using a classical pre-post/treatment-control DiD design (Y = POST + TREAT + POSTxTREAT + e).
Problem: Treatment & control obs. are from different countries. Although these countries are similar with respect to many relevant aspects, a visual check of the parallel trend assumption for the outcome variable in the pre-period (only 3 years) indicates different time trends.
Sample details: time period is 2002-2007, event happened in 2005. Treatment obs. 200/year (1200 total), control obs. ~ 100 obs./year (600 total). Obs. over time belong to the same subjects (300 subjects).
Does it make sense to use propensity-score matching based on determinants of the outcome variable in the pre-period to create a more homogenous treatment/control sample (and hopefully get rid of the different trends)?
What would be the advantage over simply controlling for the determinants used in the PSM in the DiD regression? (e.g., Y = POST + TREAT + POSTxTREAT + CONTROLS + e)
I thought of using one-on-one matching with a caliper. However, I have more treatment obs. than control obs. – are there any better ways to avoid losing too many of my obs.?
PS: I'm using Stata.