I have a longitudinal data set of individuals and some of them were subject to a treatment and others were not. All individuals are in the sample from birth until age 18 and the treatment happens at some age in between that range. The age of the treatment may differ across cases. Using propensity score matching I would like to match treated and control units in pairs with exact matching on the year of birth such that I can track each pair from their birthyear until age 18. All in all there are about 150 treated and 4000 untreated individuals. After the matching the idea is to use a difference-in-differences strategy to estimate the effect of the treatment.
The problem I face at the moment is to do the matching with panel data. I am using Stata's
psmatch2 command and I match on household and individual characteristics using propensity score matching. In general with panel data there will be different optimal matches at each age. As an example: if A is treated, B and C are controls, and all of them were born in 1980, then A and B may be matched in 1980 at age 0 whilst A and C are matched in 1981 at age 1 and so on. Also A may be matched with its own pre-treatment values from previous years.
To get around this issue, I took the average of all time-varying variables such that the matching can identify individuals who are on average the most similar over the duration of the sample and I do the matching separately for each age group 0 to 18. Unfortunately this still matches a different control unit to each treated unit per age group.
If someone could direct me towards a method to do pairwise matching with panel data in Stata this would be very much appreciated.