Repeated cross-sectional difference-in-difference with panel data on each of the 4 DiD-groups (pre/post treated/control)

[Emil Alnor]

Hi all,

I am trying to estimate the effect of a university teaching reform on the wage of its graduates. I have panel data from 2003-2017 on all university students in the same country. The university under consideration started implementing the reform in 2009, and the reform can be assummed to have no effect on graduates from 2007, 2008 and 2009, and to have an effect on graduates from 2012, 2013 and 2014. I don't consider graduates from 2010 and 2011 in my analysis since their treatment status is unclear.

My data looks something like this:

* Example generated by -dataex-. For more info, type help dataex
clear
input byte(id treated university year degree degreeyear male) int(wage wage1 wage2 wage3 wage4)
1 . 1  6 0  . 1    0    .    .    .    .
1 . 1  7 0  . 1    0    .    .    .    .
1 0 1  8 1  8 1    0    .    .    .    .
1 0 .  9 1  8 1 2000 2000    .    .    .
1 0 . 10 1  8 1 3000    . 3000    .    .
1 0 . 11 1  8 1 3500    .    . 3500    .
1 0 . 12 1  8 1 4000    .    .    . 4000
1 0 . 13 1  8 1 4000    .    .    .    .
1 0 . 14 1  8 1 5000    .    .    .    .
1 0 . 15 1  8 1 5000    .    .    .    .
1 0 . 16 1  8 1 5000    .    .    .    .
1 0 . 17 1  8 1 5000    .    .    .    .
2 . 2  6 0  . 0    0    .    .    .    .
2 0 2  7 1  . 0    0    .    .    .    .
2 0 .  8 1  . 0 2200 2200    .    .    .
2 0 .  9 1  . 0 2300    . 2300    .    .
2 0 . 10 1  . 0 2400    .    . 2400    .
2 0 . 11 1 11 0 2500    .    .    . 2500
2 0 . 12 1 11 0 2600    .    .    .    .
2 0 . 13 1 11 0 2700    .    .    .    .
2 0 . 14 1 11 0 2800    .    .    .    .
2 0 . 15 1 11 0 2900    .    .    .    .
2 0 . 16 1 11 0 3000    .    .    .    .
2 0 . 17 1 11 0 3000    .    .    .    .
3 . .  6 0  . 1    0    .    .    .    .
3 . .  7 0  . 1    0    .    .    .    .
3 . .  8 0  . 1    0    .    .    .    .
3 . .  9 0  . 1    0    .    .    .    .
3 . 1 10 0  . 1    0    .    .    .    .
3 . 1 11 0  . 1    0    .    .    .    .
3 . 1 12 0  . 1    0    .    .    .    .
3 1 1 13 1 13 1    0    .    .    .    .
3 1 . 14 1 13 1 4000 4000    .    .    .
3 1 . 15 1 13 1 4200    . 4200    .    .
3 1 . 16 1 13 1 4400    .    . 4400    .
3 1 . 17 1 13 1 4600    .    .    . 4600
4 . .  6 0  . 0 4800    .    .    .    .
4 . .  7 0  . 0    0    .    .    .    .
4 . .  8 0  . 0    0    .    .    .    .
4 . .  9 0  . 0    0    .    .    .    .
4 . 1 10 0  . 0    0    .    .    .    .
4 . 1 11 0  . 0    0    .    .    .    .
4 . 1 12 0  . 0    0    .    .    .    .
4 . 1 13 0  . 0    0    .    .    .    .
4 0 1 14 1 14 0 3800    .    .    .    .
4 0 . 15 1 14 0 4100    .    .    .    .
4 0 . 16 1 14 0 4400    .    .    .    .
4 0 . 17 1 14 0 4700    .    .    .    .
end

In the difference in difference terminology I have data on four groups:
- Pre-treatment treated: Graduates from the university which implemented the reform before the reform was implemented. In my data: university 1, from the years 2007-2009.
- Pre-treatment control: Graduates from universities which did not implement the reform before the reform was implemented. For the sake of simplicity I just show one other university in the dataexample below and call that university 2.
- Post-treatment treated: Graduates from university 1 after reform implementation (years 2012-2014)
- Post-treatment control: Graduates from university 2 after reform implementation (years 2012-2014)

I plan on using propensity score matching difference in difference. My data is panel data, but in the sense that the pre-treatment and post-treatment individuals are different, the data is included in the DiD-analysis as repeated cross-sectional. However, within each of the four groups I have panel data on the course of their wage development after their graduation.

So simply having the wage e.g. four years after graduation (wage4) as the outcome variable:

 didregress (wage4) (treated), group(university) time(year)

…would not utilize all the information I have in my dataset. I have a sense that there is a better way to perform the analysis than suggested in my code above, i.e., better in the sense of utilizing all the available information, but I don't know how. So can anyone inform me on how I can take advantage of the fact that I have panel data on each of the four groups even though the pre- and post-treatment groups are different individuals?

[Emil Alnor]

No one has any idea here? One solution that I came up with is to compute the means of the universities (then the pre- and post-treatment units would be the same), and then I could use synthetic control method instead, but this would "lose" a lot of observations since I go from some 300 observations pr. university to just 1 observation pr. university.

Edit: Asked the question on Cross-validated: https://stats.stackexchange.com/ques...on-each-of-the