Synthetic control with gradual (not staggered) adoption

[Emil Alnor]

I am trying to estimate the effect of a university teaching reform on the wage outcome of the universities students. I have wage data on all the students from the university and a set of universities which did not adopt the teaching reform, which makes them my control group.

My challenge in using the synthetic control method is, that there is not a single year which consitutes a "cut-off" point, i.e., before that year the treated university did not at all adopt the teaching reform and after that year the university 100% adopted the teaching reform. This is because the implementation was a gradual process which took years to be completed fully. In a DiD setup I suppose I could work around this by making the treatment variable continous and then saying, for example that the reform was 0% (treated==0) implemented in 2007, 20% (treated==0.2) implemented in 2008, 40% (treated==0.4) implemented in 2009 and so on - or simply not use the years where the reform was only gradually implemented. However, as far as I know, this is not possible in the synthetic control method (e.g. the help file of -synth- specifies that for the option trperiod "Only a single number can be specified".).

Can anyone point me in the direction of how to take account of the fact that real life reforms are often gradually implemented when using the synthetic control method? In other words: The synthetic control methods has been developed in cases where different units adopt the treatment at different periods, but what about cases where the treatment-unit is treated at various degrees going from 0 to 1 in different period?

[Jared Greathouse]

There are good people working on this exact subject right now, but I'm not even sure if R has this available or even Python.

So here is what I would do if I were you: I would use my command scul (ssc inst scul) to model the impact of the treatment at the 100% intervention point (say 2015), and then use the plat option to do in time placebos.

So let's say the reform was at 90% in 2014, you'd use the in time placebos to model the impact at that time, and 80% for 2013, and so on and so forth for each increase of the intervention. It isn't perfect mind you, but it's the very best solution i can think of right now.

[Emil Alnor]

There are good people working on this exact subject right now, but I'm not even sure if R has this available or even Python.

So here is what I would do if I were you: I would use my command scul (ssc inst scul) to model the impact of the treatment at the 100% intervention point (say 2015), and then use the plat option to do in time placebos.

So let's say the reform was at 90% in 2014, you'd use the in time placebos to model the impact at that time, and 80% for 2013, and so on and so forth for each increase of the intervention. It isn't perfect mind you, but it's the very best solution i can think of right now.

Interesting, do you know of any working paper or presentation or the work, which I can look into?

That could be a solution. Just to clarify: Would your suggestion then be to use the in time placebos to see if there was smaller effect, when the treatment time were set at 2014, even smaller at 2013 and so on?

[Jared Greathouse]

Yes. You can read my paper here which goes over the theoretical econometrics as well as scul's applications in numerous circumstances. You can of course email me if you've any questions.