Let there be a policy $T$ which can either be implemented or not implemented by an organisation. Suppose there are $n$ organisations and the outcome variable $Y$.
The policy is not centrally imposed- different organisations have adopted the policy on their own will at different points in time. Which suggests that there is a significant possibility of self-selection bias.
I wanted to know if there is any technique to find out if such a policy is effective or not.
I have read about Difference-in-Difference and Discontinuous Regression-- but as far as I have understood-- they need a policy implemented at a particular point in time, and two groups, one of which is treated and the other is not.
In my case, there are two groups-- one that is treated and one that is not treated, but the time of implementation is different for different organisations.
I may be unclear, so I present a simplistic example. Suppose there are 6 firms A, B, C, D, E and F, having all walls in their respective offices white or green. The $Y$ variable of interest to me is the total productivity of employees (suppose I have a way to measure that perfectly) for example.
In the beginning (suppose in the year 2000) all the firms had white walls. Then in 2003, firms C and E changed to green. Then in 2005 firm B also changed to green. The other firms have not made any changes till now (say, 2010).
I have the employee productivity data (monthly) of all the five firms from 2000 to 2010 and also the data of when they switched from white to green.
Is their any method to find out if green walls have any advantage over white walls with this data? I am aware of the possible self selection bias (maybe the firms decide to change to green when they see an unusual drop in productivity etc.) Is there any way to overcome this and evaluate if the policy of switching to green works?
If yes, where can I read more about it, the assumptions, how to test them, then how to actually conduct the analysis using software etc.