Difference-in-Differences with Aggregated Data I have access to aggregated data of a population for a 1,5 year period. I am interested in conducting an events study to check whether the implementation of a certain treatment will affect the behavior of my subjects.
Since i do not have individual level data can i conduct a Diff in Diff analysis?
If yes, could I set a certain time period, observe the alterations in the population's values there and use that as my Control Group? Then, I could take the same time period in terms of length after the implementation of the treatment and observe the population's differences there.
In other words can I create a CG and TG from the same population just by varying the time periods?
I apologize for the simplicity of my question but I have not cleared this in my head yet.
Thank you.
 A: If I am correctly understanding your description of the data then the answer is no. 
To use Differences in Differences (DID) you need: 1.) a group that receives treatment and a group that does not; 2.) a time period before treatment and a time period after treatment for both groups. 
Lets say our outcome is $Y_{g,t}$ with $g$ indexing whether you are the treatment group and $t$ indexing the time period. Thus $Y_{g=1, t=0}$ would denote the outcome for the treated group in the time period before treatment. The estimator is then simply $DID = [Y_{g=1, t=1} - Y_{g=1, t=0}] - [Y_{g=0, t=1} - Y_{g=0, t=0}]$. 
In a silly toy description: I want to know if eating an ice-cream makes me gain weight. Since only I will eat the ice cream my wife is the control. I start out weighing 180 ($Y_{g=1, t=0} = 180$), and my wife starts out a slim 400 ($Y_{g=0, t=0} = 400$). After I eat an ice cream, we both weigh ourselves and my wife is now 420 ($Y_{g=0, t=1}=420$) and I am now 210 ($Y_{g=1, t=1}=210$). Thus the DID estimator of the effect is $[210 - 180] - [420-400] = 30-20=10$. The interpretation would thus be that the ice cream caused me to gain 10, and in the counter-factual state of the world in which I did not eat ice-cream I would have weighed a mere 200. 
If I understand your description of your data, you have pre- and post-treatment observations, but you do not have some units that are treated and some that are not, thus DID would not be appropriate.
