I have cross-sectional data on firms between 2001 and 2017. The intervention occurred sometime during 2012. Each firm appears in the sample only once, so the firms before the intervention differ from those after the intervention. I have a treatment dummy and a time dummy and my interest is obviously in the interaction term. I also have covariates.

I have several outcome variables which are computed over a 4-year rolling window from t-4 to t-1 and then used at time t. So, for example, the outcome variable for a given firm in 2005 is computed based on data from 2001 to 2004. Similarly, the outcome variable for a given firm in 2006 is computed from data from 2002 to 2005. So, effectively, my pre-intervention sample used in the difference-in-differences analysis consists of firms between 2005 and 2011 (although, theoretically, I am using data from 2001 onward to construct the outcome variable). I do the same for the post-intervention period. To allow for the same 4-year rolling window, the outcome variable for a given firm in 2016 is computed from data from 2012 to 2015 (I am aware that the intervention occurs sometime in 2012, so I have to ensure that I am capturing the period after the intervention). As a result, my post-intervention sample consists of firms in 2016 and 2017. I have also tried shortening the window to even as low as one year prior which obviously increases the sample before and after the intervention with qualitatively similar results.

Assuming that I have made myself reasonably clear above, are there any issues with the above construct? Is anyone aware of papers that do something similar? Are there other things I can do, given that the outcome variables are computed based on prior data?