Randomized Intervention and endogeneity across outcomes

Question

Community,

I am looking for a proper identification strategy for a specific question which I want to answer with my data and was wondering whether anybody here would have an advise on that.

My data structure is the following:

2010: Baseline data collection

2011: Randomized intervention (Treatment and Control Group)

2012: Follow-up data collection

So far, I estimated the difference in difference for three outcome variables and the results are significant. From theory I know, that these three outcome variables are interdependent, though. My question now is, whether there is a way to identify the size or direction of causality between the three outcome variables. E.g. I would like to be able to test whether the treatment affected outcome 1, 2, and 3 independently, or whether the treatment effected outcomes 1 and 2 and this change in outcomes 1 and 2 affected outcome 3, for instance.

It seems to me that just using a plain IV strategy (e.g. using the treatment variable as instrument for outcome 1 to see what's the effect on outcome 3) would not be appropriate as the exclusion criteria is obviously not fulfilled.

Any advise on what would be the correct way to estimate this would be very much appreciated.

Thanks a lot Julianne

Answer 1

What you're trying to do is called mediation analysis. For example, the case of "the treatment effected outcomes 1 and 2 and this change in outcomes 1 and 2 affected outcome 3" would be described as outcomes 1 and 2 mediating the effect of the treatment on outcome 3. Entire textbooks have been written on mediation, but the Wikipedia article is a good place to start.