I have a panel data (21 years) and I am trying to figure out whether I should use regression discontinuity design (RDD) or panel cointegration. I do have a randomness in the assignment variable and so I don't have any problem using the RDD; I can examine the causality (local average treatment effect). My questions are: first, why one should use RDD over the panel cointegration; second how can the causality from the RDD be linked with the Granger causality resulting from the panel cointegration (assuming that there is the cointegration and hence it is possible to estimate the vector error correction model). As far as I understand, when you have assignment variable and that variable is random, you always use RDD (although it is possible to use panel cointegration), but if you don't have an assignment variable and that variable is not random or if you don't have an assignment variable, then you proceed with the panel cointegration. I would really appreciate if you could let me know whether my understanding is correct. Please suggest the papers if possible. Note that my dependent variable is in growth form (e.g. growth of wealth)in RDD, but if I have to use panel cointegration, I will have dependent variable in level form for long run and in growth form for short run.
Example: Let's suppose, I have a binary variable (treat) and the dependent variable is y. There are two different approaches in RDD: non parametric and parametric approach. In parametric approach, we use all observations and then the coefficient on the treat is called as causal effect (we can also use other control variables) .
In cointegration approach, we use all observations and we can examine the long run relationship between treat and y (plus other variables). However, the concern here is that variable treat is binary while other variables (dependent and control variables) are continuous. I test all continuous variables and found to be integrated of order 1. But, I am not sure whether it is to test for the unit root of variable treat (binary variable). Does it make any sense?. This is important before we decide to use cointegration since it should all varaibles should be integrated of order 1. How do I incorporate the varaible treat in the cointegration? How can I then compare the results of cointegration and RDD?