Suppose I run a regression discontinuity design (RDD) for two different samples - say, separately for regions A and B of the same country. I get RDD estimates that are statistically significant in each separate test. Now, I would like to show that these estimates are indeed different from each other.
What is the most appropriate way of showing that the RDD coefficients of the two regions are indeed different? Is it sufficient to just take the difference in the estimates of the two samples and use some appropriate standard error - in this case, which one should I choose?