I am working on this issue that compares two regions with the McCrary Test (Regression Discontinuity Design). It basically measures how the density of a variable of interest develops accross a pre set cut off point. In my case, we talk about density of businesses (y) and how this develops accros a geographic border [distance in m] (x). The result of the test is the log difference at the pre set cut off point. This value we call theta.
Now I have measured theta for two instances. Now I want to subtract these effect from each other (to illimate possible placebo effect). However, the question is how do I subtract these from each other and especially how do I calculate the new Standard Error and p-value (significance)
These are the results: (Standard Error in parentheses)
Test 1: 0.6298 (0.1614)
Test 2: -0.4667 (0.1048)
Net effect = Test 1 - Test 2 = 0.6298 + 0.4667 = 1.0965
Theta = 1.0965
SE = ?????