A little technical note on how correlation in regressors, which can be measured, can sometimes provide guidance in choosing what kind of standard error to use: correlation_in_x110217
This is pretty much straight Moulton factor (why is there no Wikipedia entry on Moulton factor to link to?). I still need to reconcile this stuff with what I had shown a few months ago about how the Moulton factor leads to the wrong conclusion in the context of correlated potential outcomes, even if treatment assignment is at the unit level (yes, I said unit level, not cluster level). For a refresher on that, see here: link1 link2. A big difference in the document that is attached to this post is that we are looking at a vanilla “constant effects” set-up, whereas the potential outcomes stuff was agnostic on unit-by-unit differences in effect sizes.
