Relative novice here. I am running a regression in an observational setting in which Y is the outcome and D is the treatment indicator. Observations are drawn from 3 different geographic groups designated by X. Is the proper approach to:
- Regress Y on D and cluster the standard errors by group.
- Regress Y on X and D.
- Regress Y on X and D and cluster the standard errors by group.
When pursuing option #3 I am seeing much higher statistical significance -- and I'm worried somehow that including both dummies and the clustering in a cross-sectional setting is problematic.
In principle, what are the tradeoffs between the 3 approaches? Which is most likely to offer an unbiased estimate of the treatment effect D (assuming other covariates -- not included here -- are balanced between the 2 groups)?