What are the main methods for estimating the Average Treatment Effect in Observational Studies outside of matching? I am wondering what the main methods for estimating the Average Treatment Effect in Observational Studies are outside of matching. In matching, there are weighting, stratification, propensity score methods, etc. However, are there techniques outside of this? Or are they all based on same way on matching?
 A: There is a separate class of techniques that use observational data but that leverage some specific aspect of the setting to "almost" (in a very vague sense) have an experimental setting. These are often called "quasi-experimental" settings, with two common techniques being difference in differences or instrumental variable (IV) techniques.
More generally, in any observational study where you're interested in some average treatment effect, you have some data and you impose assumptions to get a treatment effect. In experimental settings, the assumptions come for free: random assignment of treatment often gets you all you need. In observational settings, you need to instead assume something similar, and all these techniques are various assumptions that get you to where you need to be. As a researcher, you need to determine what assumptions are reasonable to impose. All the methods you define basically assume that treatment is random conditional on covariates. But this need not be true in the presence of unobserved factors. See this question for a more detailed answer about this specific point.
Finally, see this question for some more information about techniques outside of matching, and in particular check out the link provided in the comments to that question about other "techniques", which I also am linking here.
