Table 5:

Methods for Identifying and Estimating Causal Effects from Observational Data

		Allowing for Unobserved Selection?
		No*	Yes
Systematically Modeling Treatment Effect Heterogeneity?	No	regression adjustment, matching, IPW, etc.	IV, RD design, fixed effects models, etc.
	Yes	$\mathbb{E}\left(Y_1-Y_0\mid X=x\right)$, $\mathbb{E}\left(Y_1-Y_0\mid P=p\right)$	MTE(x, u), $\widetilde{MTE}(p,u)$

Note: IV=Instrumental Variables, RD=Regression Discontinuity, IPW = Inverse Probability Weighting, MTE=Marginal Treatment Effect.

^*When there is unobserved selection by treatment effect but not by the baseline outcome, matching and weighting methods can still be used to consistently estimate TT (but not ATE).