Causal Inference, Instrumental Variables, Stats 361, Stanford, Data Science.
β_0is the outcome without treatment and β_1is the additional effect by treatment. That is, E[Y|A] = E[Y|A=1] — E[Y|A=0] = (β_0 + β_1) — β_0 = β1 It can be expressed in a graph as follows: Figure 1. The image of ATE in binary treatment (KRSK, 2018) However, if there is endogenous bias (i.e. there