Corollary 2. Suppose Assumptions 1, 4 to 7, 10 and 11 hold and Y (a) ⊥ G | S(a), U, X. Then Equation (11) in Theorem 1, Equation (15) in Theorem 2 and Equation (16) in Theorem 3 all identify the average long-term treatment effect over the experimental **data** distribution, i.e.,
τ E = E [Y (1) − Y (0) | G = E] ,
In Corollary 2, we still assume the weaker conditions in Assumptions 10 and 11. But we additionally require that the experimental and observational **data** share a common conditional distribution of the potential long-term outcome. This additional assumption ensures that the bridge functions defined in terms of the observational **data** distribution can also be used to identify the average long-term treatment effect over the experimental **data** distribution.