论文信息 - Functional Restriction and Efficiency in Causal Inference

Functional Restriction and Efficiency in Causal Inference

1 2 X p 2 pU 2 0 X p 2 1 pU U 2 pU p 2 X U 2 pU 2 p 2 , respectively, where 0(X) E(Y0X), 1(X) E(Y1X), (X) 1(X) 0(X), (U) E((X)U), 1 (X) E({Y1 1(X)} 2 X), 0 (X) E({Y0 0(X)} 2 X), and p Pr(Di 1). PROOF. See Appendix, sections 1 and 2. These bounds can be compared with the asymptotic variance bounds computed without imposing the exclusion restriction on the propensity score:

Jinyong Hahn | J. Hahn

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