![]() We do this by estimating the coefficients in the control group alone. A closed-form locally semiparametric efficient estimator is obtained in the simple case of binary IV and outcome and the efficiency bound is derived for the more general case.Ĭounterfactuals Double robustness Effect of treatment on the treated Instrumental variable Unmeasured confounding. Average Treatment Effect on the Treated We illustrate now how to estimate the average treatment effect on the treated in a way that is quite robust. For inference, we propose three different semiparametric approaches: (i) inverse probability weighting (IPW), (ii) outcome regression (OR), and (iii) doubly robust (DR) estimation, which is consistent if either (i) or (ii) is consistent, but not necessarily both. It’s no coincidence that this is the average of Alfred’s and Chizue’s treatment effects, ( 1 + 3) / 2 2. In this paper, we present a novel framework for identification and inference using an IV for the marginal average treatment effect amongst the treated (ETT) in the presence of unmeasured confounding. We can see in Table 10.3 that we get an average of ( 2 + 5) / 2 3.5 among the treated people, and ( 1 + 2) / 2 1.5 among the untreated people, giving us an effect of 3.5 1.5 2. The instrumental variable (IV) design plays the role of a quasi-experimental handle since the IV is associated with the treatment and only affects the outcome through the treatment. In observational studies, treatments are typically not randomized and therefore estimated treatment effects may be subject to confounding bias. ![]()
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