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. 2013 Jul 17;178(7):1177–1184. doi: 10.1093/aje/kwt084

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© The Author 2013. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health.

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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Figure 2. — Power (left) and median standard error (right) of the subsample instrumental-variable (IV) estimate for different values of the first-stage R² and the sample size of the first-stage regression (n_X), with a constant effect size (β_XY = 0.2), a sample size for the reduced-form regression (n_Y) of 10,000, and a confounding variable with equal effects on X and Y (β_UX = β_UY = 0.2). First-stage R² values are 0.002 (filled diamond), 0.004 (open diamond), 0.007 (filled triangle), 0.01 (open triangle), 0.0015 (filled square), 0.2 (open square), 0.03 (filled circle), and 0.05 (open circle).