We conducted 4 sets of simulations in order to assess power and bias for subsample IV estimators. In order to assess how power varies according to the size of the subsample (simulation 1), we varied nX from 25 to 10,000 and βXY from 0 to 0.3, with nY set to 10,000 and the first-stage R2 set to 0.025. In order to assess how IV strength affects power (simulation 2), we varied nX from 25 to 10,000 and the first-stage R2 from 0.002 to 0.05, with nY set to 10,000 and βXY set to 0.2. In order to assess bias when IVs are weak (simulation 3), we varied the nX:nY ratio from 0.1 (a small subsample) to 1.0 (the complete-data scenario) and varied the average first-stage F statistic from approximately 1 to approximately 20, with βXY set to 0.1. Varying of F was accomplished as follows: For each nX:nY ratio, the first-stage R2 was held constant (to a value that produced an average first-stage F of 20 when nY = 10,000) and nY was varied from 100 to 10,000, with the
