Suppose Mark is analyzing an RCT randomizing the introduction of a oneon-one after-school tutoring program (T) on test scores (Y) for students in a certain school in a certain developing country. The tutoring program takes place every day and is randomized at the individual level. Because this is an RCT, he would usually run Y N T + E to determine the causal impact ofT through its coefcient. However, he remembers from doing eldwork in that country that gender (G) is highly determinant on outcome; in particular, a widespread phenomenon is that girls are often required to stay at home to help with housework instead of attending school on several days of the week. Thus he argues he must run Y N T + G + 5' to avoid omitted variable bias in estimating the average effect of T. However, Mark is told by Prof. Duflo that since the sample size is very large, it usually shouldn't matter which specication he uses. What does she mean? 0 For a randomized experiment, G is uncorrelated with Y in expectation (it has a small coefficient in the "long" model). 0 For a randomized experiment, G is uncorrelated with T in expectation For the same randomized experiment, under what circumstances does Y ~ T + G + & control possible bias in the vanilla specification Y ~ T + E? As mentioned in the previous question, controlling for G via Y ~ T + G + & is never necessary. O If in the particular sample, G and T are "accidentally" correlated (i.e. a low probability event occurs), e.g. somehow more boys were assigned to the tutoring program than girls in the randomized assignment