A researcher is interested in identifying and estimating the causal effect of conc usage on venereal disease at the high school level. The researcher uses a simple model to determine the effectiveness of condom usage on reducing sexually transmitted diseases among sexually active high school students (1) infrate=Bo+B1conuse+B2percmale +B3avginc+B4city+u1, where infrate is the percent of sexually active students who have contracted venereal disease, conuse is the percentage of boys who claim to regularly use condoms, avginc is average family income, and city is a dummy variable indicatin whether a school is in a city; the model is at the school level. The city has randor gifted free condoms in high schools to students. Denote Z as the fraction of stuc that accepted the condom gift at the school level. If Z is highly related statisticall with conuse then it could be used as since its random assignment would ensure that it is an instrumental variable; a redundant variable in equation (1) O an instrumental variable; a relevant variable in equation (1) Oa proxy variable: a redundant variable in equation (1) O control variable; a relevant yariable in eguation (1)

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