Intention to treat: Recall the imaginary example in Section 9.8.1 in which students were randomly provided vouchers to defray the cost of attending a private school. In the text, we imagined that the...

Intention to treat: Recall the imaginary example in Section 9.8.1 in which students were randomly provided vouchers to defray the cost of attending a private school. In the text, we imagined that the researchers want to determine the effect of private versus public school attendance on academic achievement, and straightforward estimation of this effect is compromised by the fact that some students who received a voucher did not attend a private school, and some who did not receive a voucher nevertheless did attend a private school. We dealt with this problem by using provision of a voucher as an instrumental variable. How, if at all, would the situation change if the goal of the research were to determine the effect on achievement of providing a voucher rather than the effect of actually attending a private school? From a social-policy perspective, why might provision of a voucher be the explanatory variable of more direct interest? This kind of analysis is termed intention to treat.