A researcher wants to study the effect of a Careers course in college on a graduate's wage at the first job out of college. The Careers course teaches students about resume-writing, attending job fairs, interviews, and finding internships. With the approval of her Colleges' Internal Review Board (IRB) and the support of her Dean, she sets out to do an experiment. She will randomly a group of 120 Seniors and send them an email invitation to enroll in the Careers course. Only these students will be permitted to enroll in the Careers course for this year. She randomly selects another 120 Seniors to form the control group. This group will not be invited nor permitted to enrolling the Careers course. She plans to collect data on the 240 Seniors, including their GPA, major, age, first-generation college student status, financial aid recipient, and so on. She will also follow up with these students about 6 months after their graduation and collect their employment status and wage.

1. Since students in the treatment group have the option to take the course or not, the researcher needs to use Instrumental Variables regression to estimate the treatment effect. Write out the two regressions needed to complete the two-state-least-squares process described inInstrumental Variables Regression.
2. When the researcher follows up, some of the 240 seniors my not respond. This representsattrition. How could the researcher check to see whether this attritionmight bias the estimated treatment effect of the Careers course?
3. Some of the students in the treatment group might withdraw from the Careers course sometime after enrolling. This presentspartial compliance. How could the researcher mitigate the bias that partial compliance might introduce regarding the estimate of the treatment effect?