Quiz 5

Question 1

A university is piloting a mentorship program to support first-year students. The program assigns upperclassmen mentors to a random group of freshmen to see if this improves their GPA. You want to analyze whether the effect of mentorship differs for students who had a high school GPA in the top half versus the bottom half of their incoming class. You run the following regression:

GPA = αα + β1β1Mentorship + β2β2Top-Half + β3β3(Mentorship * Top-Half) + ϵϵ

Where GPA is the student’s first-year college GPA, Mentorship is a binary variable indicating whether a student participated in the mentorship program, and Top-Half is a binary variable indicating if a student had a high school GPA in the top half of their class. Select all that apply (T/F):

Question 1.1

α + β1 is the average GPA for students in the bottom half of their incoming class who participated in the mentorship program.

True or false?

Question 1.2

β2 is the marginal effect of the mentorship program on GPA for students in the top half of their incoming class.

True or false?

Question 1.3

β3 is the difference in the marginal effect of the mentorship program on GPA between students in the top half and bottom half of their incoming class.

True or false?

Question 1.4

β1 + β3 is the marginal effect of the mentorship program on GPA for students in the top half of their incoming class.

True or false?

Question 1.5

α is the average GPA for students in the bottom half of their incoming class who did not participate in the mentorship program.

True or false?

Question 2

Before running your interaction regression on the different effects of the mentorship program (1), you ran the following two regressions (2 & 3).

(1) GPA = α + β1Mentorship + β2Top-Half + β3(Mentorship * Top-Half) + ϵ (2) GPA = θ1 + θ2Mentorship if Top-Half==1 (3) GPA = ρ1 + ρ2Mentorship if Top-Half==0

The following expressions use coefficients from equations (2) and (3). Which of the following expressions recovers β2 from equation 1?

1. θ1 – ρ1
2. θ2 – ρ2
3. ρ1 – θ1
4. ρ2 – θ2

Question 3

Before running your interaction regression on the different effects of the mentorship program (1), you ran the following two regressions (2 & 3).

(1) GPA = α + β1Mentorship + β2Top-Half + β3β3(Mentorship * Top-Half) + ϵϵ (2) GPA = θ1 + θ2Mentorship if Top-Half==1 (3) GPA = ρ1 + ρ2Mentorship if Top-Half==0

The following expressions use coefficients from equations (2) and (3). Which of the following expressions recovers β3 from equation 1?

1. ρ1 – θ1
2. ρ2 – θ2
3. θ1 – ρ1
4. θ2 – ρ2

Question 4

Which of the following is true about instrumental variables? Select all that apply.

1. The instrument incites an endogenous variation on our exogenous variable D.
2. The instrument should only affect the outcome Y through D.
3. To implement the IV strategy, you divide the First Stage by the Reduced Form Stage to obtain the LATE.
4. The relevance assumption is the only assumption you can directly test.

Question 5

A researcher is studying the impact of hours of private tutoring on student test scores. However, they suspect that the number of hours a student spends in tutoring is endogenous—it might be correlated with unobserved factors like parental motivation or a student’s prior academic ability, which could also influence test scores.

To address this, the researcher uses a government subsidy program that provides free tutoring vouchers to randomly selected students. Because the subsidy is assigned randomly and does not directly affect test scores other than through its impact on tutoring hours, the researcher believes it can be used as an instrumental variable (IV) for tutoring hours.

Question 5.1

What is the outcome variable in this study?

1. Number of hours of private tutoring
2. Government subsidy status
3. Student test scores
4. Parental motivation

Question 5.2

What is the explanatory variable D?

1. Number of hours of private tutoring
2. Student test scores
3. Government subsidy status
4. School funding

Question 5.3

What is the instrumental variable?

1. Number of hours of private tutoring
2. Government subsidy status
3. Student test scores
4. Student’s prior academic ability