Question

2. We want to investigate the degree how cummulative GPA for each student (GPA) is affected by the peers. This is based on the general belief that students in a group of students with higher GPA are likely to have higher GPA. The model is: GPA= Bo + B avg Peer GPA + Byability + u. where avg PeerGPA is the average GPA for the peer students and ability is a student's own ability We assume that this equation satisfies the Gauss-Markov assumptions. Let's suppose that high ability students form a group with students who have similar high ability. What do you expect the sign of bias in B, obtained from the simple linear regression of GPA on avg PeerGPA? Explain.

Answer 1

High ability students pick other students with higher ability. Higher ability translates to higher GPA. If everyone in the peer group has higher ability, it means that the average GPA of the peer group is also very high.

Therefore, there is a positive correlation between ability and average peer GPA.

Average peer GPA has a positive effect on GPA and it is positively correlated with ability. Therefore, an increase in average peer GPA is accompanied by an increase in ability.

Keeping this in mind, if we run a simple OLS regression of GPA only on average peer GPA, we will have omitted variable bias.

The coefficient of average peer GPA will not only capture the effects of movements in average peer GPA but also the effects of movements in ability. Thus, the coefficient will be higher than it would have otherwise been.

Thus, there is an upward bias.