1. You are interested in the effect teaching has on student performance. You run
ID: 3297525 • Letter: 1
Question
1. You are interested in the effect teaching has on student performance. You run the fol-
lowing experiment on a randomly selected sample of UGA undergrads. 200 participants
are evenly split according to random assignment into groups Z = 1 and Z = 0. All
participants in group Z = 1 are given the option to receive free weekly teaching for the
entire semester. All participants in group Z = 0 are given the option to purchase weekly
teaching for the entire semester at a cost of $500. At the end of the semester you collect
information on actual teaching choices and GPA.
(a) Is this experiment designed to estimate the effect a teacher has on the GPA of an
average UGA undergrad? Support your answer.
(b) At the end of the semester you calculate the following numbers. Among the Z = 1
group, 75 individuals chose the teaching and 25 did not, and the average GPA was
3.5. Among the Z = 0 group, 25 individuals chose the teaching and 75 did not, and
the average GPA was 3.0. What is the local average treatment effect of teaching
on GPA? Describe in words what this number means.
(c) How many individuals in group Z = 0 needed to choose the teaching option for
you to be able to estimate the ATT? Explain.
(d) In addition to part (c), how many individuals in group Z = 1 need to choose the
teaching option for you to be able to estimate the ATE? Explain.
Explanation / Answer
(a) No.The given experiment will not adequately measure the effect a teacher has on the GPA score of an average UGA Undergrad because it is limited by the fact that the students in group Z=1 have an "option" to receive teaching and thus not necessarily every student in the group is taking up the option of receiving the help of a teacher so, we cannot say that every student in group Z=1 have received teaching. On the other hand, in the group Z=0, the students can still receive teaching if they are willing to pay $500, thus considering a situation in which every student pays up $500 and chooses to receive the teaching there will not be enough difference between the two groups to asses the effect of teaching on the GPA score of the undergrad student. In this situation it will become hard to estimate the treatment effect of teaching for the whole population.
(b) We have the following table:
So, the local average treatment effect of teaching on GPA is given by:
LATE=(3.5-3.0)/0.75 = 0.6667
*The LATE can be estimated by dividing the Intent to treat estimate (which is the difference in the GPA scores) by the share of compliers.Difference in the average outcomes between those intended to be treated and those intended to be untreated gives you the Intent to Treat Effect on the Treated (ITT).
LATE here shows what is the local effect of the treatment on the compliers, i.e the people who were assigned to the treatment and choose to receive it. The LATE is the average of the unit level causal effect for the compliers.
(c)ATT is basically the average unit causal effect for the people who were treated.In order to compute the ATT we need to find the the average of the people who were treated i.e the average GPA score of the students who received teaching in both the groups.
(d)To calculate the ATE we need to use the formula ATE=0.5CATE + 0.5CATE. Here, CATE is the conditional average treatment effect of the two groups and since we have same proportion of people assigned to both groups we use 0.5. Thats going to give us an estimate of the ATE.
Assigned to treatment Assigned to control Average GPA 3.5 3.0 Never Takers 25 25 Compliers 75 75Related Questions
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