1. Suppose you are interested in the causal effect of taking a test prep course on a student's SAT score. (The SAT is a test which is often used by universities in the U.S. to help determine admission decisions.) The following table shows the potential SAT scores for Amanda and Filipe if they had taken the course and if they had not taken the course. Y₁ denotes the actual SAT score for person i, D, is an indicator for whether person i took the course, and the potential outcome notation is the same as used in the class notes. Y² Y₁ Amanda 1180 1220 1180 0 Felipe 1120 1230 1230 1 a. What is the causal effect of taking the course on Amanda's SAT score? What is the causal effect of taking the course for Felipe? b. What is the average treatment effect (ATE) for this population of two students? c. What is the average effect of treatment on the treated (ATT) for this population of two students? d. Suppose you only have access to the variables Y and D₁. What is the observed difference in SAT scores between Felipe and Amanda? Decompose this difference into the true causal effect of taking the course for Felipe and the selection bias.

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1. Suppose you are interested in the causal effect of taking a test prep course on a student's SAT
score. (The SAT is a test which is often used by universities in the U.S. to help determine
admission decisions.) The following table shows the potential SAT scores for Amanda and Filipe
if they had taken the course and if they had not taken the course. Y denotes the actual SAT score
for person i, D, is an indicator for whether person i took the course, and the potential outcome
notation is the same as used in the class notes.
Y₁
Y₁
Amanda
1180
1220
1180
0
Felipe
1120
1230
1230
1
a. What is the causal effect of taking the course on Amanda's SAT score? What is the causal
effect of taking the course for Felipe?
b. What is the average treatment effect (ATE) for this population of two students?
c. What is the average effect of treatment on the treated (ATT) for this population of two
students?
d. Suppose you only have access to the variables Y and D₁. What is the observed difference in
SAT scores between Felipe and Amanda? Decompose this difference into the true causal effect
of taking the course for Felipe and the selection bias.
Transcribed Image Text:1. Suppose you are interested in the causal effect of taking a test prep course on a student's SAT score. (The SAT is a test which is often used by universities in the U.S. to help determine admission decisions.) The following table shows the potential SAT scores for Amanda and Filipe if they had taken the course and if they had not taken the course. Y denotes the actual SAT score for person i, D, is an indicator for whether person i took the course, and the potential outcome notation is the same as used in the class notes. Y₁ Y₁ Amanda 1180 1220 1180 0 Felipe 1120 1230 1230 1 a. What is the causal effect of taking the course on Amanda's SAT score? What is the causal effect of taking the course for Felipe? b. What is the average treatment effect (ATE) for this population of two students? c. What is the average effect of treatment on the treated (ATT) for this population of two students? d. Suppose you only have access to the variables Y and D₁. What is the observed difference in SAT scores between Felipe and Amanda? Decompose this difference into the true causal effect of taking the course for Felipe and the selection bias.
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