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(Potential outcomes and causal effect)
Consider the following table that shows the potential wages of Rahul and Shelby if they had gone to college and if they had not gone to college. Di = 1 if i did go to college, and 0 otherwise. Yi denotes wages of i, and the rest of the notation corresponds to the textbook and class notes (e.g., Y0i is the wage of i if they didn't go to college). Rahul Shelby Y0i 10 25 Y1i 20 45 Di 0 1 Yi 10 45
a. What is the causal effect of going to college on Rahul's wages?
b. What is the causal effect of going to college on Shelby's wages?
c. What is the average causal effect?
d. Is there a difference between the potential wages of Rahul and Shelby when neither goes to college? If yes, what might be the potential causes of this difference? If no, why do you think there's no difference?
e. What is the difference between the observed wages of Rahul and Shelby? Decompose this difference into the true causal effect for Shelby and the se- lection bias.
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