Quiz 8

Total Points; 4

We will continue with the example used for last week’s quiz. The paper examined the effect of attending a flagship university on long-term earnings. The authors utilized a regression discontinuity design by looking at students right above and right below the SAT cutoff for each school.

1. What would be the basic regression equation for this research question, assuming the slopes before and after the cutoff remain the same? Where cutoff is a variable that takes the value of 1 if after the cutoff and 0 otherwise.
1. $Earnings = \alpha + \delta(Cutoff) + \beta(SAT-Cutoff)$
2. $Earnings = \alpha + \delta(Cutoff) + \beta(SAT\times Cutoff)$
3. $Earnings = \alpha + \delta(Cutoff *SAT) + \beta(SAT-Cutoff)$
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Answer
2. What would our regression look like if we thought the relationship between SAT scores and earnings differed before and after the cutoff?
1. $Earnings = \alpha + \delta(Cutoff) + \beta_1(SAT-Cutoff) +\beta_2(SAT-Cutoff)\times Cutoff))$
2. $Earnings = \alpha + \delta(Cutoff) +\beta_2(SAT-Cutoff)\times Cutoff))$
3. $Earnings = \alpha + \delta(Cutoff) + \beta_1(SAT-Cutoff)$
4. $Earnings = \alpha + \delta(Cutoff) + \beta_1(SAT-Cutoff) +\beta_2(SAT-Cutoff)+Cutoff))$
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Answer
3. You run the following regression in Stata: reg earnings cutoff sat_co sat_co#cutoff

Where earnings in annual earnings in dollars, the cutoff is your indicator variable, and sat_co is your running variable normalized to 0 at the cutoff. If you are above the cutoff (Cutoff=1), you are eligible to attend the flagship school in your state. You get the following results:

earnings	Coef.	std. err.
cutoff	232.43	110.21
sat_co	-5.21	3.59
sat_co#cutoff	7.82	5.56
constant	130.45	54.6

Which of the following statements would be an accurate regression interpretation of the results?

1. Being eligible to attend a flagship school results in a $7.82 increase in annual earnings (for those above and below the cutoff).
2. Attending a flagship school increases your annual earnings by $232.43.
3. Being eligible to attend a flagship school decreases your annual earnings by $5.21
4. Being eligible to attend a flagship school results in a $232.43 increase in annual earnings for those above and below the cutoff.
5. Before the cutoff, a one-point increase in your SAT score is associated with a $5.21 decrease in annual earnings.
6. Before the cutoff, a one-point increase in your SAT score is associated with a $7.82 increase in annual earnings.
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Answer
4. You graph a scatterplot and see the underlying data has a non-linear shape. What term(s) would we add to account for different, non-linear slopes?

a.

b.

c. $Earnings = \alpha + \delta(Cutoff) + \beta_1(SAT-Cutoff) +\beta_2((SAT-Cutoff)*Cutoff)) + \beta_3(SAT-Cutoff)^2 + \beta_4((SAT-Cutoff)^2*(Cutoff))$

d. $Earnings = \alpha + \delta(Cutoff) + \beta_1(SAT-Cutoff) +\beta_2(SAT-Cutoff)^2*Cutoff)) + \beta_3(Cutoff)^2 + \beta_4((SAT-Cutoff)*(Cutoff)^2)$