Quiz 4

Total Points: 15

1. In response to the pandemic, a school district implemented an extended-school year pilot for a handful of the schools in the district. The idea for having more school days is to see if this helps improve many educational outcomes. For now, we will be focused on how it improves test scores. You want to measure if the effect of this pilot differed for students in the top half and bottom half of the class (at baseline). You run the following regression:
$$(1)\ \ TestScore = \alpha + \beta_1Extended + \beta_2TopHalf + \beta_3(Extended \times TopHalf)$$

Where test score is a student’s test score in points, $Extended$ is a binary variable for whether a student attended a school with an extended year or not, and $TopHalf$ is a binary variable for if a student was in the top half of their class at the beginning of the year. Select all that apply (T/F):

1. $\beta_2$ is the marginal effect of the extended-year model on test scores for students in the top half of their class.
2. $\alpha$ is the average test score for students in the bottom half of their class who did not attend an extended-year school.
3. $\beta_3$ is the difference in the marginal effect of the extended-year model on test scores between students in the top half and students in the bottom half of their class.
4. $\alpha$ + $\beta_1$ is the average test score for students in the bottom half of their classes who attended an extended-year model.
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5. Before running your interaction regression on the differing effects of an extended school year above, you ran the following two regressions:
$$(2)\ \ TestScore = \gamma_1 + \gamma_2Extended \; \: if \: TopHalf==1 \\ (3)\ \ TestScore = \delta_1 + \delta_2Extended \; \: if \: Tophalf==0$$

The following expression uses coefficients from equations (2) and (3), which of the following expressions recovers $\beta_3$ from equation (1)?

1. $(\gamma_1 + \gamma_2)-(\delta_1 + \delta_2)$
2. $\gamma_2 - \delta_2$
3. $\gamma_1 - \delta_1$
4. $\gamma_2\times\delta_2$
5. None of the above
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6. You run the following regression:
$$LifeExpectancy_i = 55 + 7.2_1GDP_i - 1.8GDP_i^2 + 4.4HealthExpenditures+\epsilon_i$$
1. Life expectancy will be maximized when GDP = 0.5
2. Life expectancy will be maximized when GDP = 2
3. Life expectancy will be minimized when GDP = 2
4. Life expectancy will be minimized when GDP = 0.5
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4. You run the following regression. Income is in thousands of dollars, Voucher represents whether or not someone received a housing voucher, Black is a dummy variable for whether or not someone is Black, and the rest are dummy variables for the region. Select all that apply

$$Income = \alpha + \delta voucher + \beta_1Black +\beta_5SouthRegion+\beta_6Northwest+\beta_7Midwest + \epsilon$$

Which of the following is an appropriate interpretation of the coefficient on Black?

1. $\beta_1$ tells us the change in income associated with being black, netting out the effects of receiving a voucher and region.
2. $\beta_1$ tells us the change in income for black individuals who have received a housing voucher.
3. $\beta_1$ tell us the marginal effect of being black, holding everything constant.
4. $\beta_1$ tells us the marginal effect of being black and having a voucher on income, netting out the effects of region.

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