4️⃣

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:
      2. (1)  TestScore=α+β1Extended+β2TopHalf+β3(Extended×TopHalf)(1)\ \ TestScore = \alpha + \beta_1Extended + \beta_2TopHalf + \beta_3(Extended \times TopHalf)

      Where test score is a student’s test score in points, ExtendedExtended is a binary variable for whether a student attended a school with an extended year or not, and TopHalfTopHalf 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. β2\beta_2 is the marginal effect of the extended-year model on test scores for students in the top half of their class.
    2. α\alpha is the average test score for students in the bottom half of their class who did not attend an extended-year school.
    3. β3\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. α\alpha + β1\beta_1 is the average test score for students in the bottom half of their classes who attended an extended-year model.
      5. ‣
      Answer

      b, c, d

    5. Before running your interaction regression on the differing effects of an extended school year above, you ran the following two regressions:
        6. (2)  TestScore=γ1+γ2Extended   if TopHalf==1(3)  TestScore=δ1+δ2Extended   if Tophalf==0(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 β3\beta_3 from equation (1)?

      1. (γ1+γ2)−(δ1+δ2)(\gamma_1 + \gamma_2)-(\delta_1 + \delta_2)
      2. γ2−δ2\gamma_2 - \delta_2
      3. γ1−δ1\gamma_1 - \delta_1
      4. γ2×δ2\gamma_2\times\delta_2
      5. None of the above
        6. ‣
        Answer

        b

    6. You run the following regression:
        7. LifeExpectancyi=55+7.21GDPi−1.8GDPi2+4.4HealthExpenditures+ϵiLifeExpectancy_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
        5. ‣
        Answer

        B

      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=α+δvoucher+β1Black+β5SouthRegion+β6Northwest+β7Midwest+ϵIncome = \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. β1\beta_1 tells us the change in income associated with being black, netting out the effects of receiving a voucher and region.
      2. β1\beta_1 tells us the change in income for black individuals who have received a housing voucher.
      3. β1\beta_1 tell us the marginal effect of being black, holding everything constant.
      4. β1\beta_1 tells us the marginal effect of being black and having a voucher on income, netting out the effects of region.
      ‣
      Answer

      a and c

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