Quiz 3

Total Points: 21

1. You are interested in understanding the effects of housing vouchers on income. Your initial regression is run at the individual level (hence index $i$), where $Income$ is their current monthly income in thousands of dollars and $Voucher$ indicates if they received a voucher in the last year) :
$$Income_{i} = \alpha + \delta voucher_{i} + \epsilon_{i}$$

You know that vouchers are not randomly distributed except for a few cases, so your simple regression results will be biased. One of your friends suggests adding controls to get closer to the causal effect. Which of the following would be an appropriate control to add? (Select all that apply).

1. An index that gives you a sense of how “good” a neighborhood voucher recipient lives in (this index looks at things like poverty rates, crime rates, quality of schools, etc.).
2. A dummy variable for what region of the U.S. they lived in when they received the housing voucher.
3. A dummy variable for the race of the recipient.
4. A dummy variable for their current employment status.
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Answer:
2. You run the regression above, adding in the control variables for race and region (where the variables are included as dummy variables with baseline being white and west respectively), resulting in the following regression:
$$Income = \alpha + \delta voucher + \beta_1Black +\beta_2Asian+\beta_3Hispanic+\beta_4OhterRace + \beta_5SouthRegion+\beta_6Northwest+\beta_7Midwest + \epsilon$$

You may still be concerned about bias. Particularly, you wonder how using other government assistance programs might bias your results; however, you don’t have access to this data. In what direction do you think the omission of government assistance programs might bias your results? (select all answers that are internally consistent)

1. Omitting the use of other government assistance programs as a variable would lead to a smaller effect than the true effect. This is because people who use government assistance programs are more likely to also use vouchers (they are more familiar with government programs) but also more likely to have lower incomes.
2. Omitting the use of other government assistance programs as a variable would lead to a larger effect than the true effect. This is because people who use government assistance programs are less likely to use vouchers (they have limited time and may already get the support they need) and have lower incomes.
3. Omitting the use of other government assistance programs as a variable would lead to a larger effect than the true effect. This is because people who use government assistance programs are more likely to also use vouchers (they are more familiar with government programs) but also more likely to have lower incomes.
4. Omitting the use of other government assistance programs as a variable would lead to a smaller effect than the true effect. This is because people who use government assistance programs are less likely to use vouchers (they have limited time and may already get the support they need) and have lower incomes.

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Answer:
1. You want to know if more education leads to greater job satisfaction. The education variable takes the following values: 1=less than high school, 2=high school, 3=Some College, 4= College Grad, 5 = Post Grad. You regress job satisfaction on dummy variables for education level, giving you the:
$$Job Satifaction = \alpha + \beta_1(High School) + \beta_2(Some College) + \beta_3(CollegeGrad) + \beta_4(PostGrad) + \epsilon$$

Select true or false for each statement:

2. We need to add a dummy variable for “less than HS” (did not graduate high school) to compare our education levels fully.
3. $\beta_2$ represents the difference in job satisfaction for people with some college education relative to people who did not graduate high school.
4. $\beta_4$ represents the difference in job satisfaction for people with educational attainment beyond a Bachelor’s degree (PostGrad) relative to those with a Bachelor’s degree (CollegeGrad).
5. The average job satisfaction for College Graduates is equal to $\alpha+\beta_3$
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Answer:

4. You and your friends are discussing whether sleeping more during the week helps your grades. You compare your grades and see that those with higher grades sleep more, and your friends with lower grades don’t usually sleep as much. What comparison are you making in conditional expectation language? (Sleep is measured in hours)
$$E[Sleep|HighGrades = 1] - E[Sleep|HighGrades = 0]$$

1. You want to understand how the effect of basketball practice on the number of basketball game wins differs between the men’s and women’s teams. You run the following regression, where $Wins$ represents the number of wins within a basketball season, $Practice$ is a continuous variable that represents the hours of practice a team has per week, and $MaleTeam$ is a binary variable, equal to 0 for the women’s team and 1 for the men’s team.

4. You want to understand the effect of a driver’s age on car crash incidents. You believe this is a nonlinear relationship, so you run the following regression. Which of the following is true?
$$CarCrash_i\ =\ \beta_0\ +\ \beta_1Age\ +\ \beta_2Age^2$$
1. $\beta_0+\beta_1+2\beta$ Represents the change in car crash incidents when age increases by one year.
2. The sign of $2\beta_2$ will tell us if the equation has a relative maximum or minimum.
3. $\beta_1$ represents the change in car crash incidents when age increases by one year.
4. The sign of $\beta_1+2\beta_2$ will tell us if the equation has a relative maximum or minimum.
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answer