Homework answers / question archive / University of California, Los Angeles FINAL 13 1)In a study relating college GPA to time spent in various activities, you distribute a survey to several students asking them how many hours they spend each week in four activities: studying, sleeping, working, and leisure

University of California, Los Angeles FINAL 13 1)In a study relating college GPA to time spent in various activities, you distribute a survey to several students asking them how many hours they spend each week in four activities: studying, sleeping, working, and leisure

Economics

Share With

---

University of California, Los Angeles

FINAL 13

1)In a study relating college GPA to time spent in various activities, you distribute a survey to several students asking them how many hours they spend each week in four activities: studying, sleeping, working, and leisure. Any activity is put into one of the four categories, so that for each student the sum of hours in the four activities must be 168. True or false: the following model is misspecified and you will not be able to estimate its coe cients: GPA = ₀ + ₁study + ₂sleep + 3work + ₄leisure + u.

2. The overall regression F statistic tests the null hypothesis that all slope parameters are zero, with the intercept unrestricted.
3. Consider the following model: Score = 1.15 + 2.56 Skipped + 0.25 GPA, where Score is the score on the Econ 103 final exam, Skipped is the number of classes skipped, GPA is the grade point average at the beginning of the term, and the correlation between Skipped and GPA is negative. John estimates the model Score = ₀ + ₁ Skipped+u. True or false: John will obtain an estimate ˆ₁ that is biased upwards.
4. You have a dataset with information on the smoking behavior of adults in the US. The variable Smoke measures the average number of cigarettes smoked per day. True or false: the variable Smoke is likely to follow a standard normal distribution, i.e., N(0,1).
5. You have estimated the following model (numbers in parentheses are standard errors):

 

 Education_i + 10.50 Education ? IQ_i

 

(5.08)   (1.5)     (2.12)

True or false: Your estimates indicate that education has no e↵ect on wages.

6. A researcher studying the demand for cigarettes has obtained the following estimates:

Q = 5000 + 5P³, where Q is the quantity demanded and P the price in dollars.

True or false: the price elasticity of demand is equal to 5 when P = 10.

7. Consider the multiple regression model Y = ₀ + ₁X₁ + ₂X₂ +v. True or false: ₂ measures the amount of variation in Y explained by X₂ in the model.
8. The dummy variable Male is 1 for males and 0 for females. Married is equal to 1 if a person is married, 0 otherwise. Consider the following regression ( standard errors in parenthesis):

 

 Male_i + 2.16 Married_i    1.00 Married_i ? Male_i

 

(1.25)   (0.10)

True or false: the estimates above imply that the average wage for single males is statistically lower than that of single females.

9. Consider the following regression of house selling prices (PRICE) on house size measured in square feet (SQFT), number of bedrooms (ROOMS), and house age in years (AGE): PRICE = 100 + 20 SQFT + 150 ROOMS 50 AGE. Mario is considering two possible renovation projects. The first one would increase the size of his house by 10 square feet and take 3 years to complete. The second one would add one extra bedroom and take 1 year to complete. True or false: if Mario wants to maximize the house’s selling price by the time he finishes the renovation, he should choose the first project.

 

10. You estimate the following model: Wage = ₀ + ₁ Education + u and find that ˆ₀ = 117 and ˆ₁ = 298. The confidence interval for the e↵ect of education on wages is [102, 494]. True or false: the standard error of ˆ₁ is greater than 10.

 

Consider the following model:

ERV = ₀ + ₁HI + ₂female + ₃age + ₄linc + u

where ERV measures the number of times an individual has visited a hospital emergency room in the last year, HI is an indicator variable equal to 1 if the person has health insurance and 0 otherwise, female is equal to 1 for females and 0 otherwise, age is age in years, and linc the log of yearly income.

Instructions for this exercise:

• • • • The regression above is estimated using a sample of Los Angeles residents. Use the Stata output from this regression, provided on page 9 of the exam, to answer the questions.
      • One key variable a↵ecting the number of emergency room visits is the health status of an individual. You cannot observe which individuals in your sample are healthy and which are in poor health. Focus on this omitted variable when answering questions 2. and 3. below.
    • What does the parameter ₄ measure? (Hint: note which variables in this model are in logs). .
    • Provide an intuition for why the variable female is likely to be exogenous.
    • Provide an intuition for why the variable HI is likely to be endogenous.
    • Describe the factors that determine the sign of the omitted variable bias. Based on your answer, is the estimate of ˆ₁ in Regression 1 likely to be too high or too low? (Hint: the output for Regression 1 can be found on page 9)
    • Which two conditions would a variable have to satisfy to be a valid instrument for HI? (Hint: write the conditions formally in the context of this model). 
    • You find the following two possible instruments for the variable HI: the variable discount is equal to 1 for individuals who were randomly chosen by the City Council to be o↵ered health insurance at a discounted price. The variable distance measures the distance to the nearest business selling health insurance. Explain intuitively why the two are likely to be valid instruments.
    • Explain how you would obtain the two-stage least squares (TSLS) estimate for the parameter ₁ using the two instruments. Write the equations for the two stages. (10 points) First stage:
    • Explain why using the command ivreg, as is done in Regression 2, is preferable to running the two stages separately.
    • Can you test for exogeneity in this context? Why?

 

1. 1. 1. What does the parameter ₄ measure? (Hint: note which variables in this model are in logs). .
      2. Provide an intuition for why the variable female is likely to be exogenous.
      3. Provide an intuition for why the variable HI is likely to be endogenous.
      4. Describe the factors that determine the sign of the omitted variable bias. Based on your answer, is the estimate of ˆ₁ in Regression 1 likely to be too high or too low? (Hint: the output for Regression 1 can be found on page 9)
      5. Which two conditions would a variable have to satisfy to be a valid instrument for HI? (Hint: write the conditions formally in the context of this model). (10 points)
      6. You find the following two possible instruments for the variable HI: the variable discount is equal to 1 for individuals who were randomly chosen by the City Council to be o↵ered health insurance at a discounted price. The variable distance measures the distance to the nearest business selling health insurance. Explain intuitively why the two are likely to be valid instruments.
      7. Explain how you would obtain the two-stage least squares (TSLS) estimate for the parameter ₁ using the two instruments. Write the equations for the two stages. (10 points) First stage:
      8. Explain why using the command ivreg, as is done in Regression 2, is preferable to running the two stages separately.
      9. Can you test for exogeneity in this context? Why?