Midterm 1 Sample

1 Economics 1629 Fall 2014 Midterm 1 NAME: ____________________________________ Instructions: • You may use a calculator. You will also find a formula sheet to help you set up any necessary calculations on the last page. You may not use or share any other materials. • We have provided space on the exam for your answers. Don’t feel compelled to use up all the space provided (if you are doing so, you are probably spending too much time on that question.) • Show how you arrived at your answer, including all calculations.

2 PART I - Flu Shots and Sick Days Public health officials spend a great deal of time encouraging people to receive a vaccination for influenza (“the flu shot”) every year. In addition to health concerns about widespread outbreaks of the flu, other reasons to encourage widespread vaccination rates include minimizing the number of sick days people must take from work (and school) during flu season. Some employers, recognizing the productivity implications of employee illness, have begun sponsoring flu vaccinations in the workplace. To investigate a possible link between flu vaccination rates and number of sick days taken by employees, researchers obtained data on a random sample of 1,000 employers. The data include the total number of sick days taken by employees at each workplace in the January 2007-March 2007 period and a binary indicator (dummy variable) for whether the employer offered a flu shot on site (i.e. in its premises) between September and December 2006. Consider the following regression results: . regress sickdays flushot, robust; Linear regression Number of obs = 1,000 R-squared = 0.092 ------------------------------------------------------------------------------ | Robust sickdays | Coef. Std. Err. -------------+---------------------------------------------------------------- flushot | -42 20 _cons | 272 198 ------------------------------------------------------------------------------ where: sickdays= total number of employee sick days flushot= 1 if employer offered flu shots on site 0 if employer did not offer flu shots on site 1. (3 points) Write the sample regression function (i.e. estimated equation)

4 4. Test the null hypothesis that the population coefficient on flushot is 0 at the 5% significance level. In doing so, specify: a) (1 point) Null hypothesis: b) (1 point) Alternative hypothesis: c) (1 point) Test Statistic: d) (2 points) What can you conclude from this test? Interpret your results in language specific to this context.

5 5. (4 points) An analyst argues that since the study used a random sample of employers, the results provide a good estimate of the causal effect of flu vaccination rates on the number of sick days. Do you agree with this analyst? Why or why not? 6. (4 points) Do you think assumption 1 (Zero Conditional Mean of the Error Term, E[u|X]=0) is satisfied in the regression equation being estimated above? Explain in a language specific to this context.

7 1. (2 points) Using the regression results, interpret the relationship between crime and poverty (without controlling for anything else) in language that a person not well versed in statistics can understand. 2. When we control for population density (Regression 2), the coefficient on poverty changes. (2 points) Explain why this occurs. (2 points) Describe what we can learn from this change, using language specific to this context.

8 3. (2 points) In Regression 2, interpret the coefficient on population density in language a person not well versed in statistics can understand. 4. (3 points) Using Regression 2: compute the predicted crime rate for a state with 10% poverty and a population density of 100 people per square mile. 5. (3 points) Using Regression 2, compute the predicted difference in crime rate between a state with 10% poverty and 30% poverty, both having a population density of 100 people per square mile.

10 9. (1 point) What is the average crime rate in states with population densities below the 25 th percentile? (Numeric answer) - (1 point) What is the difference in average crime rates between states above the 75 th percentile of population density and those in the 25-75 th percentile? (Numeric answer) 10. (4 points) What do the estimates from regression 6 tell us about the relationship between crime and poverty?

11 FORMULAS: 0 : : T C A T C H H μ μ μ μ = ≠ 1) ( ) T C T C Y Y t SE Y Y − = − 2) 2 2 ( ) ( ) ( ) C T Y Y T C T C SE Y Y n n σ σ − = + 3) ( ) 1.96 ( ) T C T C Y Y SE Y Y − ± − 4) X Y X X Y Y X X i i i 1 0 2 1 ˆ ˆ ) ( ) )( ( ˆ β β β − = − − − = ∑ ∑ 5) 1 2 2 1 1 ( )( ) ( ) ( ) n i i i XY n n i i i i X X Y Y r X X Y Y = = = − − = − − ∑ ∑ ∑ 6) [ ] 2 2 2 2 ˆ 1 ) ( ˆ ) ( ) ˆ ( 1 ∑ ∑ − − = = X X u X X s SE i i i β β 7) ) ˆ ( 96 . 1 ˆ 1 1 β β SE ± 8) 1 1 ˆ ˆ ( ) a t SE β β − =