1. Macro economists are interested in why countries have different gross domestic products (GDP). The following regression for 112 countries relates the natural log of GDP to the natural log of the country's population, whether or not the country is landlocked (i.e. no access to oceans), whether the country is a democracy, and the interaction of landlocked and democracy.
ln(GDP)^ i = 26.65 + 0.73lnpopi - 0.19 landlocki + 0.25 demi + 0.08 landlock*dem
(4.97) (0.15) (0.08) (0.06) (0.05)
a) Test the hypothesis that being a landlocked country has a statistically significant effect on GDP at the 95% confidence level for a country that is not a democracy.
b) You suspect that the elasticity of GDP with respect to population is 1 (a 1% difference in population is associated with a 1% difference in GDP). Do you reject this hypothesis at the 90% level?
c) Interpret the coefficient on the interaction between "landlock" and "dem".
d) What is the p-value of coefficient on the interaction term? Interpret the p-value in a sentence.
e) What is the 99% confidence interval of the effect of being a democracy on GDP for a country that is not landlocked?
2. The following regression results examine how long 616 employees stay with a company as a function of how well they are paid and the value of the benefits they receive. "Earn" is hourly wage. The variables "vacation", "sick", "insur", and "pension" are the dollar value per month of vacation days, sick days, health insurance, and retirement pension.
(years)^i = 6.49 + 0.20earni
SSR: 36,598 SST: 37,182
(years)^i = 3.66 + 0.04earni + 0.03vacation + 0.01sick
SSR: 32,714 SST: 37,182
(years)^i = 3.66 + 0.02earni + 0.02vacation + 0.01sick + 0.03insur + 0.02pension
SSR: 32,117 SST: 37,182
a) Are vacation and sick days jointly predictive of how many years an employee works at a company?
b) Compute the R-squared of the first two regressions and use them to conduct the test in part a). How do the F-statistics and answers compare?
c) Are health insurance and retirement pensions jointly predictive of how many years an employee works at a company?
d) You are interested in testing if health insurance has a larger effect on years of employment than the other three benefits. State a new regression that you can run to test this, define the relevant variables, and state how you would test the hypothesis.
3. The following regression is based on a survey of 1,000 individuals aged 20 to 50. Each participant was asked to rank their happiness on a scale from 1 to 10 and to state how many hours they slept the prior night.
(happiness)^I = 4.45 + 0.32hourssleep
a) Suppose that depression causes people to report lower happiness but also causes people to sleep more. Explain the implications of omitting depression for the coefficient on sleep.
b) The variance of hours slept in the data is 2.8 hours. What is the covariance of sleep and happiness?
c) People are not good at reporting how long they sleep each night. Thus hours of sleep is measured with random error η that has mean zero but standard deviation of 0.5. Estimate the correct coefficient on "hourssleep" after accounting for this issue. How does the corrected coefficient compare to the one shown above?
d) Suppose that sleeping was measured accurately in the original equation. However, people are not good at reporting their happiness and tend to make small mistakes. This measurement error has a variance of 1. Estimate the coefficient on "hourssleep" after accounting for this issue. How does the corrected coefficient compare to the one shown above?
e) People who are happier have an easier time sleeping. Discuss the implications of this issue for interpreting the coefficient on "hourssleep".
4. Porter College implements a curfew that requires all students to be in their dorm rooms by 11:00 PM each night. Administrators hope that this will increase attendance and reduce citations for underage drinking. They collect data on class attendance in the 2015-2016 academic year and then again in the 2016-2017 academic year after the policy is in place.
Absenteeism Rate:
|
College
|
2015-2016
|
2016-2017
|
|
Porter College
|
0.37
|
0.38
|
|
Control College
|
0.28
|
0.33
|
Alcohol Citations:
|
College
|
2015-2016
|
2016-2017
|
|
Porter College
|
42
|
55
|
|
Control College
|
47
|
53
|
a) What is the single difference estimate of the effect of the curfew on the absenteeism rate? Write the complete regression equation for single differences using the table above.
b) The composition of students living at college changes from year-to-year. Identify two characteristics that you think should be added to the regression to control for such changes.
c) You wish to estimate the effect of the curfew at Porter College using a difference-in-differences strategy. List three characteristics you would look for in a potential control college.
d) What is the difference-in-differences estimate of the effect of the curfew on the absenteeism rate? Write the full regression equation based on the table above.
e) What is the difference-in-differences effect of the curfew on citations? Write the complete regression that you would get based on the table above.
f) Suppose that Porter College also hired additional security officers at the time of the policy. Explain how this complicates the results in part e) and how it could potentially explain the results.