Q1. Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity (roe, in percentage form), and return on the firm's stock (ros, in percentage form):
log(salary) = β0 + β1 log(sales) + β2roe + β3ros + u
Use data in "CEO" to estimate this model and answer the following questions.
Test the null hypothesis that ros has no effect on salary using the estimated model. Would you include ros in a final model explaining CEO compensation in terms of firm performance?
Q2. The data "Houseprice" are for houses that sold during 1981 in North Andover, Massachusetts. 1981 was the year construction began on a local garbage incinerator.
1. To study the effects of the incinerator location on housing price, consider the simple regression model
log(price) = β0 + β1 log(dist) + u
Where price is housing price in dollars and dist is the distance from the house to the incinerator measured in feet. Interpret this equation causally, what sign do you expect for β1 if the presence of the incinerator depresses housing prices? Estimate the equation and interpret the results.
2. Now add the variables log(intst), log(area), log(land), rooms, baths and age where intst is distance from the home to the interstate, area is square foot age of the house, land is the lot size in square feet, rooms is total number of rooms, baths is number of bathrooms and age is age of the house in years. What do you conclude about the effects of the incinerator?
Q3. Use the data in SLEEP75 to study whether there is a tradeoff between the time spent sleeping and the time spent in paid work. Variable definitions are included in SLEEP75 variable de?nition.pdf
1. Estimate the model sleep = β0 + β1totwrk + u, Where sleep is minutes spent sleeping at night per week and totwrk is total minutes worked during the week. Interpret the estimated β0 and β1.
2. Now estimate the model sleep = β0 + β1totwrk + β2educ + β3age + u, where sleep and totwrk are measured in minutes per week and educ and age are measured in years.
3. If someone works five more hours per week, by how many minutes is sleep predicted to change? Is it a large tradeoff?
4. Discuss the sign and magnitude of the estimated coefficient on educ.
5. Discuss the sign and magnitude of the estimated coefficient on age.
Q4. Professor Hsieh decides to run an experiment to measure the effect of time pressure on final exam scores. He gives each of the 50 students in his course the same final exam, but some students have 90 minutes to complete the exam, while the others have 120 minutes. Each student is randomly assigned one of the examination times based on the flip of a coin (25 students will be assigned to the 90 minutes group and vice versa). Let Yi denote the test score of student i and let Xi denote the amount of time assigned to student i (Xi = 90 or 120). Consider the regression model Yi = α + βXi + ui.
1. Explain why E[ui|Xi] = 0 for this regression model.
2. Instead of flipping a coin, Prof. Hsieh decides to assign 90 minutes to junior and 120 minutes to senior. Will this cause any problem?
3. It is reasonable to assume that senior students have higher math ability in general as they might have completed more math-related courses. If so, will the assignment in (B) lead to upward or downward bias of OLS estimation? Hint: think about the correlation of ui and Xi. Is it positive or negative? Read the class handout about population regression.
Attachment:- Assignment.zip