Problem 1
To complete this problem, open the ceosal dataset included with the assignment on OWL (A2 ceosal.xls). This is dataset containing information on the salary of CEOs and other relevant variables in different industries. Your primary interest is to study how the salary of CEOs affect sales. You think that higher paid CEOs will put more effort into their business, which should result in higher sales. There are 4 possible industries: finance, consumer product, industrial and transport/utilities. The main model of interest is as follows:
lsalesi = β0+β1utilityi+β2consprodi+β3indusi+β4lsalaryi+β5(lsalaryi∗utilityi)
+ β6(lsalaryi consprodi) + β7(lsalaryi indusi) + β8lroei + β9rosi + ui
(1)
The variables in the dataset are as follows:
• lsalesi: natural log of sales
• lsalaryi: natural log of salary
• lroei: natural log of return on equity
• rosi: return on stock price
• financei: indicator for finance industry
• indusi: indicator for manufacturing industry
• consprodi: indicator for consumer product industry
• utilityi: indicator for transport/utilities industry You are asked answer the following questions:
1. Explain why financei was removed from the model in (1). Write down one alternative version of the same model that would include financei.
2. What is the interpretation of β0, β1, β2 and β3?
3. Provide a summary statistics of the data. In particular, show the average value for each variables.
4. Estimate the model in (1), and show regression results in a concise table.
5. Construct a graph of the predicted relationship between lsalaryi and lsalesi for each industry (you may construct 4 different graphs, or plot all 4 relationships in the same graph). Then, provide a detailed explana- tion of the relationship between lsalaryi and lsalesi across industries.
6. Perform a joint hypothesis test of the following null hypothesis that tests whether we should include the different industries in the model:
H0 : β1 = β2 = β3 = β5 = β6 = β7 = 0
Do you reject the null at the 90% confidence level? What about the 95% and 99% confidence level?
Problem 2
To complete this problem, open the wage dataset included with the assignment on OWL (A2 wage.xls). This is a dataset containing information on the average wages and education level across U.S. states between 1950 and 1990. You are interested in estimating the returns to schooling, β1, in the following model:
lnwageit = β0 + β1educit + β2ageit + β3age2 + uit (2) The variables in the dataset are as follows (you will have to create age2 )
• lnwageit is the average (log) wage in state i at year t
• educit is the average number of years of education for the population in state i and at t
• ageit and age2
are the average age and squared of age for the population
in state i at year t
• cait is the compulsory number of years of education in state i at year t
• clit is the minimum age required for a child to start working in state i at year t
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