Economics 415 Homework #1 Professor Thornton

Economics 415 Homework #1 Professor Thornton

Econometrics 100 Points Winter 2010

The homework is due Wednesday, February 3th at the beginning of class. Homework submitted late is subject to a penalty. You may consult lab assistants or other students in the class about SAS programming questions for this assignment. Any other questions should be directed at me. You cannot seek help from anyone else in answering the homework questions. You may “cut and paste” SAS output into your answers. In addition, include as an appendix a copy of the SAS statements used to create your programs and the output generated by these statements. When answering questions, integrate relevant output into your answers along with text; do not refer to appendix, as this makes grading questions extremely difficult.

OBJECTIVE OF EMPIRICAL STUDY (5 Points)

You have been hired as a consultant by the Congressional Budget Office (CBO) to conduct an empirical study of the influence of chief executive officer (CEO) compensation on the financial performance of corporations in the U.S. The CBO wants to know if paying a typical CEO a higher salary and bonus motivates her to improve the performance of the firm, where firm performance is measured by profit. Therefore, the objective of your study is to explain the relationship between CEO compensation and profit.

1. What specific questions will you address to explain the relationship between CEO compensation and profit? Make sure you clearly explain the meaning of the questions you are addressing.

DESIGN OF EMPIRICAL STUDY (15 Points)

To explain the relationship between CEO compensation and profit you must design your study to account for four possibilities: confounding variables, reverse causation, sample selection, and chance.

2. What is a confounding variable? The variable assets can be interpreted as a measure of firm size. The more assets the bigger the firm. Explain why the dollar value of a firm’s assets may be a confounding variable. Identify one other variable that you believe may be a confounding variable. Clearly explain why you believe this other variable may be a confounder.

3. What is reverse causation? Do you believe there may be reverse causation in the relationship between CEO compensation and profit? Make sure you give an argument to support your answer.

4. What role does chance play in analyzing the relationship between CEO compensation and profit? Briefly explain how you can account for chance.

DATA (10 Points)

The data for your study are contained in the dataset CEOPAY. The data are for year 1998 for 447 corporations that make up the list of Fortune 500 firms, which is the largest 500 firms in the U.S. Fifty-three of the firms were excluded because of missing data. The variables are as follows. Salary is annual CEO salary plus bonus in thousands of dollars. Tenure is the number of years as CEO of firm. (Note that if an individual has been CEO of a firm for less than 6 months, then tenure equals zero). Sales is the firm’s sales measured in millions of dollars Profits is the firm’s profit measured in millions of dollars.. Assets is the firm’s assets measured in millions of dollars. Age is a dummy variable for CEO age. Age = 1 if CEO is younger than age 55; Age = 0 if CEO is age 55 or older.

5. What is the population in which you are interested? Do you believe your sample is a random or nonrandom sample from the population of interest? Make sure you give an argument to support your answer. What is the advantage of a random sample? What is the disadvantage of a nonrandom sample?

6. Use the ascii data file CEOPAY to create a SAS dataset named CEOPAY1 that contains all of the variables in the ascii data file. (No answer or printout required).

DESCRIPTIVE STATISTICS: GET TO KNOW THE DATA

The next step in an empirical study is to get to know the data. This involves the following. 1) Get to know your variables. 2) Get to know your observations. 3) Organize, summarize, and describe the data.

Get to Know the Variables and Observations (20 Points)

7. For this study, what is the unit of observation? That is, what is the unit for which the data were collected and to which the variables apply?

8. Which variable(s) are quantitative variables, and which variable(s) are qualitative variables? Justify your answer.

9. Which variable(s) are discrete variables, and which variable(s) are continuous variables? Justify your answer.

10. Give an example of a univariate observation, bivariate observation, and multivariate observation. Give the observed values for each of these types of observations for unit #1 in the sample (SAS identifies units by observation number when you display the data in the output window).

Organize, Summarize and Describe the Data: Univariate Statistics (25 Points)

11. Construct and print a histogram of the absolute frequency distribution for the variables profits and salary. Describe the shapes of the histograms (e.g., symmetric, skewed, bimodal, etc.). What do they tell you about the distributions of these variables in the sample?

12. Report the maximum and minimum values for the variables. Do these values seem reasonable, or might they indicate one or more possible response errors or coding errors?

13. Report the sample means for all variables. Interpret the mean of the variable age. What information does it give you about the sample? Use the sample means to describe a “typical” corporation in the sample.

14. Report the sample standard deviation for all variables. Interpret the standard deviation for the variable salary. What information does this statistic give you about this variable? Explain.

15. Choose a descriptive statistic that can be used to compare the dispersion of the variables. Explain why you selected this particular statistic. Report this statistic. Based on this statistic, rank the 6 variables in the sample from most to least dispersion.

Organize, Summarize and Describe the Data: Bivariate Statistics (25 Points)

16. Construct a scatter diagram for the variables salary and profits. Measure profits on the vertical axis and salary on the horizontal axis. What does the scatter diagram suggest about the relationship between CEO salary and profit?

17. On the scatter diagram for salary and wage, draw vertical and horizontal lines at the sample means for the two variables. This breaks up the scatter diagram into four quadrants. Use this scatter diagram to explain the logic that underlies the measure of sample covariance between the variables salary and profits. Make sure to explain how sample covariance is calculated and what it measures.

18. Report the correlation coefficients between profits and each of the other five variables. Rank these five variables in terms of the strength of linear association with profits, from strongest to weakest. Do any of the variables appear to have no linear association with profits? Yes/no. Explain.

19. Are the algebraic signs of all correlation coefficients consistent with your expectations regarding the economic relationship between the profits and each of the other variables? Yes/no. Explain.

20. Can the correlation coefficient for salary and profits be used to answer any of the questions in which you are interested about the relationship between CEO salary and profit? Carefully explain.

NOTE: Homework #2 will extend this example to cover the remaining steps in your empirical study: 4) statistical model; 5) estimation, hypothesis testing, goodness-of-fit; and 6) conclusions.

GRADUATE STUDENT QUESTIONS

Only graduate students are required to do the following questions.

Creating and Using Subsamples (20 Points)

It is often times useful to decompose the sample into two or more meaningful subsamples, calculate descriptive statistics for each subsample, and compare the characteristics of the different subsamples. Because you are interested in the relationship between CEO salary and profits it may be informative to decompose the sample into subsamples that differ in terms of CEO salaries.

21. Create the following three subsamples. 1) corporations with CEO salaries less than $1,200 thousand; 2) corporations with CEO salaries between $1,200 and $2,000 thousand; 3) corporations with CEO salaries greater than $2,000 thousand. To do this create three temporary SAS data sets, one for each subsample.

22. Report the sample mean for profits for each subsample. Compare the sample means for the three subsamples? What does this comparison suggest about the relationship between salary and profits? Does the difference in sample means of profits for the three subsamples provide strong evidence with which to answer any of the questions in which you are interested about the relationship between CEO salary and profit? Carefully explain.

23. Report the sample mean for assets for each subsample. Compare the sample means for the three subsamples. Carefully explain why this comparison suggests the variable assets may be a confounding variable when analyzing the relationship between CEO salary and profits.

24. Report the sample standard deviation for profits for each subsample. Compare the standard deviations for the three subsamples. What information does this give you?

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