Part I: Data Analysis

This first part of the problem set introduces you to Stata for simple data analysis. For each question, first copy and paste the Stata output into a word-processing document (use the "copy as picture" option), then type your answer. You can download the Stata file WAGE2.dta from

D2L. It contains information on monthly earnings, employment history, education, demographic characteristics, and two test scores for 935 men in year 1980. In particular, it contains the following variables:

wage monthly earnings (in 1976 USD)
hours average weekly hours of work
IQ IQ (intelligence quotient) score
educ years of education
age age in years
married =1 if the person is married; 0 othrewise
black =1 if the person is black; 0 otherwise

1. Find the average years of education in the sample (that is, the mean for variable educ). What are the lowest (minimum) and the highest (maximum) years of education in the sample? Hint: Use the Stata command sum var1.

2. How many black men are there in the sample?. How many non-black men? What is the percentage of non-black men in the sample? Hint: Use the Stata command tab var1.

3. What is the average monthly wage for all men in the sample? What is the sample mean monthly wage for blacks? For non-blacks? Do black men in the sample earn more or less than non-black men, on average? Hint: Use the Stata command tab var1, sum(var2). In this case, var1 is black, and var2 is wage, so the command to type in the command window is tab black,
sum (wage).

4. Now find the sample average years of education for blacks and non-blacks separately. Which group has a higher mean education in this sample? Hint: Use the Stata command tab var1, sum(var2) again, but this time var2 is educ.

5. What is the sample correlation between variables IQ (IQ test score) and educ (years of education)? What is the sign of this correlation and what does it mean? Hint: Use the Stata command corr var1 var2.

6. Compute the average IQ test score for each year of education in the sample. Do you find any relationship between the two variables? Does it make sense to you? Hint: Use the Stata command tab var1, sum(var2). In this case, var1 is educ and var2 is IQ.

Part II: Statistical Theory

Use a word processor to type your answer to the following questions. Suppose you want to know the average earnings of all men in East Lansing between the ages of 18 and 54. It would be prohibitively expensive to survey everyone in East Lansing, so you randomly select 500 men residing in East Lansing in this age group and ask them about their earnings.

1. What is the population of interest in this example? What is the sample? What the sample size, N?

2. Suppose you use the sample mean as an estimator of the population mean. Is this an unbiased estimator of the population mean? Is it an efficient estimator of the population  mean? Why or why not? Hint: See Wooldridge, Appendix C.1 and C.2.

3. As an alternative to the sample mean, you decide to try another estimator of the population mean. This estimator uses just three observations chosen at random from your sample:

(1/3) (X₁ + X₂ + X₃)

Is this an unbiased estimator of the population mean? Is it an efficient estimator of the population mean? Why or why not? Hint: Again, see Wooldridge, Appendix C.1 and C.2.

Part III: The Summation Operator (2 points total)

For the following question, you can either use a word processor or write out the answer legibly. Show that the sum of deviations from the sample mean is always zero; that is, show