1. Test whether the difference in mean height for men and women is statistically significant? Is it?
2. Does the distribution of height for men and women in the US follow the normal distribution? Answer by looking at detailed summary statistics and high order moments of the data.
3. If you were to select one al observation from the data at random, what is the probability that individual is than sixty seven inches tall?
4a. Run the following regressions and interpret the coefficient on the height variable.
I. Regress earnings on height
II. Regress log of earning on height
III. Regress log earnings on log of height
4b. which model is preferred?
5a. Regress log of earnings on height and height²
5b. is there a non-linear relationship between height and log earnings?
5c. Give a-formula for the effect of a change in height on the change in log earnings.
6. Create the following variables:
I. A dummy variable for being-Hispania.
ii. A dummy variable for being black.
iii. A dummy variable for being female.
iv. A set of region dummy variables.
7a. Run the following regression separately by gender:
Regress log earnings on height education age black Hispanic
7b. Is there a difference in the estimated effect of height on earnings by gender?
8. Run the following regression: Regress log earnings on height education age black Hispanic female and a set of region indicators, and perform the following tests (and interpret the results): I. Test for the equality of coefficients on the Hispanic and black variables.
ii. Test the hypothesis that the coefficients on female, black and Hispanic are all zero.
9a. Run the following regression for men: Regress log earnings on height height² education age black Hispanic and a set of region indicators. Is there evidence of a non-linear relationship between height andlog earnings for men?
9b. Estimate the effect of a one inch increase in height on log earnings for a man starting an average height)
10. Discuss the following threats to internal validity regarding the model in (8):
I. measurement error focusing on earnings and height)
ii. Omitted variables bias
Stock and Watson’s Introduction to Econometrics, 3rd Updated Edition
Documentation for Earnings_and_Height
These data are taken from the US National Health Interview Survey for 1994. They are a
subset of the data used in Anne Case and Christina Paxson’s paper “Stature and Status:
Height, Ability, and Labor Market Outcomes,” Journal of Political Economy, 2008,
116(3): 499-532, and were graciously supplied by the authors for empirical exercises in
the Stock-Watson textbook.
The dataset contains information on 17,870 workers. The table on the next page
describes the variables.
Stock and Watson’s Introduction to Econometrics, 3rd Updated Edition
Variable Name Description
age Age, in years
cworker Class of Worker:
1 = Private company Employee
2 = Federal Government Employee
3 = State Government Employee
4 = Local Government Employee
5 = Incorporated Business Employee
6 = Self Employed
earnings annual labor earnings, expressed in $2012 (see Table notes)
educ years of education
height height without shoes (in inches)
mrd Marital Status
1 = Married, Spouse in household
2 = Married, Spouse not in household
3 = Widowed
4 = Divorced
5 = Separated
6 = Never Married
occupation Occupations in 15 categories:
1 = Exec/Manager
2 = Professionals
3 = Technicians
4 = Sales
5 = Administrat
6 = Household service
7 = Protective service
8 = Other Service
9 = Farming
10 = Mechanics
11 = Construction/Mining
12 = Precision production
13 = Machine Operator
14 = Transport
15 = Laborer
race race/ethnicity
1 = non-Hispanic white
2 = non-Hispanic black
3 = Hispanic
4 = other
region Region of the U.S.
1 = Northeast
2 = Midwest
3 = South
4 = West
sex Sex, 1=Male, 0 = Female
weight weight without shoes (in pounds)
Notes: In the survey, labor earnings are reported in 23 brackets (for example, $26,000-$30,00). For each of
these brackets Professors Case and Paxson estimated a value of average earnings based on information in
the Current Population, and these average values were assigned to all workers with incomes in the
corresponding bracket. The earnings values for 1994 were converted to $2012 using the consumer price
index.
Stock and Watson’s Introduction to Econometrics, 3rd Updated Edition