ECON7310: Elements of Econometrics
Research Project 1
Fu Ouyang
August 30, 2021
Instruction
Answer all questions following a similar format of the answers to your tutorial questions. When
you use R to conduct empirical analysis, you should show your R script(s) and outputs (e.g.,
screenshots for commands, tables, and figures). You will lose 2 points whenever you fail to
provide R commands and outputs. When you are asked to explain or discuss something, your
response should be brief and compact. To facilitate tutors’ grading work, please clearly label all
your answers. You should upload your research report via the “Turnitin” submission link (in
the “Research Project 1” folder under “Assessment”) by 12:00 PM on the due date September
13, 2021. Do not hand in a hard copy. You are allowed to work on this assignment in groups;
that is, you can discuss how to answer these questions with your group members. However, this
is not a group assignment, which means that you must answer all the questions in your own
words and submit your report separately. The marking system will check the similarity, and
UQ’s student integrity and misconduct policies on plagiarism apply.
Background
You are interested in estimating the effect of education on earnings. The data file cps4 small.csv
contains 1,000 observations on hourly wage rates, education, and other variables from the 2008
Current Population Survey (CPS):
? wage: earnings per hour
? educ: years of education
? exper: post education years experience
? hrswk: working hours per week
? married: dummy for married
? female: dummy for female
? metro, midwest, south, west: location dummies
? black: dummy for black
? asian: dummy for Asian
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Research Questions
1. (20 points) Load this dataset in R (2 points). Obtain summary statistics (mean, stan-
dard deviation, 25, 50 (median), and 75 percentiles) for the variables wage and educ (5
points). Plot histograms for these two variables to explore their distributions. Make your
histograms reader-friendly; that is, give informative titles and variable names instead of
just using the default titles and variable names (6 points). For example, you could use
Years of Education in place of educ. Create a new variable ln(wage) (2 points)1 and
draw a scatter plot of ln(wage) versus educ (3 points). Comment on the correlation
between these two variables (2 points).
2. (25 points) Estimate the simple linear regression model:
ln(wagei) = β0 + β1educi + ei.
where ei is the error and β0 and β1 are the unknown population coefficients.
(a) (3 points) Report the estimation results in a standard form as introduced in Lecture
5. For example, see page 5, where the estimates are presented in an equation form,
along with standard errors (SE) and some measure for goodness of fit.
(b) (3 points) Plot the estimated regression line you obtained in (a) on the scatter plot
you constructed in Question 1.
(c) (6 points) Interpret the estimated coefficient on educ (3 points) and test whether
or not the population coefficient β1 is zero at the 1% significance level (3 points).
(d) (6 points) You suspect that the hourly wage could depend on working hours per
week. Under what condition(s) would the estimates in (a) be biased and inconsistent
due to the omission of the weekly working hours (2 points)? Give a reasonable and
intuitive story on why omission of the weekly working hours would cause omitted
variable bias in the regression in (a) (2 points). Based on your story, explain whether
the coefficient on educ in (a) would be overestimated or underestimated (2 points).
Hint: Review pages 4 and 5 of Lecture 4.
(e) (7 points) The variable hrswk is the average weekly working hours for each indi-
vidual in the data. Regress ln(wage) on educ and hrswk and report the estimation
results in a standard form (3 points). Discuss the estimation results. In particular,
how would you revise your answer in (c) (2 points)? Are the estimates statistically
significant (2 points)?
3. (40 points) You are still concerned about omitted variable bias (OVB) in the regressions
of Question 2. For that reason, you decide to regress ln(wage) on all other variables in
the dataset and use this model as a benchmark.
(a) (11 points) Report a 95% confidence interval for the slope coefficient on educ (3
points), explain the relationship between the confidence interval and hypothesis test-
ing (4 points), and test the hypothesis that one year of additional education would
increase hourly wage by 12% (4 points).
(b) (7 points) Assuming there is no OVB, discuss the estimated coefficient on female
in the benchmark model. In particular, explain what the estimated coefficient on
female means on hourly wage (3 points), compare the effect of being female and
the effect of one year of additional education (2 points), and discuss whether being
female has a statistically significant effect on hourly wage (2 points).
1In R, the function log() computes logarithms, by default natural logarithms.
2
(c) (5 points) Using the estimation results of the benchmark model, test the hypothesis
that the hourly wage is not affected by the geographic location (3 points). Explain
how you reach your conclusion (2 points).
(d) (5 points) Using the estimation results of the benchmark model, test the hypothesis
that the wage differential associated with African American is equal to the wage
differential associated with Asian American (3 points). Explain how you reach your
conclusion (2 points).
(e) (7 points) How would you modify the benchmark model to estimate the effects
on hourly wage of one additional year of education separately for each gender (4
points). How do the effects of education differ between genders and is the difference
statistically significant (3 points)? Hint: See pages 27–39 of Lecture 6.
(f) (5 point) Keoka is an African American woman, working in a metropolitan area.
After she obtained her high school diploma, she got a job and started working instead
of getting a higher education. She has never been married. Now she has a five-year
of experience in the industry and is working full time (40 hours per week).2 Using
the benchmark model, predict her hourly wage.
4. (15 points) It may be more useful to estimate the effect on earnings of education by using
the highest diploma/degree rather than years of schooling. Define four dummy variables
to indicate educational achievements:
? lt hs = 1 if educ < 12
? hs = 1 if educ = 12
? col = 1 if educ ≥ 16
? some col = 1 for all other values of educ.
(a) (6 points) Create the dummy variables lt hs, hs, col, and some col as defined
above (4 points) and compute the sample means of hourly wage for each of the four
education categories (2 points).
(b) (9 points) Regress wage on the four dummies lt hs, hs, col, and some col. Can
you obtain the OLS estimates? What is the problem here? Under what circum-
stances would you face this problem (4 points)? To avoid this problem, you now
regress wage on three dummies (lt hs, col, some col) excluding hs. Interpret the
estimated intercept (2 points) and compare the estimation results with the sample
means calculated in (a) (3 points).
2Be careful! the left-hand side variable is ln(wage), but you are asked to predict Keoka’s wage.