ECON7310: Elements of Econometrics

Research Project 1

April 4, 2025

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, etc.). 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 our grading work, please clearly label all your answers. You should upload your research report (in PDF or Word format) via the “Turnitin” submission link (in the “Research Project 1” folder under “Assessment”) by 16:59 on the due date April 17, 2025. 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

Use the cps09mar.csv dataset to estimate the effect of education on earnings. Data description and variable definitions can be found in the document cps09mar description.pdf. For all questions below, use the sub-sample of non-Hispanic women at least 23 years old.

Research Questions

1. (20 points) Load this dataset in R (2 points). Create a new variable

wage = earnings/(hours × week).

Obtain summary statistics (mean, standard deviation, 25, 50 (median), and 75 percentiles) for wage and education (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 Schooling in place of education. Create a new variable ln(wage) and draw a scatter plot of ln(wage) versus education (5 points). Comment on the correlation between these two variables (2 points).

2. (25 points) Estimate the simple linear regression model:

ln(wagei ) = β0 + β1educationi + ei .                             (1)

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 education (3 points) and test whether or not the population coefficient β1 is zero at the 1% significance level (3 points).

(d) (6 points) The hourly wage could also depend on one’s work experience. Under what condition(s) would the estimates in (a) be biased and inconsistent due to the omission of the work experience (4 points)? Explain whether the coefficient on education in (a) would be overestimated or underestimated (2 points). Hint: Review pages 4 and 5 of Lecture 4.

(e) (7 points) Create a new variable experience = age − education − 6 to measure one’s work experience. You want to include experience in regression (1) and regress ln(wage) on education and experience. However, you are not sure whether to also add a quadratic term, such as experience2 , to the regression equation along with experience. Use a hypothesis test to help you choose the more appropriate model (4 points). Estimate your selected model and report the results in a standard form. (3 points).

3. (43 points) With the regression model that you selected in 2(e), you are still concerned about omitted variable bias. For that reason, you decide to include more control variables in the regression.

(a) (11 points) Include a set of dummy variables for regions and marital status and estimate the extended model (4 points). For regions, create dummy variables for Northeast, South, and West so that Midwest is the excluded group. For marital status, create variables for married (marital ≤ 3), widowed or divorced, and separated, so that single (never married) is the excluded group. Report a 95% confidence interval for the slope coefficient on education (2 points), explain the relationship between the confidence interval and hypothesis testing (2 points), and test the hypothesis that one year of additional education would increase hourly wage by 12% (3 points).

(b) (5 points) Using the estimation results, test the hypothesis that the hourly wage is not affected by the geographic location (3 points). Explain how you reach your conclusion (2 points).

(c) (8 points) Include a dummy variable black for black workers (race = 2) in the model you considered in 3(b) and run OLS estimation. Explain what the estimated coefficient on black means on hourly wage (3 points), compare the effect of being a black worker and the effect of one year of additional education (2 points), and test whether these two effects are of the same magnitude (3 points).

(d) (7 points) How would you modify the model to test if the effects on hourly wage of one additional year of education differ between black and non-black workers (4 points). Implement your proposed test and report the results (3 points). Hint: See pages 27–39 of Lecture 6.

(e) (7 points) Kate has 31 years of work experience. Using the regression model of 3(d), test if one additional year of work experience has significant effects on her hourly wage (5 points). Provide a formula for calculating this effect (2 points). Hint: Read pp. 9–17 of Lecture 6.

(f) (5 points) Betty is a married, white woman, working in Boston. After she obtained her college degree (= 16 years of schooling), she got a job and started working instead of getting a higher education. Now she has a five-year of experience in the industry. Predict Betty’s hourly wage.

4. (12 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 education < 12

• hs = 1 if education = 12

• col = 1 if education ≥ 16

• some col = 1 for all other values of education.

(a) (4 points) Create the dummy variables lt hs, hs, col, and some col as defined above and compute the sample means of hourly wage for each of the four education categories.

(b) (5 points) Replace the education in the regression model of 3(d) with these dummies and estimate their coefficients. Can you obtain the OLS estimates for all these four dummies? Explain your answer (3 points). Interpret the coefficient on hs (2 points).

(c) (3 points) Report estimation results of regressions in 2(e), 3(a), 3(c), 3(d), and 4(b) using a table similar to those presented in your Tutorials 5–6. Hint: If you are not familiar with LATEX, you can use the screenreg() function instead of texreg().