Applied Econometrics

These are your free-response questions: Question 1 does not require the use of Stata but Question 2 requires the use of Stata. Please upload your answers in the appropriate place under ASSIGNMENTS. Please carefully read also the guidelines. You must submit separate PDF files with your answers: one for each question. You are also required to provide the Stata Code and Outputs in your computer based questions. Make sure you also write on your code a comment that includes YOUR name and student ID. Please make sure you upload the correct files. Please make sure you write your name and student ID in your pdfs.

For full credit please make sure that you:

– provide us with complete answers with details on how you perform your calculations.

Question 1 (20 points):

Supposed that you were asked to examine the relationship between the height of children and their parents. To conduct such a study you have collected data from 110 college students, and estimated the following relationship:

Student_hat = 19.6 + 0.73 × Midparh,   R2 = 0.45, SER = 2.0

(7.2)  (0.10)

where Studenth is the height of students in inches, and Midparh is the average of the parental heights. Values in parentheses are heteroskedasticity robust standard errors. Both variables were adjusted so that the average female height was equal to the average male height.

(a) Interpret the estimated coefficients.

(b) What is the meaning of the regression R2 ?

(c)  What is the prediction for the height of a child whose parents have an average height of 70.06 inches?

(d)  What is the interpretation of the SER here?

(e)  Given the positive intercept and the fact that the slope lies between zero and one, what can you say about the height of students who have quite tall parents? Those who have quite short parents?

(f) Test for the statistical significance of the slope coefficient.

(g) If children, on average, were expected to be of the same height as their parents, then this would imply two hypotheses, one for the slope and one for the intercept.

(i) What should the null hypothesis be for the intercept? Calculate the relevant t-statistic and carry out the hypothesis test at the 1%                  level. For full credit make sure that you show ALL the steps including a graphical representation of your test.

(ii) What should the null hypothesis be for the slope? Calculate the relevant t-statistic and carry out the hypothesis test at the 5% level.              For full credit make sure that you show ALL the steps including a graphical representation of your test.

(h) Can you reject the null hypothesis that the regression R2 is zero?

Question 2 (20 points): This is a computer-based question that requires the use of Stata. The data file HW1 contains data for full-time, full-year workers, age 25–34, with a high school diploma or B.A./B.S. as their highest degree. A detailed description of the dataset and the dataset are provided under FILES> Homework > HW1. In this exercise, you will investigate the relationship between a worker’s age and earnings. Please keep in mind that generally, older workers have more job experience, leading to higher productivity and earnings.

a) Provide a scatterplot with average hourly earnings on the vertical axis and age on the horizontal axis.

b) Run a regression of average hourly earnings (AHE) on age (Age). What is the estimated intercept? What is the estimated slope? How much do earnings increase as workers age by 1 year?

c) Mary is a 26-year-old worker. Predict Mary’s earnings using the estimated regression. Patrick is a 30-year-old worker. Predict Patrick’s earnings using the estimated regression.

d) Does age account for a large fraction of the variance in earnings across individuals? Explain.

e) Is the estimated regression slope coefficient statistically significant? Make sure you present all the steps for full credit.

f) Construct a 95% confidence interval for the slope coefficient.