INTRODUCTORY ECONOMETRICS

23571: INTRODUCTORY ECONOMETRICS

AUTUMN SEMESTER, 2015

ASSIGNMENT PART A (INDIVIDUAL ASSESSMENT)

COVER SHEET

Due March 24 2015, 17:00 This assignment is worth 10% of your final grade.

Limit your answer to 5 pages (single-sided).

The assignment should be submitted to the assignment drop box. Due to the recent

move of the Business School to the new building, the location of the drop box is still

to be determined and will be announced as soon as possible. No late submissions

will be accepted. Please ensure that the coversheet is attached. The assignment

must be stapled with the coversheet. Write your name and student number at the

top of each page of the answer sheet.

In our experience, neater assignments receive higher marks, conditional on content.

As such, you are strongly encouraged (but not required) to type your assignments.

Mathematical symbols and formulas can remain hand-written.

Although you are allowed to verify your answers using statistical software, to help

yourself prepare for the examinations you are strongly encouraged to attempt the

assignment questions without the aid of statistical software. You can use a calculator

to answer the questions.

Please complete the declaration and list the student number and name of the

student contributing to this assignment.

Declaration We hereby certify that this assignment is our own work, based on our personal study and/or research and that we have acknowledged all material and sources used in the preparation of this assignment. We also certify that the assignment has not previously been submitted for assessment and that we have not copied in part or whole or otherwise plagiarised the work of other students or authors.

Student Number Family Name First Name Signature

23571 Introductory Econometrics

Autumn 2015

Assignment A

You must attach the coversheet to your answers. Read the instructions on the

coversheet. Try to keep your answers short and clear. Questions (h) and (i)

require knowledge from “Two-variable regression: hypothesis testing”. This

assignment has a total of 10 marks.

In an earlier tutorial, you were introduced to a data set that came from a job training

experiment conducted for low-income men in the United States in 1976. In this

question, you are given extra information for 5 individuals in the data set. The data is

given as follows:

Observation re78 educ age

1 9.93 16 25

2 3.59 12 20

3 7.50 9 55

4 4.05 12 21

5 8.47 12 40

You will operate on the above data of 5 observations throughout this assignment. The

variables are defined as follows:

re78 = earnings in 1978, measured in thousand dollars

educ = years of education

age = individual’s age in years

(a)(1pt) Reconstruct the following frequency table on your answer sheet and fill in the

missing information.

Age<30 Age>=30

Educ<10

Educ>=10

(b)(1pt) Reconstruct the following table on your answer sheet. Compute the

conditional means.

Answer

E(re78|educ=12)

E(re78|educ<10)

E(re78|educ<10 and age<30)

E(re78|educ>=10 and age<30)

(c)(1pt) Compute the sample variance of age, as well as the sample covariance

between re78 and age.

(d)(1pt) Use the OLS formula in lecture 2 to compute the sample regression line of

the regression of re78 on age. (Note: round your answers to 3 significance figures)

(e)(1pt) Suppose you regress re78 on age using observation 1 only. What result will

you get? Briefly explain why this result occurs.

(f)(2pt) Suppose the population model is

re78 = 1 + 0.1*age + u.

On your answer sheet, reconstruct the following table and fill in the missing

information.

Observation re78 (Y) age (X) E(Y|X) u Predicted

Y ( ̂)

Residual

( ̂

1 9.93 25 3.5 6.43 6.10 3.83

2 3.59 20

3 7.50 55

4 4.05 21

5 8.47 40

(g)(1pt) In part (f), the random errors are all larger than zero. Does it imply that the

population model is incorrect? Briefly explain.

(h)(1pt) This question continues part (d). The rest of the estimation result is:

𝑟𝑒78 = �̂�1 + �̂�𝑎𝑔𝑒 ∗ 𝑎𝑔𝑒

se: (3.310) (0.095)

t-stat: (1.207) (0.889)

p-val: (0.314) (0.440)

Briefly interpret the coefficients (values given in part (d)) and the p-values in this

regression.

(i)(1pt) We are interested in testing the following hypothesis:

H0: age = -0.1; H1: age > -0.1

With the aid of a statistical table, find the critical value associated with a significance

level of 10 percent. Is the null hypothesis rejected at the 10 percent significance level?