ECS3706
EXAM PACK
FOR ASSISTANCE WITH THIS MODULE +27 67 171 1739
,UNIVERSITY EXAMINATIONS
Oct/Nov 2023
ECS3706
ECONOMETRICS
100 marks
Duration: 4 hours
EXAMINERS:
FIRST: PROF S NHAMO
SECOND: DR M ZUKA
EXTERNAL: DR L RAPUTSOANE
CONFIDENTIAL
This paper consists of 11 pages, including a formulae sheet (page 8), three statistical tables
(pages 9 to 11), and the special front page.
Instructions:
(1) This paper consists of two sections.
Section A: Answer all three (3) questions, which together count for 60 marks:
(20 + 20 + 20 ) = 60.
(2) Section B: Answer any two (2) of the three (3) questions. Each question counts
for 20 marks: (2 x 20) = 40.
(3) Once you have completed your answers, submit your answers as a single document
in PDF format using the e-Assessment tool on the myExams portal. It is
preferable for you to type your answers (font: Arial 12) and then convert your
document to PDF for submission. However, if this is impossible, you may write your
answers down and scan them into a PDF file. Please write legibly.
(4) Start with a cover page stating the module code (ECS3706) and your student
number.
(5) This should be followed by your answers to the questions.
(6) There is no need for a table of contents, an introduction, a conclusion, or a list of
references (as was required in your assignments). Simply answer the questions
asked.
(7) Ensure that each question and sub-question is clearly numbered.
(8) While you are not required to cite your sources, this does not mean that you can copy
information from any source. You need to answer the questions in your own words.
Plagiarism will not be tolerated and will result in disciplinary action if detected.
(9) Ensure that your PDF document is NOT encrypted to a “secured” mode and that it is
NOT password protected, as these files cannot be marked. Virus-infected files will
also not be marked.
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, Page 2 of 11 ECS3706
CONFIDENTIAL Oct/Nov 2023
ECS3706
Date: 2 November 2023
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, Page 3 of 11 ECS3706
CONFIDENTIAL Oct/Nov 2023
SECTION A (60 marks)
Answer ALL three (3) questions in section A.
Section A requires brief and to-the-point answers.
In most cases, list or briefly explain what is required.
Using statistical notations (mathematical symbols) to explain concepts may be advantageous – but
please ensure that you also explain their meaning.
You do not need to re-explain concepts that have been previously dealt with. If required, you may refer
to your previous answer/s.
In general, each mark represents one correct fact or correct interpretation.
QUESTION A1 (20 marks)
(a) In a regression model where economic growth (GDP) is explained by the volume of
exports (EXP) and foreign direct investment (FDI), a researcher estimates equation 1.
After adding a nonsensical variable (NONS), new results are obtained in Equation 2.
̂ 𝒕 = 𝟔. 𝟏𝟎𝟓 − 𝟎. 𝟏𝟔𝟏𝑬𝑿𝑷𝑶𝑹𝑻𝑺 + 𝟎. 𝟑𝟐𝟕𝑭𝑫𝑰……………………Equation1
𝑮𝑹𝑶𝑾𝑻𝑯
𝑅2 = 0.74
̂ 𝒕 = 𝟓. 𝟗𝟗𝟔 − 𝟎. 𝟏𝟑𝟐𝑬𝑿𝑷𝑶𝑹𝑻𝑺 + 𝟎. 𝟐𝟖𝟗𝑭𝑫𝑰 + 𝟎, 𝟎𝟖𝑵𝑶𝑵𝑺……Equation 2
𝑮𝑹𝑶𝑾𝑻𝑯
𝑅2 = 0.75
i. The coefficient of EXPORTS and FDI changed when a nonsensical variable was
added. Does that make sense? (2)
ii. Theoretically, Economic growth has nothing to do with the nonsensical variable.
How is it possible that adding a nonsensical variable increases 𝑅2 ? (2)
iii. If the Growth is unrelated to NONS, how is it possible that the coefficient of the
nonsensical variable is non-zero? (2)
(b) Interested in assessing if online class attendance (CLA) improves students' final grades in
econometrics (GR), researchers estimated the following model.
̂ 𝒊 = 𝟐. 𝟎𝟖 + 𝟐. 𝟖𝟓𝑪𝑳𝑨𝒊 + 𝟎. 𝟕𝟓𝑨𝑺𝑪𝒊 ……………………..(Equation 3)
𝑮𝑹
Where
GR= The student’s final grade in econometrics
CLA= the percentage of online class lectures that the student attended
ASC= the percentage of assignments completed
i. Interpret the coefficients of CLA and ASC (4)
ii. What additional variables could be included in this model? (2)
iii. In this model, have we proved that CLA and ASC cause higher grades? Explain. (2)
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CONFIDENTIAL Oct/Nov 2023
(c) Explain the difference between the null and alternative hypothesis. Provide examples of both one-
sided and two-sided tests. (6)
[20]
QUESTION A2 (20 marks)
In a model that seeks to establish the location of a food chain restaurant, “Royal Monate,” you obtain
the following:
̂ 𝒊 = 𝟓𝟏𝟎𝟗𝟔 − 𝟒𝟓𝟑𝟕𝑵𝒊 + 𝟎. 𝟏𝟕𝟕𝑷𝒊 + 𝟎. 𝟔𝟒𝟒𝟐𝑰𝒊 + 𝟏𝟎. 𝟗𝟗𝟒𝑫𝒊 ……………………..Equation 4
𝒀
Where
Yi= Gross sales volume
Ni= Competition -the number of direct market competitors
Pi = Population – the number of people living within a 5km radius of the Royal Monate’s location
I= Income – the average household income of the population
D=Dummy variable
D=1: When traffic is heavy in front of the restaurant
D=0 Otherwise
(a) What is the expected sign of the dummy variable? Explain. (2)
(b) Interpret the coefficients of Ni, Pi, Ii and Di (8)
(c) Using equation 4, illustrate the difference between an intercept dummy and a slope dummy
variable [10]
[20]
QUESTION A3 (20 marks)
To prepare for next year’s “World No Tobacco Day” (31 May 2024), you decide to carry out a study on
205 local municipalities. You obtain the following results:
̂ 𝒊 = 𝟓𝟎 − 𝟒. 𝟓𝑬𝑫𝑼𝒊 + 𝟎. 𝟓𝑰𝑵𝑪𝒊 − 𝟎. 𝟎𝟒𝑻𝑨𝑿𝒊 − 𝟒𝑽𝑰𝑫𝒊 + 𝟐. 𝟓𝑹𝑨𝑫𝒊
𝑪𝑰𝑮
Where
CIGi = the number of cigarettes consumed per day per person in the ith municipality
EDUi = the average years of education for persons over 18 in the ith municipality
INCi = The average income in the ith municipality (thousands of rand)
TAXi = the tax per package of cigarettes in the ith municipality (rand)
VID I = the number of video ads against smoking aired on three TV channels in the ith
municipality
RAD I = the number of radio ads of five radio stations in the ith municipality
(a) Are there any irrelevant variables in this model? Explain. (4)
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