UNIVERSITY EXAMINATIONS
May/June 2022
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 pages of statistical
tables (pages 9 to 11), plus 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.
Section B: Answer any two (2) of the three (3) questions. Each question counts
for 20 marks: (2 x 20) = 40.
(2) 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 not possible, you may also write
your answers down and scan them to a PDF file. Please write legibly.
(3) Start with a cover page stating the module code (ECS3706) and your student
number.
(4) This should be followed by your answers to the questions.
(5) 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.
(6) Ensure that each question and sub-question is clearly numbered.
(7) While you are not required to cite your sources, this does not mean that you can
simply 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.
(8) 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.
[TURN OVER]
, Page 2 of 11 ECS3706
CONFIDENTIAL May/June 2022
INSTRUCTIONS ON THE DAY OF ASSESSMENT:
Ensure you are connected to the internet in order to log into the YOUR EXAM QR CODE & EXAM
Invigilator App and scan this QR code. ACCESS CODE
If you encounter difficulty in scanning the QR code, you can
alternatively enter the Exam Access Code below the QR code to start
the invigilation.
Unless otherwise specified by your institution, note that you can only
scan this QR code once. If your assessment has multiple online sections,
tests or attempts, you should NOT finish the invigilation until your entire
assessment has been completed.
Only scan the QR code when the assessment formally commences.
Exam Access Code: 2ddc291c
The QR code is only scannable for a limited time and it should
therefore be scanned as soon as possible to start the
invigilation.
Once the QR code is scanned, ensure your media volume Is turned up and place your smartphone next to you. The
Invigilator App will notify you with a notification beep when you are required to action a request, which you should then
perform.
We recommend that you keep your smartphone on charge for the duration of the assessment.
If you only have one device you may access your assessment in the application by pressing the ‘Access Exam’ button
in the top right corner of your app.
Keep the Invigilator App open on your cell phone for the full duration of the assessment. You are not
allowed to minimise or leave the app.
Ensure you are connected to the internet in order to commence the invigilation as well as at the end of the
assessment. No internet connection is required during the assessment.
You have to adhere to the assessment time limit communicated to you by your institution as the time
displayed in the Invigilator App could differ from the time allocated to complete your assessment.
You can click the "Finish Assessment" button in the app if you finish your assessment early.
If you are performing a written or Scan-and-Upload assessment:
The Invigilator App may request you to take a picture of every page of your answer sheet at the end of the
assessment. Unless otherwise specified by your institution, this does NOT replace the normal upload of
your script to your institutions online portal
After completing invigilation and following all app instructions, you must upload your Invigilation App data. If however
there is a delay in the upload of the app data at the end of the assessment, you should prioritise the upload of your
script to your university portal and you can temporarily minimise the app to do so. Uploading of app data is not time
sensitive and you can come back and do it after you have successfully uploaded your script to the exam portal.
Should you encounter any technical difficulty, please WhatsApp The Invigilator Helpdesk on 073 505 8273.
[TURN OVER]
, Page 3 of 11 ECS3706
CONFIDENTIAL May/June 2022
SECTION A (60 marks)
Answer ALL three (3) questions in section A.
Section A requires brief and to- the- point answers.
In most cases simply list, or briefly explain, what is required.
It may be advantageous to use statistical notations (mathematical symbols) to explain concepts – 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 simply
refer to your previous answer/s.
In general, each mark represents one correct fact or correct interpretation.
QUESTION A1 (20 marks)
(a) Distinguish between the following terms (5)
i. Cross- section and time-series data
ii. Categorical and continuous data
iii. Significance tests and confidence intervals
(b) Including the disturbance or stochastic error term in your model implies that one does not have
to worry about specification errors in the model. Discuss. (6)
(c) You estimate two models. The second one has two fewer explanatory variables. You observe
that R-squared decreases in the second model. Does this prove that the first model is better?
(4)
(d) Provide three examples of situations where you would use a one-tailed hypothesis test
rather than a two-tailed hypothesis test. (5)
[20]
QUESTION A2 (20 marks)
(a) State four valid criteria for determining whether a given variable belongs in an equation. (4)
(b) Consider the following Cobb-Douglas production function which relates production to factors of
𝛽 𝛾
production: 𝑄𝑡 = 𝐾𝑡𝛼 𝐿𝑡 𝑆𝑡 𝑒 𝑢 – where Q is production, K is capital, L is labour, and S is other
knowledge-based inputs such as research and development. You have obtained firm-level data
for all the key variables in your model. Explain how you would estimate the production
parameters using regression analysis. (5)
[TURN OVER]
May/June 2022
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 pages of statistical
tables (pages 9 to 11), plus 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.
Section B: Answer any two (2) of the three (3) questions. Each question counts
for 20 marks: (2 x 20) = 40.
(2) 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 not possible, you may also write
your answers down and scan them to a PDF file. Please write legibly.
(3) Start with a cover page stating the module code (ECS3706) and your student
number.
(4) This should be followed by your answers to the questions.
(5) 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.
(6) Ensure that each question and sub-question is clearly numbered.
(7) While you are not required to cite your sources, this does not mean that you can
simply 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.
(8) 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.
[TURN OVER]
, Page 2 of 11 ECS3706
CONFIDENTIAL May/June 2022
INSTRUCTIONS ON THE DAY OF ASSESSMENT:
Ensure you are connected to the internet in order to log into the YOUR EXAM QR CODE & EXAM
Invigilator App and scan this QR code. ACCESS CODE
If you encounter difficulty in scanning the QR code, you can
alternatively enter the Exam Access Code below the QR code to start
the invigilation.
Unless otherwise specified by your institution, note that you can only
scan this QR code once. If your assessment has multiple online sections,
tests or attempts, you should NOT finish the invigilation until your entire
assessment has been completed.
Only scan the QR code when the assessment formally commences.
Exam Access Code: 2ddc291c
The QR code is only scannable for a limited time and it should
therefore be scanned as soon as possible to start the
invigilation.
Once the QR code is scanned, ensure your media volume Is turned up and place your smartphone next to you. The
Invigilator App will notify you with a notification beep when you are required to action a request, which you should then
perform.
We recommend that you keep your smartphone on charge for the duration of the assessment.
If you only have one device you may access your assessment in the application by pressing the ‘Access Exam’ button
in the top right corner of your app.
Keep the Invigilator App open on your cell phone for the full duration of the assessment. You are not
allowed to minimise or leave the app.
Ensure you are connected to the internet in order to commence the invigilation as well as at the end of the
assessment. No internet connection is required during the assessment.
You have to adhere to the assessment time limit communicated to you by your institution as the time
displayed in the Invigilator App could differ from the time allocated to complete your assessment.
You can click the "Finish Assessment" button in the app if you finish your assessment early.
If you are performing a written or Scan-and-Upload assessment:
The Invigilator App may request you to take a picture of every page of your answer sheet at the end of the
assessment. Unless otherwise specified by your institution, this does NOT replace the normal upload of
your script to your institutions online portal
After completing invigilation and following all app instructions, you must upload your Invigilation App data. If however
there is a delay in the upload of the app data at the end of the assessment, you should prioritise the upload of your
script to your university portal and you can temporarily minimise the app to do so. Uploading of app data is not time
sensitive and you can come back and do it after you have successfully uploaded your script to the exam portal.
Should you encounter any technical difficulty, please WhatsApp The Invigilator Helpdesk on 073 505 8273.
[TURN OVER]
, Page 3 of 11 ECS3706
CONFIDENTIAL May/June 2022
SECTION A (60 marks)
Answer ALL three (3) questions in section A.
Section A requires brief and to- the- point answers.
In most cases simply list, or briefly explain, what is required.
It may be advantageous to use statistical notations (mathematical symbols) to explain concepts – 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 simply
refer to your previous answer/s.
In general, each mark represents one correct fact or correct interpretation.
QUESTION A1 (20 marks)
(a) Distinguish between the following terms (5)
i. Cross- section and time-series data
ii. Categorical and continuous data
iii. Significance tests and confidence intervals
(b) Including the disturbance or stochastic error term in your model implies that one does not have
to worry about specification errors in the model. Discuss. (6)
(c) You estimate two models. The second one has two fewer explanatory variables. You observe
that R-squared decreases in the second model. Does this prove that the first model is better?
(4)
(d) Provide three examples of situations where you would use a one-tailed hypothesis test
rather than a two-tailed hypothesis test. (5)
[20]
QUESTION A2 (20 marks)
(a) State four valid criteria for determining whether a given variable belongs in an equation. (4)
(b) Consider the following Cobb-Douglas production function which relates production to factors of
𝛽 𝛾
production: 𝑄𝑡 = 𝐾𝑡𝛼 𝐿𝑡 𝑆𝑡 𝑒 𝑢 – where Q is production, K is capital, L is labour, and S is other
knowledge-based inputs such as research and development. You have obtained firm-level data
for all the key variables in your model. Explain how you would estimate the production
parameters using regression analysis. (5)
[TURN OVER]
