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Email:
http://theeconomistsoe.com/
, 1
UNIVERSITY EXAMINATIONS
May/June 2020
ECS3706
Solutions For JUNE 2020
ECONOMETRICS
100 Marks Duration 4 Hours EXAMINERS:
FIRST: PROF S NHAMO
SECOND: DR M ZUKA
This paper consists of 11 pages, including a formulae sheet (p8), 3 pages of statistical tables
(pp 9 to 11), plus the special front page.
Instructions:
(1) This paper consists of two sections
Section A: Answer all 4 questions which together count 60 marks (15+15+15+15) = 60
Section B: Answer any 2 of the 3 questions. Each question counts 20 marks (2X20)=40
(2) Submit your answers as a single document in PDF format. It is preferable for you to
type your answers (Font: Arial 12) and then convert your document to PDF format 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, introduction, conclusion or list of references
(as was required in your assignments). Simply answer the questions asked.
(6) Make sure 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) Please ensure that you submitted a declaration of honesty on myUnisa.
(9) Please 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.
(10) Submit your answers in one PDF document by using the Assessment Info tool on
myUnisa. Detailed instructions are provided in Tutorial Letter ECS3706/102/1/2020.
, 2
SECTION A (60 marks)
Answer ALL four 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 notation (mathematical symbols) to explain concepts, but make
sure to also explain their meaning.
It is not required 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 1 (15 marks)
(a) Using words and/or equations, briefly explain the following concepts. (6)
(i) Degrees of freedom (2)
These refer to the excess of the number of observations (N) over the number of
coefficients (including the intercept) estimated (K+1), There are essentially the number
of estimates that remain after a statistical procedure has been undertaken.
(ii) The difference between the stochastic error term and the residual. Make sure that you
define both terms, state how they are similar, state how they are different and provide
examples of an equation with a stochastic error term and one that contains a
residual.(4)
A stochastic error term is a term that is added to a regression equation to introduce all of the
variation in Y that cannot be explained by the included Xs. It is, in effect, a symbol of the
econometrician’s ignorance or inability to model all the movements of the dependent variable.
The difference between the estimated value of the dependent variable and the actual value of
the dependent variable (Yi) is defined as the residual (ei).
(b) What are the major consequences of including an irrelevant variable in a regression equation?(3)
The inclusion of an irrelevant variable will increase the variance of the estimated coefficients, and this
increased variance will tend to decrease the absolute magnitude of their t-scores. Also, an irrelevant
variable usually will decrease the adjusted r-squared (but not the r-squared).
(c) You are a labour economist and wish to explain salaries of various workers. In the process, you omit
an important variable “experience”. What is the sign of the bias on the coefficient of the included variable
“age”? (3)
In general this leads to biased estimates of the remaining (included) coefficients of the remaining
(included) variables .The direction of bias will depend on the correlation between age and
experience which is expected to be positive. The coefficient of age is likely to be overestimated.
, 3
(c) Do you think that unbiased estimates are always better than biased ones? Why or why not?
For example, B1 is unbiased if the mean of its sampling distribution equals the number B being
estimated. In other words an unbiased estimator provides the researcher with an estimate of the true
population parameter using a sample. N.B Note that our goal in econometrics is to estimate the true
population. The result from bias is over estimation of parameters.
[15] QUESTION 2 (15 marks)
Consider the following least squares estimates of the relationship between interest rates and the
budget deficit in South Africa:
(a) What do you understand by “least squares estimates”? (4)
Generally the Betas produced by OLS are called estimates. In equation (2) the beta hats are estimates,
they are a result after a regression has been run. Thus, OLS is an estimator, and a
(Beta hats) produced by OLS is an estimate.
(b) In model A, R2=0. Explain what this means. Is it possible to have a negative R2? (3)
For the r-squared a value of zero shows a failure of the estimated regression equation to explain the
values of Yi better than could be explained by the sample mean Y-bar. ESS=0, and the unexplained
portion, RSS, equals the total squared deviations TSS; thus, R2=0. There is no negative r squared the
mathematical derivation does not allow that. Check example in study guide.
(c.)Comment on the expected signs for the estimated slope coefficients in both Model A and Model B.(4)
(c) Which of the two models is better? Provide reasons. (4)
[15]
QUESTION 3 (15 marks)
Email:
http://theeconomistsoe.com/
, 1
UNIVERSITY EXAMINATIONS
May/June 2020
ECS3706
Solutions For JUNE 2020
ECONOMETRICS
100 Marks Duration 4 Hours EXAMINERS:
FIRST: PROF S NHAMO
SECOND: DR M ZUKA
This paper consists of 11 pages, including a formulae sheet (p8), 3 pages of statistical tables
(pp 9 to 11), plus the special front page.
Instructions:
(1) This paper consists of two sections
Section A: Answer all 4 questions which together count 60 marks (15+15+15+15) = 60
Section B: Answer any 2 of the 3 questions. Each question counts 20 marks (2X20)=40
(2) Submit your answers as a single document in PDF format. It is preferable for you to
type your answers (Font: Arial 12) and then convert your document to PDF format 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, introduction, conclusion or list of references
(as was required in your assignments). Simply answer the questions asked.
(6) Make sure 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) Please ensure that you submitted a declaration of honesty on myUnisa.
(9) Please 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.
(10) Submit your answers in one PDF document by using the Assessment Info tool on
myUnisa. Detailed instructions are provided in Tutorial Letter ECS3706/102/1/2020.
, 2
SECTION A (60 marks)
Answer ALL four 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 notation (mathematical symbols) to explain concepts, but make
sure to also explain their meaning.
It is not required 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 1 (15 marks)
(a) Using words and/or equations, briefly explain the following concepts. (6)
(i) Degrees of freedom (2)
These refer to the excess of the number of observations (N) over the number of
coefficients (including the intercept) estimated (K+1), There are essentially the number
of estimates that remain after a statistical procedure has been undertaken.
(ii) The difference between the stochastic error term and the residual. Make sure that you
define both terms, state how they are similar, state how they are different and provide
examples of an equation with a stochastic error term and one that contains a
residual.(4)
A stochastic error term is a term that is added to a regression equation to introduce all of the
variation in Y that cannot be explained by the included Xs. It is, in effect, a symbol of the
econometrician’s ignorance or inability to model all the movements of the dependent variable.
The difference between the estimated value of the dependent variable and the actual value of
the dependent variable (Yi) is defined as the residual (ei).
(b) What are the major consequences of including an irrelevant variable in a regression equation?(3)
The inclusion of an irrelevant variable will increase the variance of the estimated coefficients, and this
increased variance will tend to decrease the absolute magnitude of their t-scores. Also, an irrelevant
variable usually will decrease the adjusted r-squared (but not the r-squared).
(c) You are a labour economist and wish to explain salaries of various workers. In the process, you omit
an important variable “experience”. What is the sign of the bias on the coefficient of the included variable
“age”? (3)
In general this leads to biased estimates of the remaining (included) coefficients of the remaining
(included) variables .The direction of bias will depend on the correlation between age and
experience which is expected to be positive. The coefficient of age is likely to be overestimated.
, 3
(c) Do you think that unbiased estimates are always better than biased ones? Why or why not?
For example, B1 is unbiased if the mean of its sampling distribution equals the number B being
estimated. In other words an unbiased estimator provides the researcher with an estimate of the true
population parameter using a sample. N.B Note that our goal in econometrics is to estimate the true
population. The result from bias is over estimation of parameters.
[15] QUESTION 2 (15 marks)
Consider the following least squares estimates of the relationship between interest rates and the
budget deficit in South Africa:
(a) What do you understand by “least squares estimates”? (4)
Generally the Betas produced by OLS are called estimates. In equation (2) the beta hats are estimates,
they are a result after a regression has been run. Thus, OLS is an estimator, and a
(Beta hats) produced by OLS is an estimate.
(b) In model A, R2=0. Explain what this means. Is it possible to have a negative R2? (3)
For the r-squared a value of zero shows a failure of the estimated regression equation to explain the
values of Yi better than could be explained by the sample mean Y-bar. ESS=0, and the unexplained
portion, RSS, equals the total squared deviations TSS; thus, R2=0. There is no negative r squared the
mathematical derivation does not allow that. Check example in study guide.
(c.)Comment on the expected signs for the estimated slope coefficients in both Model A and Model B.(4)
(c) Which of the two models is better? Provide reasons. (4)
[15]
QUESTION 3 (15 marks)
