Microsoft Word - Assignment24118.docx
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ECON241: Introductory Econometrics
ASSIGNMENT (S2, 2018)
Instructions
Due date: 5pm, Friday 26 October 2018 (Week 11)
Submission: Submit your report and Gretl output as two separate PDF files using the
co
esponding turnitin links on the unit homepage. Your submission will be complete only
if both files have been submitted.
ï‚· All 10 questions are of equal value.
ï‚· All questions should be answered clearly and in your own words.
ï‚· All relevant working must be shown.
ï‚· No appendices should be attached to your main report. Collect all Gretl outputs, on which
your answers are based, in a single PDF file and submit it using a separate link. The Gretl
output itself will not be marked, but your answers must be consistent with your Gretl
output.
ï‚· Your assignment should be typed using a word-processing program (e.g. Microsoft Word,
Li
eOffice Writer, etc) or a typesetting language (e.g. LaTeX) and saved as a PDF file.
ï‚· Your submission is final and whatever you submit will be marked. You will not be given
an opportunity to resubmit, so make sure that the document that you submit is the final
draft of your assignment and not some other document that is on your computer.
ï‚· The only acceptable form of submission is via the relevant link in iLearn. In particular,
assignments that are emailed to the teaching staff will not be accepted.
ï‚· No extensions will be granted. There will be a deduction of 10% of the total available
marks made from the total awarded mark for each 24 hour period or part thereof that the
submission is late (for example, 25 hours late in submission – 20% penalty). This penalty
does not apply to cases in which the University grants the student Special Consideration.
No submission will be accepted after the marked assignments have been returned to the
students. Students who wish to submit the assignment after the deadline should contact the
unit convenor so that the necessary a
angements may be made.
ï‚· It is intended that students will work on the assignments independently. Students who
submit an assignment that is substantially copied from another source may receive a mark
of zero, and may be refe
ed to the Faculty for further action.
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QUESTIONS
How much an employee earns per hour (hourly wage rate) depends on the person’s education
level, work experience, and cognitive skills. Two alternative regression models are
considered to analyse this relationship for Australian workers in 2017.
ï‚· Model A
RHWi = α1 + α2EDUi + α3EXPi + α4EXPi2 + α5CTESTi + ei
ï‚· Model B
ln(RHWi) = β1 + β2EDUi + β3EXPi + β4EXPi2 + β5CTESTi + ui
where
RHW = real hourly wage rate ($),
EDU = number of years of education (years),
EXP = experience in paid work (years), and
CTEST = score for cognitive skills test (out of 100).
The data file, Assignment24118.gdt, contains the above variables for a randomly-selected
500 full-time workers in Australia.
Estimate the above models using the OLS method, and answer the following questions.
Q1. Model A & Model B
(1) Provide a summary report for each model by writing down the estimated equation and
elevant statistics including the standard e
ors.
(2) Discuss whether each of the estimated coefficients has the expected sign.
Q2. Model A
Interpret the estimated coefficients. (N.B. Do not try to interpret α3 and α4 separately, but
interpret the marginal effect of experience on wage rate, which includes both α3 and α4.)
Q3. Model A
(1) Test if each regression coefficient is significantly different from zero. Use the 5%
significance level. For your tests, clearly state the hypotheses, test statistic, its
distribution under the null hypothesis, the observed value of the test statistic, the critical
value (or p-value), decision to reject or not to reject the null hypothesis, and
interpretation of the test result.
(2) Note that the distribution of the random e
or term is unknown. Explain why the use of
the specific distribution that you have used for these tests is justified.
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Q4. Model A
(1) Estimate and interpret the elasticity of wage rate with respect to education, evaluated at
the sample mean values of the variables.
(2) Estimate and interpret the elasticity of wage rate with respect to experience, evaluated at
the sample mean values of the variables.
Q5. Model A
Test if the model as a whole is significant. Use the 5% significance level. For your test,
clearly state the hypotheses, test statistic, its distribution under the null hypothesis, the
observed value of the test statistic, the critical value (or p-value), decision to reject or not to
eject the null hypothesis, and interpretation of the test result. (Assume that the random e
or
term follows a normal distribution.)
Q6. Model A
Assume that, in another data set, wage rate is measured in hundreds of dollars and education
is measured in months. Explain what would happen to (i) the estimate of α2, (ii) its standard
e
or, (iii) R2, (iv) the unexplained variation (SSE), and (v) the sample mean of the dependent
variable, if the model were estimated using this data set.
Q7. Model B
Estimate the model using the OLS method, and interpret the regression coefficients. (N.B.
Again, do not try to interpret β3 and β4 separately.)
Q8. Model B
(1) Estimate and interpret the elasticity of wage rate with respect to education, evaluated at
the sample mean values of the variables.
(2) Construct a 95% confidence interval for the coefficient for education and interpret it.
Q9. Model B
Test if the coefficient for education equals the coefficient for experience (i.e., β2 = β3) against
the alternative hypothesis that the former is larger than the latter (i.e. β2 > β3). Use the 5%
significance level. Your answer must include the hypotheses, test statistic, its distribution
under the null hypothesis, the observed value of the test statistic, the critical value (or p-
value), decision to reject or not to reject the null hypothesis, and interpretation of the test
esult.
Q10. Model B
Test the hypothesis that experience is not important in determining log wage rate (i.e., both β3
and β4 are jointly insignificant). Use the 5% significance level. Your answer must include the
hypotheses, the unrestricted model and the restricted model, test statistic, its distribution
under the null hypothesis, the observed value of the test statistic, the critical value (or p-
value), decision to reject or not to reject the null hypothesis, and interpretation of the test
esult. (Assume that the random e
or term follows a normal distribution.)