ES50108: Econometrics for Finance 2022
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DEPARTMENT OF ECONOMICS
ES50108: Econometrics for Finance
Mock or Sample Final Exam and Instructions
January 2022
Instructions
Exam Instructions:
1. Window will open for four hours to complete and submit (upload) your exam. For example, suppose window opens at 9:30 AM than will be closed at 13:30.
2. Contains three questions. You must answer all three questions. All three questions have equal weight. This means you have 60 minutes per question (3hours for exam and 1 hour for management, e.g. scanning, login, uploading etc.).
3. Material is covered by lectures, computer labs and seminars.
4. You must submit your paper within the scheduled time of4 hours.
• We are unable to grant extensions!
• late submissions will appear as a 0 NS (Zero marks, no-show).
5. It is paramount that you manage your time properly (start early with the preparation ofthe upload).
6. In general, we recommend handwritten solutions unless you have a DAP.
7. Handwritten solutions must be scanned - familiarise yourself with the procedure.
8. You can use a calculator in an exam.
9. It is your responsibility to make sure that
• your working environment is quiet and you are not destructed
• your internet connection is working
• your computer is working
10. In case of technical disruptions
• continue to work on your paper
• create your submission file before the submission window has closed.
• send your file - and only if you were unable to submit on Inspera - via email to your admin office (PG or UG) as soon as this is possible again.
• in general we are not allowed to accept submissions via email.
• submissions via email still require approval of the Associate Dean Learning and Teaching, i.e. it is not in our hands whether these submissions will be accepted!
• it is therefore important that you collect relevant evidence (screenshots, etc.).
Assessment Instructions:
1) I expect you to be able to explain things that were covered in the lectures or the seminars, computer labs, book chapters. Try to understand connections between topics.
2) The statement "derive and explain"’ requires a DERIVATION and an EXPLANATION.
3) Explain briefly" means that you can economise your explanation on the most crucial things.
4) If you think there is a mistake in the question, make a note of what you think is wrong and answer the question given your additional assumptions.
5) Any ambiguity in the interpretation of a question is not your responsibility and will be mitigated correspondingly.
6) Numerical answers should be rounded to three decimal places.
7) If not further specified, all references in addition to the lecture material must be detailed in a reference list.
8) Formulae and Statistical Tables to be used in this assessment can be downloaded from the Unit Moodle page.
9) Make sure that your first page contains your candidate number & the unit details.
10) Pages are numbered and sequentially ordered.
11) Save your answer in PDF format using the following name: CandidateNumberUnitCode.pdf
12) We require students to submit their answers in PDF format (one PDF file) via Inspera before the deadline. Please reflect your ability to explain things critically train your ability to explain things in your own words.
13) Avoid the impression that you just have memorised things without understanding those by just replicating the slides.
14) I am more likely to think that you understand if you present your answers in a consistent and innovative way, i.e., not by replicating the slides. The latter is important for marks above 69. Where possible make use of diagrams and equations.
1.
a) Discuss the concept of a simple linear regression using the ordinary least squares method. In this context, develop the concepts of population, sample and regression. Explain how the model works, discuss the underlying assumptions, and give some examples of violations ofthese assumptions.
[30 marks]
Word limit for question 1a: 400 words
b) Explain the nature of autocorrelation and illustrate typical patterns of autocorrelation in a couple of diagrams and compare to absence of autocorrelation. Building on this, explain why autocorrelation is a problem.
[25 marks]
Word limit for question 1b: 350 words
c) The following regression was run using quarterly data, amounting to 90 observations:
= 0.22 − 0.43 + 0. 11
(0.45) (0. 14) (0.03)
2 = 0.32, = 1.96, (3) = 13.44
where is the demand for textbooks, is the price of a book and is the total level of income, all variables are in logarithms (standard errors in parentheses). LM(2) is the Lagrange Multiplier test for second order autocorrelation and DW the Durbin-Watson test.
Word limit for question 1c: 500 words
(i) Interpret the coefficients (including the constant) in the above model.
[10 marks]
(ii) Using a t-test and a 1% level of statistical significance, are the individual estimated coefficients
(including the constant term), each statistically significantly different from zero?
[15 marks]
(iii) Does the above regression suffer from first order autocorrelation?
[10 marks]
(iv) Briefly describe how you would conduct the LM test for autocorrelation, does the above model suffer
from third order autocorrelation at the 1% and 5% level of significance?
[10 marks]
2.
a) Briefly discuss the impact of non-constant variance of error terms in regression analysis. For this, develop the concept of heteroscedasticity, with a focus on which assumption of the classical linear regression model is violated, and why.
[30 marks]
Word limit for question 2a: 400 words
b) An economist has the following data for 2008 for 40 cities across the United States:
BUSTRAVL: the demand for urban transportation by bus in thousands of passengers per hour
FARE: the bus fare in dollars
INCOME: the average income per capita in dollars
POP: the city population in thousands
DENSITY: the city population density in persons/square mile
She is analysing the effect of bus fares, income, population and density on demand for urban transportation by bus, so she regresses BUSTRAVL on FARE, INCOME, POP and DENSITY. The EViews output of that estimated model is given in Table 1.
Table 1 |
Dependent Variable: BUSTRAVL Method: Least Squares Sample: 1 40 Included observations: 40 |
Coefficient Std. Error t-Statistic Prob. |
C FARE INCOME POP DENSITY |
Mean dependent 0.919868 var 1933. 175
0.910710 S.D. dependent var 2431.757 Akaike info 726.6434 criterion 16. 13122
18480373 Schwarz criterion 16.34233 Hannan-Quinn -317.6243 criter. 16.20755 F-statistic 100.4449 Durbin-Watson stat 1.995180 Prob(F-statistic) 0.000000 |
Notes: Use appropriate significance levels for all tests. State the null and alternative hypotheses, the test statistic to compute and its distribution, and the criteria for accepting or rejecting the null hypothesis for all tests.
Word limit for question 2b: 700 words
(i) Carefully interpret each coefficient obtained in the regression you ran in Table 1. Are the signs ofthe coefficients consistent with your expectations? Why or why not?
[15 marks]
(ii) Perform a test of individual significance for the parameters of the variables FARE, INCOME, POP
and DENSITY using the critical value of the corresponding distribution and the test p-value. Interpret the test results. What do you conclude?
[20 marks]
(iii) The economist formulates a hypothesis that the effect of the city population density (DENSITY) is
five times larger than the effect of the bus fare (FARE), on the variable BUSTRAVL. Perform a Wald test for the analyst’s hypothesis, specifying the null hypothesis and the equation of the restricted model, in the knowledge that the sum of the squared residuals (RSS) of the restricted model for that test is 18542143. Interpret the test results.
[15 marks]
(iv) Figure 1 (below) plots the squared residuals obtained from the regression in Table 1. Figure 2
(below) plots INCOME (in the X axis) and the estimated residuals (in the Y axis) from the regression in Table 1. Use these plots to graphically test that assumption. Explain your conclusions.
[10 marks]
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Figure 1 |
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3,000,000
2,500,000 |
RESIDUALS^2 |
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2,000,000 |
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1,500,000 |
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500,000
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15 20 25 |
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Figure 2 |
2,000 1,600 1,200 800 400 0 -400 -800 -1,200 12,000 14,000 16,000 18,000 20,000 22,000 INCOME |
(v) The analyst hypothesises that the residuals of the regression have heteroscedasticity. Using the EViews output in Table 2 (below), explain how the analyst would test for heteroscedasticity and what would his conclusion be? Based on the results of that test, what can you say about the properties of the OLS estimator ofthe model?
[10 marks]
2022-01-22