I only need help with Q3

TAKE-HOME ONLINE EXAMINATIONS AUGUST/SEPTEMBER 2022
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Please read through this exam paper thoroughly before you start
the exam
August/September 2022 IC205 2021/2 A 800
IC205 2021/2 A 850
Guidance on Notation for Online Setup
UNIVERSITY OF READING
INTRODUCTORY ECONOMETRICS FOR FINANCE (IC205)
(RESIT)
Three hours (writing time) PLUS
Thirty minutes additional time for scanning and uploading
documents(time restricted exam, upload time)
Three hours and 30 minutes in total.
Answer ONE question from Section A and ONE question from Section B
Questions carry equal marks
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IC205 2021/2 A 800
Section A
1. A regression model for individuals 𝑖 = 1, 2, … , 𝑁 is given by:
𝑦𝑖 = 𝛽1 + 𝛽2𝑥2𝑖 + 𝛽3𝑥3𝑖 + 𝛽4𝑥4𝑖 + 𝑢𝑖
a) Suppose that an investigator wishes to test whether all of the
explanatory variables (other than the constant term) could in fact
be dropped from the equation without significantly worsening the
fit of the equation to the data. Describe a suitable test, including
the regression(s) and the null and alternative hypotheses, and
give the distribution of the test statistic under the null
hypothesis. (30%)
[maximum word count: 300 words]
b) How could the investigator test whether 𝛽3 = 0 without imposing
any restrictions on the effects of the other variables? Describe a
suitable test and give the distribution of the test statistic under
the null hypothesis. (20%)
[maximum word count: 200 words]
c) Suppose the sample consists of Males and Females. How could
the investigator test whether the same relationship between the
dependent variable and the explanatory variables holds for
Males and Females? Describe a suitable test and give its
distribution under the null hypothesis. If any new variables need
to be created, carefully define those. (25%)
[maximum word count: 250 words]
d) Suppose instead that the investigator was only interested in the
possibility that the effect of 𝑥2 might be different for Males and
Females, assuming that the other variables affect the dependent
variable in the same way for both Males and Females. How
would this hypothesis be tested, again explaining how the test
statistic would be calculated, and its distribution under the null
hypothesis. (25%)
[maximum word count: 250 words]
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IC205 2021/2 A 800
2. a) Assume a researcher runs a model with ERMSOFT as
dependent variable and the following independent variables:
ERSANDP, DPROD, DCREDIT, DINFLATION, DMONEY,
DSPREAD, RTERM. The data is monthly data and the regression
model is estimated over the sample March 1990 to March 2018.
The researcher presents you with the EViews regression output, as
shown below:
Dependent Variable: ERMSOFT
Method: Least Squares
Sample: 1990M03 2018M03
Included observations: 337
Variable Coefficient Std. Error t-Statistic Prob.
C 0.944958 0.470738 2.007398 0.0455
ERSANDP 1.268958 0.098789 12.84511 0.0000
DPROD -0.402748 0.692321 -0.581735 0.5611
DCREDIT -0.013304 0.025420 -0.523363 0.6011
DINFLATION 1.806419 1.216315 1.485157 0.1385
DMONEY -0.005412 0.014625 -0.370030 0.7116
DSPREAD 2.690804 3.972932 0.677284 0.4987
RTERM 3.802662 1.721644 2.208739 0.0279
R-squared 0.350038 Mean dependent var 1.219088
Adjusted R-squared 0.336209 S.D. dependent var 8.909452
S.E. of regression 7.258830 Akaike info criterion 6.825767
Sum squared resid 17335.21 Schwarz criterion 6.916451
Log likelihood -1142.142 Hannan-Quinn criter. 6.861912
F-statistic 25.31193 Durbin-Watson stat 2.288189
Prob(F-statistic) 0.000000
i) The researcher would like to know which of the variables are
statistically significant. Explain how you can evaluate the
statistical significance of the individual variables and name
those that are statistically significant. What does it mean if a
variable is not statistically significant? (20 %)
[maximum word count: 200 words]
ii) The researcher thinks that the constant term is insignificant
and suggests excluding it from the model. Is the researcher
correct and do you agree with his/her suggestion? Explain
which effect removing the constant term has on the other
coefficient estimates. (20 %)
[maximum word count: 200 words]
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IC205 2021/2 A 800
iii) The researcher would like to test whether all of the
independent variables could be dropped from the model
without significantly affecting the model fit. Can you use any
of the information provided in the regression output to
answer this query? Explain your answer. (20 %)
[maximum word count: 200 words]
iv) The 𝑅
2 value of the regression model shown above is
0.350038 and the adjusted 𝑅
2
is stated as 0.336209. What
do these numbers tell you and how do you interpret them?
(10 %)
[maximum word count: 100 words]
v) Assume that you add a new variable to the model and reestimate the model using the sample as shown above. Your
𝑅
2 value of the new regression increases to 0.38 but your
adjusted 𝑅
2 value drops to 0.31. What do these changes in
the 𝑅
2 and adjusted 𝑅
2 values tell you about the explanatory
power of the newly added variable? (15 %)
[maximum word count: 150 words]
b) You have two time-series: 𝑦𝑡 and 𝑥𝑡
. You want to test the null
hypothesis that the average of the difference between the two
series is equal to 0. How can you test this? Explain the steps of
the testing procedure including the model and hypothesis that
you test. (15 %)
[maximum word count: 150 words]
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IC205 2021/2 A 800
Section B
3. a) State whether the below statements are correct or incorrect and
explain why.
[maximum word count: 250 words]
i) A random sample is a selection from the population that is
representative of the population. (5%)
ii) The F-test has both a positive and a negative critical value.
(5%)
iii) Transforming the variables into logs can be a viable solution
for heteroscedasticity. (5%)
iv) If there are no patterns in the residuals of an OLS
regression, then all assumptions of the CLRM hold. (5%)
v) The t-statistic is a special case of the t-ratio. (5%)
b) A researcher presents you with the scatter plot below including
the fitted regression line based on an OLS regression.
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IC205 2021/2 A 800
The researcher comments: “This plot is very useful because
now I can see what values 𝑦𝑡
is likely to take if 𝑥𝑡 was zero.” Is
this statement correct? Based on your knowledge of
econometrics, what would you respond to the researcher?
(15%)
[maximum word count: 150 words]
c) A researcher tells you that there is a trade-off between making a
Type 1 and a Type 2 error in hypothesis testing. Explain what
s/he means by that.
Is there a way that you can decrease the likelihood of making
both errors? If so, explain how you can achieve this. (20%)
[maximum word count: 200 words]
d) Imagine that you have a regression model with quarterly stock
returns as the dependent variable and three quarter dummies as
independent variables together with a constant:
𝑟𝑡 = 𝛽1 + 𝛽2𝑄2𝑡 + 𝛽3𝑄3𝑡 + 𝛽4𝑄4𝑡 + 𝑢𝑡
i) How do you interpret the coefficient estimate of 𝛽1?
(10 %)
[maximum word count: 100 words]
ii) How do you interpret the coefficient estimate of 𝛽3?
(10 %)
[maximum word count: 100 words]
iii) If you want to know the average return of the stock during
quarter 2 (Q2), how could you determine this?
(10 %)
[maximum word count: 100 words]
iv) Why is there no dummy for quarter 1 included in the model?
(10 %)
[maximum word count: 100 words]
4. a) A researcher runs two models and obtains the following
estimates of the 𝑅
2
figures:
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IC205 2021/2 A 800
Model 1: 𝑦𝑡 = 𝛽1 + 𝛽2𝑥2𝑡 + 𝛽3𝑥3𝑡 + 𝑢𝑡
;
𝑅
2 = 0.108 ; 𝑎𝑑𝑗. 𝑅
2 = 0.092
Model 2: 𝑦𝑡 = 𝛽1 + 𝛽2𝑥2𝑡 + 𝛽3𝑥3𝑡 + 𝛽4𝑥4𝑡 + 𝑣𝑡
;
𝑅
2 = 0.112; 𝑎𝑑𝑗. 𝑅
2 = 0.089
The two models contain the same dependent variable and
independent variables 𝑥2𝑡 and 𝑥3𝑡 and are estimated over the
same sample.
Based on your knowledge of the 𝑅
2 and adjusted 𝑅
2 statistic, can
you make a statement whether the variable 𝑥4𝑡 should be kept in
the model or should be removed? Explain your answer. (20%)
[maximum word count: 200 words]
b) The graph below shows the OLS fitted line. What value do you
expect the 𝑅
2
to take?
(10%)
[maximum word count: 100 words]
c) Firms’ salary costs have been found to react slowly to
occurrences of economic downturns, e.g. the imposing and
lifting of the Covid-19 related lockdown, due to significant firing
and hiring costs.
i) Which type of problem can this cause when running an
econometric model with the salary costs as dependent
variable and economic production as independent variable?
State which of the assumptions of the CLRM would be
violated. (10 %)
[maximum word count: 100 words]
t y
t x
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IC205 2021/2 A 800
ii) How could you address this issue using a dynamic model?
(10 %)
[maximum word count: 100 words]
d) Why might we use dummy variables to test for structural change
rather than a Chow test? (20 %)
[maximum word count: 200 words]
e) You have the following econometric model:
∆𝑦𝑡 = 𝛽1 + 𝛽2∆𝑥2𝑡 + 𝛽3∆𝑥3𝑡 + 𝛽4∆𝑥2𝑡−1 + 𝛽5∆𝑥3𝑡−1 + 𝑢𝑡
.
You are interested in the long-run solution of this model, but a
researcher tells you that this model does not have a long-run
solution.
Is the researcher correct? Explain why or why not. Support your
explanation by appropriate transformations of the model.
Explain, in words, what the long-run solution tells you about the
relation between y and the explanatory variables (20%)
[maximum word count: 200 words]
f) What are the consequences of including an irrelevant variable in
a model? (10 %)
[maximum word count: 100 words]
(End of Question Paper)