# 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

Page 2

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)