BE314-5-SP/1
UNIVERSITY OF ESSEX
SECOND YEAR EXAMINATION 2020
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FINANCIAL MODELLING
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Time allowed: 24 hours
Time to spend on your assessment: 2 hours
Maximum word count for assessment: 2000 words
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The paper consists of FIVE questions.
Candidates must answer TWO questions:
ONE question from Section A and ONE question from Section B.
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BE314-5-SP/2
SECTION A
Answer ONE question in Section A.
QUESTION ONE
a) List the four Gauss-Markov conditions and briefly explain what they mean. When doing
OLS, why do we need those conditions to hold? Briefly explain.
(15 marks)
b) Briefly explain the difference between the population regression function and the sample
regression function. Use equations to support your answer
(10 marks)
c) You are studying the effects of a single explanatory variable, X, on the dependent variable,
Y, using the following simple linear regression model:
= 0 + 11 +
Show briefly the steps for testing the null hypothesis that the true population value of the
slope coefficient (1) equals 1. Explain what the two possible outcomes of the test are, and
the decision rule used to determine which of these outcomes has occurred.
(15 marks)
d) Following the previous question, you want to include two new independent variables, 2
and 3, giving the new multiple regression model:
= 0 + 11 + 22 + 33 +
You argue that the two new independent variables 2 and 3 are jointly important for
explaining the value of Y. Explain briefly how you could test would test your argument
using an appropriate hypothesis testing procedure. Clearly state the null hypothesis you
would use in the test.
(10 marks)
[TOTAL 50 MARKS]
END OF QUESTION ONE
BE314-5-SP/3
QUESTION TWO
Sir Francis Galton examined the relationship between the height of children and their parents
towards the end of the 19th century. You decide to update his findings by collecting data from 110
college students, and estimate the following relationship:
where Studenth is the height of students in inches, and Midparh is the average of the parental
heights in inches. Values in parentheses are standard errors.
a) How would you interpret the estimated values of the intercept and slope coefficients?
(10 marks)
b) Test the null hypothesis that the true value of the slope coefficient equals zero. Clearly state
the null and alternative hypotheses, the relevant critical value(s) and explain how you reach
your conclusion. Use a two-sided test, at a significance level of 5%.
(15 marks)
c) If the average height of a student’s parents is 67 inches, then what is the predicted value of
the student’s height?
(10 marks)
d) You now extend the model by adding two new explanatory variables, nutrition and income.
The R-squared of the new regression model is 0.69. Use this information to test the null
hypothesis that coefficients the two new variables are jointly statistically insignificant using
the F-test. Clearly state the null and alternative hypotheses, the value of the F-statistic and
the critical value you use.
(15 marks)
[TOTAL 50 MARKS]
END OF QUESTION TWO
END OF SECTION A
BE314-5-SP/4
SECTION B
Answer ONE question in Section B
QUESTION THREE
a) A researcher is trying to model the level of UK personal consumption expenditure i.e. the
total amount spent by households on goods and services for consumption. Using quarterly
data from quarter 1 1997 to quarter 4 2019, the following regression model is estimated
(with t-ratios given below in parentheses):
where Ct is UK personal consumption expenditure in millions of £s, time is a linear trend
variable, Q2t is a dummy variable that equals 1 in the second quarter of each year and zero
otherwise, Q3t is a dummy variable that equals 1 in the third quarter of each year and zero
otherwise and Q4t is a dummy variable that equals 1 in the fourth quarter of each year and
zero otherwise.
i) Interpret and discuss the estimated values of the regression coefficients on the dummy
variables Q2, Q3 and Q4.
(10 marks)
ii) Using the t-ratios given above, determine whether there is evidence of significant
seasonality in UK personal consumption expenditure. Clearly explain how you reach
your conclusion.
(10 marks)
iii) Using two separate equations, write the estimated regression model that applies in the
second quarter of each year and the regression model that applies in the third quarter of
each year.
(10 marks)
b) Define and briefly explain the concept of a ‘structural break’. Explain how you could test for
the existence of a structural break in personal consumption expenditure after the financial
crisis of 2008. When answering the question, clearly write out the regression model that you
would use (you may ignore the seasonal effects discussed above to keep things simple) and
clearly define the dummy variables that are used in the model.
(20 marks)
[TOTAL 50 MARKS]
END OF QUESTION THREE
BE314-5-SP/5
QUESTION FOUR
a) Models (1) and (2) below are estimated using information on a cross-sectional sample of
data for 2500 employees at financial institutions in the UK. In all cases stands for natural
logarithm.
� = 8.44 + 0.06 + 0.02 (1)
� = 5.82 + 0.81 + 0.11 − 0.0012 (2)
where:
is the annual salary of the worker in GB£
is the number of complete years of education of the worker
is the age of the worker in years
Clearly explain what the estimated values of the slope coefficients in the two models imply
about the relationship between each explanatory/independent variable and salary (you do not
need to discuss the intercept/constant coefficient in each model).
(25 marks)
b) Explain in general terms what is meant by the problem of ‘incorrect functional form’ in the
context of regression analysis. What are the potential consequences of the problem?
(12 marks)
c) What are the possible methods that could be used to test whether a particular regression
model you have estimated suffers from incorrect functional form?
(13 marks)
[TOTAL 50 MARKS]
END OF QUESTION FOUR
BE314-5-SP/6
QUESTION FIVE
a) A researcher intends to use the regression model below to investigate the effects of the two
independent variables, 1 and 2 on the dependent variable Y:
= 0 + 11 + 22 +
The researcher knows based on previous empirical analysis that both independent variables
are likely to be relevant for explaining variation in the dependent variable but is worried that
there may be a problem with multicollinearity between the two independent variables.
i) Explain what the problem of multicollinearity is. Briefly describe what the possible
effects of this problem would be in the context of the model above.
(12 marks)
ii) The researcher estimates the model above and obtains the following results:
� = 126.22 + 12.891 − 0.482 +
The R2 for the model is 0.91. The sample t-ratios for the estimated coefficients on 1
and 2 are 0.54 and -4.21 respectively. In addition, the sample correlation coefficient
between 1 and 2 is 0.89. Based on this information, does there appear to be evidence
of multicollinearity between the two independent variables? What are the possible
actions the researcher could take if there appears to be a multicollinearity problem (you
do not need to explain them in detail)?
(13 marks)
b) Explain the consequences of omitting relevant independent/explanatory variables and the
consequences of including irrelevant independent/explanatory variables in a regression
model. What methods are available to test for these two problems (you do not need to
describe them in detail)?
(25 marks)
[TOTAL 50 MARKS]
END OF QUESTION FIVE
END OF SECTION B
END OF QUESTION PAPER
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