Msf 502 Econometrics I Town Campus Question Paper
Msf 502 Econometrics I Town Campus
Course:Masters Of Science In Commerce
Institution: Kca University question papers
Exam Year:2014
UNIVERSITY EXAMINATIONS: 2013/2014
EXAMINATION FOR THE MASTERS OF SCIENCE (MSC) IN COMMERCE
(FINANCE AND INVESTMENT)
MSF 502 ECONOMETRICS I TOWN CAMPUS
DATE: AUGUST, 2014
TIME: 3 HOURS
INSTRUCTIONS: Answer Question One and Any Other Three Questions
QUESTION ONE (31 MARKS)
a)
Briefly explain, with relevant equations, the difference between the following terms as used in
Econometrics:
(i) (ii)
b)
A statistic and a Parameter
Population regression line and Estimated regression line
Using the least squared estimator for the multivariate regression, briefly explain and illustrate
the Gauss-Markov Theorem
c)
(4 Marks)
(6 Marks)
Suppose we have a multivariate model:
we want to test whether independent variables
and
jointly have effects on .
(i) Write the null hypothesis (2 Marks)
(ii) Write the restricted model. (1 Mark)
(iii) How many restrictions are there in this test? (1 Mark)
(iv) Now consider an estimated regression model given as:
When the model was estimated without the second and third explanatory variables the
following was obtained:
,
1
Are the second and third explanatory variables jointly significant in the original function
at 5%?
d)
(7 Marks)
An MSC student in an Econometrics class performed a multiple regression analysis in her MSC
term paper and presented the following output from STATA. Use the output to answer the
following questions.
. reg retention benefits training office
Source
SS df Model 57.98569 3 19.3285633
Residual 27.61431 11 2.51039182
Total 85.6 14 6.11428571
retention Coef.
benefits .0329424
training .7241937
office -.2422948
_cons 1.027568
(i)
MS
Std. Err.
.026882
.2182178
.3507851
1.528358
t
1.23
3.32
-0.69
0.67
Number of obs
F( 3,
11)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.246
0.007
0.504
0.515
=
=
=
=
=
=
15
7.70
0.0048
0.6774
0.5894
1.5844
[95% Conf. Interval]
-.0262244
.2438995
-1.014368
-2.336326
.0921093
1.204488
.5297779
4.391462
Write down the regression equation and the fitted regression equation from this output
(4 Marks)
(ii)
Discuss the significance level of the independent variables in the fitted model. What is
your conclusion?
(iii)
(4 Marks)
How well does the model fit the data? (2 Marks)
QUESTION TWO (23 MARKS)
Given the following over 30 observations
,
and
a) Obtain the OLS estimates and specify the estimated function (5 Marks)
b) Determine the standard errors of the coefficient estimates (8 Marks)
c) Test the significance of the independent variables in the estimated function at 5% level of
2
significance
(10 Marks)
QUESTION THREE (23 MARKS)
Suppose we have a model:
(Note that: total sample size = 100)
,
,
,
Where: Y = Matrix of the outcome variable.
X = Matrix of the independent variables;
ß = Vector of coefficients; and
e = Vector of error terms
a) Find
b) Suppose that we can divide the sample into two groups (50 observations each) where
dummy
(4 Marks)
variable
for
group
1
(
and
. Find
c)
ˆ
Find OLS estimates, ? , and Interpret
and
in numbers.
that:
(9 Marks)
.
?
Note that
is a
(10 marks)
QUESTION FOUR (23 MARKS)
Regression analysis can be used to test whether the market efficiently uses information in valuing
stocks. For concreteness, let return be the total return from holding firm''s stock over the four-year
period from end of 1990 to the end of 1994. The efficient markets hypothesis says that returns should
not be systematically related to information known in 1990. If firm characteristics known at the
beginning of the period help to predict stock returns, then we could use this information in choosing
stocks. For 1990, let dkr be a firm''s debt to capital ratio, let eps denote the earnings per share, let netinc
denote net income, and let salary denote total compensation for the CEO. Using the data the following
equation was estimated:
Note: The standard errors are shown in parenthesis.
(29.30)
(0.854)
(0.332)
(0.020)
(0.009)
3
a) How would the coefficient for salary and
value be interpreted?
(2 Marks)
b) Test whether the explanatory variable salary is significant at the 5% level of significance.
(8 marks)
c) Explain the use of Ramsey''s RESET test in a econometric analysis
d) How is the RESET test conducted?
(3 Marks)
(10 Marks)
QUESTION FIVE (23 MARKS)
a) What assumptions are necessary for OLS estimator to be BLUE?
(4 Marks)
b) What would the consequence be for a simple linear regression model if the errors were not
homoskedastic? Explain
c)
(6 Marks)
State in algebraic notation and explain the assumption about the CLMs referred to as
"multicollinearity" and "autocorrelation".
d)
(4 Marks)
Explain the procedures that are used to test for "multicollinearity" and "autocorrelation".
(9 Marks)
QUESTION SIX (23 MARKS)
Consider a zoo that has only chimps and elephants where
animal j produces on a given day,
is the amount (in pounds) of
= 1 if the animal is a elephant, and zero otherwise. The amount of
animal j produces on a given day is a draw from a Poisson distribution (some animals on some
days are constipated) with parameter
where
. The director of the zoo likes only
chimps, but knows that chimps like to ride on the backs of elephants, so has 90 chimps and 10
elephants (lots of chimps can ride one elephant).
Required:
(i) Write down the density function for the amount of
(ii) Explain why this is the density function.
(iii) Derive the expected amount of
(iv) Comment briefly on the likelihood of the
distributed.
for this population.
(5 Marks)
(3 Marks)
produced per day.
(10 Marks)
being Poisson distributed rather than normally
(5 Marks)
4
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