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Econometrics Question Paper

Econometrics

Course:Master Of Economics

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF
MASTER OF ECONOMICS
EES 500: ECONOMETRICS

DATE: Thursday 26th November, 2009

TIME: 9.00 am -12.00Noon

INSTRUCTIONS: Answer ALL Questions

1.
a)
What is meant by OLS method of estimating the ‘best’ straight line that

fits the sample of XY observations.

[2.5 marks]
b)
i)
Given
Bˆ = [X' X
] 1
- X 'y , Find the variance of Bˆ (var Bˆ )

[7 marks]
~
~
ii)
Show that the var ( Bˆ ) = var ( B ) where B is a series of
coefficients got using any other method.

[ 8 marks]
2.
a)
State Gauss Markov theorem.

[2.5 marks]

b)
In the presence of measurement errors, ordinary least square estimates are

not only biased (even asymptotically) but also in consistent. Proof
?xy
inconsistency
given
that
ˆ
ß =

[8 marks]
1
? 2x
? 1 ?

c)
Given the AR(1) scheme, show that Var ( ˆ

U ) = E( U ) 2 = 6 2
t
t
u
?
?
? - 2
1 p ?

{7 marks]
3.
The first year earnings (in thousands Kshs) of students with Masters degree from

five (5) universities and for 3 class rankings from graduation are given as follows

Page 1 of 2

Universities
Class ranks Moi
Kenyatta
Nairobi
Kiriri
Methodist
First
class
20 18 16 14 12
Second
19 16 13 12 10
Upper
Second
18 14 10 10 8
Lower

Required
a)
Show whether the means are identical for
i)
The
school
populations.
[5
marks]
ii)
The
class
ranking
population.
[5
marks]
b)
State and briefly explain (using proof where applicable) three (3) properties of
ordinary
least
square
estimates.
[7.5
marks]
4.
a)
i)
What is meant by Multicollinearity?

[2 marks]
ii)
Given
Y
=
a + ß X + ß X +U, show that the least square
1
1
2
2
estimates
become
underminute
in presence of multicollinearity.

[6 marks]
b)
i)
State three (3) assumptions underlying the Durbin Watson ( ? )

statistic.

[3 marks]
?e e
ii)
Show that ? = 2 (1-P), where P=
t
t -1
?

[
6
marks]
2
et-1

Page 2 of 2

Econometrics Question Paper

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