Econometric Models And Methods Question Paper

Econometric Models And Methods

Course:Bachelor Of Commerce

Institution: Kenyatta University question papers

Exam Year:2008

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2008/2009
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
COMMERCE
BMS 404: ECONOMETRIC MODELS AND METHODS

DATE: Wednesday 3rd December, 2008

TIME: 11.00 a.m. – 1.00 p.m.

INSTRUCTIONS
Answer question 1 and any other TWO questions.

1.
(a)
(i)
Distinguish between an economic model and an econometric
model.

[2 marks]
(ii)
Studies have shown that econometrics is an amalgam of economic
theory, mathematical economics, economic statistics and
mathematics.
Why then does econometrics deserve to be studied as a separate
discipline?

[8 marks]

(b)
Explain the following variables:
(i)
exogenous variables.
(ii)
Endogenous variables
(iii)
Discretionary variables

[3 marks]
(c)
Estimation of econometric models and their reliability depends upon the
availability of appropriate data. State and explain any four types of data.

[8 marks]
(d)
Consider the model below:
Y = ß0 + ß1 X + u where
Y = consumption
X = income

2
u = random disturbance.
n = number of observations = 10
Given that:
?XY = 249700,

?X = 1775 and ?X2 = 335225

?Y = 1350 and ?Y2 = 187800,
(i)
Determine the values of the parameter estimates.
[4 marks]
(ii)
Write down the estimated regression model for the data.
[2 marks]
(e)
(i)
What do you understand by R square statistic (for simple
regression with intercept)?

[1 mark]
(ii)
Explain why an econometrician uses an adjusted R square statistic
other than R square statistic to interpret multiple regression fit.
[2 marks]
2.
(a)
State three criteria one may use to decide whether estimates of parameters
are theoretically consistent and statistically significant.
[3 marks]
(b)
The table below show cross-section data collected for various families:
Family
1
2
3
4
5
6
7
8
9
10
Income (X)
200 300 300 400 150 130 250 380 350 440
Consumption (Y) 70
90
80
100 65
60
80
100 90
110

(i)
Explain why it is necessary to study the scatter diagram before
proceeding with further analysis.

[2 marks]
(ii)
Determine the parameter estimates for the model Y = ?0 + ?1X + U
[6 marks]
(iii)
Write down the Keynesian function and determine whether the
data set from the families supports the Keynesian theory.

[3 marks]
(iv)
Test the hypothesis H0: ?1 = 0
H1: ?1 ? 0

At significance level at ? = 0.05.

[6 marks]

3

3.
(a)
The Gaussian (standard) or Classical Linear Regression Model (CLRM),
which is the cornerstone of most econometric theories, operates under
several assumptions.
State any three of these assumptions.

[3 marks]

(b)
The manager of a supermarket would like to determine the relationship
between the quantity demanded Y and two independent variables X1 and
X2 where X1 represents the price of quantity demanded Y and X2
represents the income of customers.

The results of analysis using SPSS are shown in the tables below:

Table 1A

Coefficients

Model
?
Std error t

(constant) 4.895
-
1.825

PRICE
-
0.376
-0.955
INCOME -
0.213
3.603

Table 1B

Coefficients
Model
?
Std error
t
Sig.

(constant) -
0.558
4.280
0.003

INCOME -
0.083
11.426 0.000

(i)
Using the output table 1A above, (for all variables entered),
calculate the missing values in the table.

[6 marks]
(ii)
From your results in (i) above, estimate the value of the quantity
demanded (Y) given X1 = 100, X2 = 500 (arbitrary units).
[3 marks]

4

(iii)
Using table IB (obtained by stepwise model selection criterion),
determine the values of missing regression coefficients
( ? ˆ
ˆ
? a
n
d ? . Hence predict the quantity demanded for this
0
1 ?
parsimonious model given that X2 = 400 (arbitrary units).
[5 marks]
(iv)
From the table IB, make decisions for the hypotheses:
H0: ?0 = 0, and H0: ?1 = 0
H1: ?0 ? 0 H1: ?1 ? 0
4.
(a)
(i)
What are the two consequences of perfect multicollinearity on the
estimates of regression coefficients?

[2 marks]
(ii)
Describe any two observations you can make after fitting the
model that would indicate presence of multicollinearity.
[2 marks]
(b)
The table below shows sales (Y) and advertisement expenditure (X) (in
arbitrary units).

Sales
5
7
10
12
15
Advertisement 11
12
15
17
20
expenditure

(i)
Calculate the Pearson correlation coefficient (?) between sales and
advertisement expenditure.

[8 marks]
(ii)
Test the hypothesis:
H0: ? = 0

H1 : ? ? 0

[5 marks]
at 5% level of significance.

(iii)
Distinguish between correlation and regression.
[3 marks]
5.
Consider the table below, which shows gross national product (X) and demand for
food (Y) measured in arbitrary units in an underdeveloped country over a 10 year
period.
Year
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
Y
6
7
8
10
8
9
10
9
11
10
X
50
52
55
59
57
58
62
65
78
70

5

(a)
Using ordinary least squares method, obtain parameter estimates for the
model Y = ?0 + ?1X + U

[6 marks]
(b)
Compute the standard errors for the parameter estimates. [4 marks]
(c)
Calculate the adjusted R2 statistic.

[3 marks]
(d)
Write a hypothesis for testing whether regression is significant. Hence test
at ? = 0.05 significance level.

[7 marks]

…………

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