LOYOLA COLLEGE (AUTONOMOUS), CHENNAI  600 034.
B.A. DEGREE EXAMINATION  ECONOMICS
FOURTH SEMESTER  APRIL 2003
ST 4204  ECONOMETRICS
26.04.2003
9.00  12.00
Max : 100 Marks
PART  A
(10 2=20 marks)
Answer ALL the questions.
01.
02.
03.
04.
05.
06.
07.
08.
09.
10.
Define Expectation of a random variable in the discrete and continuous cases.
Distinguish between parameter and statistic.
Define Best Linear Unbiased Estimator.
State any two conditions underlying the ordinary least square (O.L.S.) technique.
Define ‘residuals’ in the case of two variable linear model and state its properties.
Define coefficient of Determination.
Explain the term ‘Linear Hypothesis’ with an example.
State any two ways in which ‘specification Error’ occurs.
Write down the AR (1) model for the disturbance term stating the assumptions.
If X ~ N (3, 4), find P(3 < x < 5).
PART  B
(5 8=40 marks)
Answer any FIVE questions.
11. X and Y are random variables whose joint distribution is as follows:
X
-1
0
1
2
Y
2
1/10 3/10
0
2/10
3
2/10 1/10
1/10
0
Find means and variances of X and Y.
12. Construct a 95% confidence internal for the mean  of a normal population (variance
unknown) given the following observations:
3.25,
4.10, 4.72, 3.64, 3.50, 3.90, 4.85, 4.20, 4.30, 3.75 .
13. For the two variable linear model, obtain the decomposition of the total variation in the
data. Present the ANOVA for testing H0: 2 = 0. Also, give a heuristic motivation for the
ANOVA procedure.
14. Fit a regression line through the origin for the following data on the annual rate of return
on a fund (Y) and market portfolio (X) and test the significance of the regression
coefficient
Y
40.3
3.6
63.7
-35.2
67.5
37.5
20.0
19.3
-42.0
19.2
X
35.3
9.5
61.9
-29.3
19.5
31.0
14.0
45.5
-26.5
8.5
15. Briefly discuss the test for significance of a subset of regression coefficients in a
kvariable linear model. In a fivevariable model Y= 1+2 X 2 +3 X3 + 4 X4 + 5 X5 ,
suppose that one wants to test H0 : 4 = 5 = 0 with 15 observations and computes the
residual sums of squares under the full and restricted regression as 12.25 and 21.37
respectively. Can the hypothesis be rejected at 5% level of significance?
16. Explain the use of Dummy variables in regression analysis with an illustration.
17. Give the motivation for Generalized least squares (GLS). For two variable linear model,
state the GLS estimate of the slope parameter.
18. “Econometrics is an amalgam of economic theory, mathematical economics and
Mathematical Statistics; Yet, it is a subject on its own right”  Explain.
PART  C
(220=40 marks)
Answer any TWO questions.
19. Let (X,Y)have joint p.d.f. f (x, y) = 2xy , 0  x  1 , 0  y  1 , Find correlation
coefficient between X and Y.
20. To study the labour force participation of urban poor families, the following data were
obtained from 12 regions:
Region
% Labour force
Mean family
Mean family size
(Y)
Income
(X3)
(in’ 100 Rupees)
(X2)
1
64.3
19.98
2.95
2
45.4
11.14
3.40
3
26.6
19.42
3.72
4
87.5
19.98
4.43
5
71.3
20.26
3.82
6
82.4
18.53
3.90
7
26.3
16.66
3.32
8
61.6
14.34
3.80
9
52.9
15.13
3.49
10
64.7
20.08
3.85
11
64.9
17.04
4.69
12
70.5
15.25
3.89
Carry out the regression of Y on (X2 , X3). Test the significance of the overall
regression at 5%level of significance.
21. (a) Explain the term structural change. Discuss the test procedure for the hypothesis of no
structural change against the alternative hypothesis of structural change.
(b) Discuss two methods of detecting heteroscedasticity and the remedies.
(10+10)
22. What is ‘Multi collinearity’ problem. Discuss a method of detecting multi collinearity in a
given data. Also, describe in detail, the remedial measures to overcome the undesirable
effects of multi collinearity.
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