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.
- 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.
- X and Y are random variables whose joint distribution is as follows:
| X
Y |
-1 0 1 2 |
| 2
3 |
1/10 3/10 0 2/10
2/10 1/10 1/10 0 |
Find means and variances of X and Y.
- Construct a 95% confidence internal for the mean m 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 .
- For the two variable linear model, obtain the decomposition of the total variation in the data. Present the ANOVA for testing H0: b2 = 0. Also, give a heuristic motivation for the ANOVA procedure.
- 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 |
- Briefly discuss the test for significance of a subset of regression coefficients in a
k-variable linear model. In a five-variable model Y= b1+b2 X 2 +b3 X3 + b4 X4 + b5 X5 , suppose that one wants to test H0 : b4 = b5 = 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? - Explain the use of Dummy variables in regression analysis with an illustration.
- Give the motivation for Generalized least squares (GLS). For two variable linear model, state the GLS estimate of the slope parameter.
- “Econometrics is an amalgam of economic theory, mathematical economics and Mathematical Statistics; Yet, it is a subject on its own right” –
PART – C (2´20=40 marks)
Answer any TWO questions.
- Let (X,Y)have joint p.d.f. f (x, y) = 2-x-y , , , Find correlation coefficient between X and Y.
- To study the labour force participation of urban poor families, the following data were obtained from 12 regions:
| Region | % Labour force
(Y) |
Mean family Income
(in’ 100 Rupees) (X2) |
Mean family size
(X3) |
| 1
2 |
64.3
45.4 |
19.98
11.14 |
2.95
3.40 |
| 3
4 |
26.6
87.5 |
19.42
19.98 |
3.72
4.43 |
| 5
6 |
71.3
82.4 |
20.26
18.53 |
3.82
3.90 |
| 7
8 |
26.3
61.6 |
16.66
14.34 |
3.32
3.80 |
| 9
10 |
52.9
64.7 |
15.13
20.08 |
3.49
3.85 |
| 11
12 |
64.9
70.5 |
17.04
15.25 |
4.69
3.89 |
Carry out the regression of Y on (X2 , X3). Test the significance of the overall
regression at 5%level of significance.
- (a) Explain the term structural change. Discuss the test procedure for the hypothesis of no
structural change against the alternative hypothesis of structural change.
- Discuss two methods of detecting heteroscedasticity and the remedies. (10+10)
- 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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