Econometrics Theory & Application
2009
Time Allowed: 3 hours Maximum Marks: 100
Note: Attempt any four questions. All questions carry equal marks.
1. (a) What are the major assumptions of OLS (Ordinary Least Square)?
(b) Consider the following linear regression model:
Y1 = β1 + β2X2t + β3X3t +t1 and the data given below:
|
|
Y – Y |
X2 – X2 |
X3 – X3 |
|
Y – Y |
2000 |
100 |
90 |
|
X2 – X2 |
100 |
10 |
5 |
|
X3 – X3 |
90 |
5 |
5 |
And Y = 1200, X2 = 100, X3 = 50 and X = 100
(i) Calculate the best linear unbiased estimates of β1, β2 and β3. Also interpret them.
(ii) Calculate coefficient of determination R2 and adjusted R2.
(iii) Test overall goodness of fit of regression model.
(iv) Compute standardized regression coefficient and determine the relative importance of X2 and X3, as regressors of Y.
(v) Calculate individual significance test for β2 and β3 and also interpret them.
2. Clearly bring out the difference between conditional and unconditional forecasting.
(b) Derive the variance of unconditional forecast error from the model:
Y1 = α + βX1 + U1
When:
(i) α is estimated β is known
(ii) Both α and β are estimated.
(c) A relationship between Grade Point Average of a student (Y) and income of the parents of student (X) is hypothesized and estimated as:
Y = 1.375 + 0.12X
The data used to estimate the above result:
Y 4.0 3.0 3.5 2.0 3.0 3.5 2.5 2.5
X (‘000) 21.0 15.0 15.0 9.0 12.0 18.0 6.0 12.0
Predict the grade point average of a student when parent’s income is Rs. 14,000. Also estimate its variance of forecast error.
3. (a) What do you understand by Heteroscedasticity?
(b) What are the causes of Heteroscedasticity?
(c) What are its consequences?
(d) A researcher has a data on X and Y with 15 observations:
|
N |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
|
X |
20 |
25 |
23 |
18 |
26 |
27 |
29 |
31 |
22 |
27 |
32 |
35 |
40 |
41 |
39 |
|
Y |
18 |
17 |
16 |
10 |
8 |
15 |
16 |
20 |
18 |
17 |
19 |
18 |
26 |
25 |
23 |
Apply Goldfeld Quant test on the above data to test whether there is Heteroscedasticity prevent or not.
4. (a) What do you understand by Auto-correlation?
(b) What are its consequences?
(c) Based on the data given below a researcher estimated a consumption function by OLS.
C = – 3.0 + 0.9277 income
|
Year |
Consumption |
Income |
Residual |
|
1988 |
236 |
257 |
0.52 |
|
1989 |
254 |
275 |
1.82 |
|
1990 |
267 |
293 |
-1.87 |
|
1991 |
281 |
309 |
-2.71 |
|
1992 |
290 |
319 |
-2.99 |
|
1993 |
311 |
337 |
1.30 |
|
1994 |
325 |
350 |
3.25 |
|
1995 |
335 |
364 |
0.26 |
|
1996 |
355 |
385 |
0.78 |
|
1997 |
375 |
405 |
2.23 |
|
1998 |
401 |
437 |
-1.45 |
|
1999 |
431 |
469 |
1.14 |
Apply Durbin Watson test for auto-correlation at 5% level of confidence. State clearly the null and alternative hypothesis and draw graph.
5. (a) Prove that two techniques ILS (Indirect Least Square) and 2SLS (Two Stages Least Square) are equivalent to estimate an exactly identified equation.
(b) Estimate α2 by 2SLS and ILS independently from the following model:
Y1t = α2y2t + μ1t
and data given below:
|
y1 |
y2 |
x1 |
|
-4 |
2 |
-2 |
|
0 |
3 |
-1 |
|
3 |
2 |
0 |
|
1 |
-7 |
3 |
6. (a) Consider the following demand and supply model:
Qdt = α1 + α2Pt + α3Yt + ut
Qst = β1 + β2Pt + u2t
Qdt = Qst
Examine the identification state of the model by reduced form approach.
(b) Given the model:
Y1 = α1 + α2Y2 + u1
Y2 = β1 + β2Y1 + u2
and the data given below:
|
Y1 |
8 |
5 |
6 |
4 |
|
Y2 |
12 |
6 |
8 |
5 |
|
Y3 |
4 |
3 |
2 |
1 |
Estimate α1 and α2 by the most appropriate method. Can you estimate β1, β2 and β3. Give reasons.
7. Write a short note on any two of the following:
(a) Multi-collinearity
(b) Recursive Equation System
(c) Koyck Transformation.
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