Problem set 5

Topics: Regression analysis, Linear regression, Statistics Pages: 6 (900 words) Published: April 24, 2014
ECONOMETRICS: PS5
PROBLEM SET 5: ESTIMATION PROBLEMS

1

We have the following variables:

Y: Food expenditure in USA.
X: Family income.
P: Price index.
Two different regressions are estimated with the following estimation results (standard errors are in brackets):
Coefficient for
Regression X
Y/P
Y / X; P

0.112
(0.003)

Coefficient for
P
2.462
(0.407)
-0.739
(0.114)

Determination
coefficient
0.614
0.978

Assuming that the true equation for Y includes both X and P and that P and X are positively correlated, find and discuss the sign of the bias in the estimated coefficient if X is eliminated of the regression model (hint: find the expected value for the OLS coefficient associated to P in the first regression of the above table and discuss).

2

There is an econometric study at IE University which relates the average grade in Econometrics with the time students employ in different activities during the week. Some students are asked about how many hours they employ in four different activities: study, sleep, work and leisure. Any activity must be included in one of these four categories such that the time spent in the four activities is 168 hours for each student.

The model is the following:
‫ݑ + ݁ݎݑݏ݈݅݁ 4ߚ + ݇ݎ݋ݓ 3ߚ + ݌݈݁݁ݏ 2ߚ + ݕ݀ݑݐݏ 1ߚ + ߙ = ܧܩܣ‬

a- Find the assumption that does not hold in this model and explain why. b- How would you rewrite the model in order to solve the problem?

1

ECONOMETRICS: PS5
3

We have the following information for the annual growth rates (%) in different countries:

Country
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Germany
India
Ireland
Israel
Italy
Japan
Mexico
Netherlands
New Zealand
Sweden
UK
USA

Stock prices
(Y)
5
11.1
3.2
7.9
3.8
11.1
9.9
13.5
1.5
6.4
8.9
8.1
13.5
4.7
7.5
4.7
8
7.5
9

Consumer prices
(X)
4.3
4.6
2.4
2.4
4.2
5.5
4.7
2.2
4
4
8.4
3.3
4.7
5.2
3.6
3.6
4
3.9
2.1

Predicted Estimation
Y
Residuals

Knowing that: ‫, ݅ݔ102.0 + 38.6 = ݅ݕ‬


Answer to the following questions:
a- Complete the missing values in the above table.
b- Show both graphically and formally if the above data suffers from an outlier problem.
c- If the answer to b is positive, please explain any strategy you would perform in order to solve the problem.

2

ECONOMETRICS: PS5
4

The following table provides information about the annual disposable income per capita (‫ ) ݅ݔ‬and the annual consumption per capita (‫ ) ݅ݕ‬in 14 countries:

Country
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Income
1.6 1.7 2.5 2.9 3 3.8 4.7 5.3 5.5 5.6 6 6.2 6.5 6.6
Consumption 1.5 1.6 1.7 4 1.3 3 1.5 0.7 3.5 4.8 7.7 6.1 1 3

Knowing that using the above information:
‫݅ݔ784.0 + 108.0 = ݅ݕ‬

(1.44)

ܴ2 = 0.176

ܴܵܵ = 46.53

(0.304)

a- Draw a scatter plot using Y and X in each of the axes and explain why the researcher should suspect that there may be a heteroscedasticity problem. b- Draw a scatter plot using the predicted values of Y and the estimation residuals, why the researcher should suspect that there may be a heteroscedasticity problem?

c- Next, two sub-regressions are performed, one of them using the 5 countries with the lowest values of X and the other one for the 5 countries with the highest values of X. As a result of these two regressions, the researcher obtains that RSS=4.106 in the first regression and RSS=17.988 in the second regression. Calculate Goldfeld-Quandt test at a 5% level and explain your result.

5

We have the following data for 17 countries:
Country

M

G

Belgium
Canada
Denmark
France
Germany
Greece
Ireland
Italy
Japan

849
778
853
1000
1331
185
399
554
679

2652
3888
3159
2777
3095
1091
1331
1731
1887

3

Country
Luxembourg
Netherlands
Norway
Portugal
Spain
Sweden
U.K.
U.S.A.

M

G

1368
704
634
215
239
1025
609
1248

3108
2429
1881
718
957
4101
2174
4799

ECONOMETRICS: PS5...
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