# Problem set 5

**Topics:**Regression analysis, Linear regression, Statistics

**Pages:**6 (900 words)

**Published:**April 24, 2014

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 + ݇ݎݓ 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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