Problem set 5
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 + ݇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
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