ECONOMETRICS EXAM WITH
COMPLETE SOLUTIONS
A nonlinear function:
A.
is a function with a slope that is not constant.
B.
can be adequately described by a straight line between the dependent variable and one
of the explanatory variables.
C.
makes little sense, because variables in the real world are related linearly.
D.
is a concept that only applies to the case of a single or two explanatory variables since
you cannot draw a line in four dimensions. - Answer- A.
is a function with a slope that is not constant.
The interpretation of the slope coefficient in the model
1nYi=β0+β11nXi+μi
is as follows: - Answer- a 1% change in X is associated with a
β1%
change in
Y.
Assume that you had estimated the following quadratic regression model:
Test Score=607.3+3.85Income−0.0423Income2
If income increased from 10 to 11 ($10,000 to $11,000), then the predicted effect on test
scores would be: - Answer- 2.96
The interpretation of the slope coefficient in the model
ln(Yi)
=
β0
+
β1
ln(Xi)+
ui
is as follows: - Answer- a 1% change in X is associated with a
β1
% change in
Y.
,Sales in a company are $191 million in 2009 and increase $200 million in 2010.
Compute the percentage increase in sales using the usual formula
100×(Sales(2010)−Sales(2009))/(Sales(2009))
Compare this value to the approximation
100×ln (Sales(2010))−ln (Sales(2009))
100×((Sales(2010)−Sales(2009))/(Sales(2009))
= ____(a)_____%
100×ln (Sales(2010))−ln (Sales(2009))
= ____(b)_____%
Now, assume that sales in a company are $191 million in 2009 and increase $263
million in 2010.
100×((Sales(2010)−Sales(2009))/(Sales(2009))
= ____(c)_____%
100×ln (Sales(2010))−ln (Sales(2009))
= ____(d)_____%
The approximation performs
_______(e)________ when the change is small. The quality of the approximation
______(f)_____as the percentage change increases. - Answer- a) 4.712
b) 4.604
c) 37.696
d) 31.989
e) better
f) deteriorates
A "Cobb-Douglas" production function relates production (Q) to factors of production,
capital (K), labor (L), raw materials (M), and an error term u using the equation
Q=λKβ1Lβ2Mβ3eu,
where λ, β1, β2, and β3 are production parameters.
Suppose that you have data on production and the factors of production from a random
sample of firms with the same Cobb-Douglas production function. Which of the following
regression functions provides the most useful transformation to estimate the model? -
Answer- logarithmic regression function.
(a) Consider a man with 17 years of education and 5 years of experience who is from a
western state. Use the results from column (4) of the table and the method in Key
Concept 8.1LOADING... to estimate the expected change in the logarithm of average
hourly earnings (AHE) associated with an additional year of experience.
, The expected change in the logarithm of average hourly earnings (AHE) associated with
an additional year of experience is ______(a)_____%. (Round your response to two
decimal places.)
(b) Consider a man with 17 years of education and 11 years of experience who is from
a western state. Use the results from column (4) of the table and the method in Key
Concept 8.1LOADING... to estimate the expected change in the logarithm of average
hourly earnings (AHE) associated with an additional year of experience.
The expected change in the logarithm of average hourly earnings (AHE) associated with
a - Answer- (a) 1.22%
(b) 0.98%
(c)The regression is nonlinear in experience.
(d) 7.80 (potential experience ^2 row 4 top devided by bottom (no negatives)
(e) Yes
(f) Include interaction terms
Female×Potential
experience and
Female×(Potential
experience)2.
This problem is inspired by a study of the "gender gap" in earnings in top corporate jobs
[Bertrand and Hallock (2001)]. The study compares total compensation among top
executives in a large set of U.S. public corporations in the 1990s. (Each year these
publicly traded corporations must report total compensation levels for their top five
executives.)
Let Female be an indicator variable that is equal to 1 for females and 0 for males. A
regression of the logarithm of earnings onto Female yields
ln(Earnings)=6.44−0.43Female, SER=2.48.
(0.01) (0.05)
Calculate the average hourly earnings for top male and female executives.
The hourly earnings for top male executives is $____(a)____ per hour. (Round your
response to two decimal places.)
The hourly earnings for top female executives is $______(b)_____ per hour. (Round
your response to two decimal places.)
What is the estimated average difference between ear - Answer- a) 626.41
b) 407.48
c) 218.93
d) 2.48
e) -8.60
f) Yes
g) No
h) 0.65
COMPLETE SOLUTIONS
A nonlinear function:
A.
is a function with a slope that is not constant.
B.
can be adequately described by a straight line between the dependent variable and one
of the explanatory variables.
C.
makes little sense, because variables in the real world are related linearly.
D.
is a concept that only applies to the case of a single or two explanatory variables since
you cannot draw a line in four dimensions. - Answer- A.
is a function with a slope that is not constant.
The interpretation of the slope coefficient in the model
1nYi=β0+β11nXi+μi
is as follows: - Answer- a 1% change in X is associated with a
β1%
change in
Y.
Assume that you had estimated the following quadratic regression model:
Test Score=607.3+3.85Income−0.0423Income2
If income increased from 10 to 11 ($10,000 to $11,000), then the predicted effect on test
scores would be: - Answer- 2.96
The interpretation of the slope coefficient in the model
ln(Yi)
=
β0
+
β1
ln(Xi)+
ui
is as follows: - Answer- a 1% change in X is associated with a
β1
% change in
Y.
,Sales in a company are $191 million in 2009 and increase $200 million in 2010.
Compute the percentage increase in sales using the usual formula
100×(Sales(2010)−Sales(2009))/(Sales(2009))
Compare this value to the approximation
100×ln (Sales(2010))−ln (Sales(2009))
100×((Sales(2010)−Sales(2009))/(Sales(2009))
= ____(a)_____%
100×ln (Sales(2010))−ln (Sales(2009))
= ____(b)_____%
Now, assume that sales in a company are $191 million in 2009 and increase $263
million in 2010.
100×((Sales(2010)−Sales(2009))/(Sales(2009))
= ____(c)_____%
100×ln (Sales(2010))−ln (Sales(2009))
= ____(d)_____%
The approximation performs
_______(e)________ when the change is small. The quality of the approximation
______(f)_____as the percentage change increases. - Answer- a) 4.712
b) 4.604
c) 37.696
d) 31.989
e) better
f) deteriorates
A "Cobb-Douglas" production function relates production (Q) to factors of production,
capital (K), labor (L), raw materials (M), and an error term u using the equation
Q=λKβ1Lβ2Mβ3eu,
where λ, β1, β2, and β3 are production parameters.
Suppose that you have data on production and the factors of production from a random
sample of firms with the same Cobb-Douglas production function. Which of the following
regression functions provides the most useful transformation to estimate the model? -
Answer- logarithmic regression function.
(a) Consider a man with 17 years of education and 5 years of experience who is from a
western state. Use the results from column (4) of the table and the method in Key
Concept 8.1LOADING... to estimate the expected change in the logarithm of average
hourly earnings (AHE) associated with an additional year of experience.
, The expected change in the logarithm of average hourly earnings (AHE) associated with
an additional year of experience is ______(a)_____%. (Round your response to two
decimal places.)
(b) Consider a man with 17 years of education and 11 years of experience who is from
a western state. Use the results from column (4) of the table and the method in Key
Concept 8.1LOADING... to estimate the expected change in the logarithm of average
hourly earnings (AHE) associated with an additional year of experience.
The expected change in the logarithm of average hourly earnings (AHE) associated with
a - Answer- (a) 1.22%
(b) 0.98%
(c)The regression is nonlinear in experience.
(d) 7.80 (potential experience ^2 row 4 top devided by bottom (no negatives)
(e) Yes
(f) Include interaction terms
Female×Potential
experience and
Female×(Potential
experience)2.
This problem is inspired by a study of the "gender gap" in earnings in top corporate jobs
[Bertrand and Hallock (2001)]. The study compares total compensation among top
executives in a large set of U.S. public corporations in the 1990s. (Each year these
publicly traded corporations must report total compensation levels for their top five
executives.)
Let Female be an indicator variable that is equal to 1 for females and 0 for males. A
regression of the logarithm of earnings onto Female yields
ln(Earnings)=6.44−0.43Female, SER=2.48.
(0.01) (0.05)
Calculate the average hourly earnings for top male and female executives.
The hourly earnings for top male executives is $____(a)____ per hour. (Round your
response to two decimal places.)
The hourly earnings for top female executives is $______(b)_____ per hour. (Round
your response to two decimal places.)
What is the estimated average difference between ear - Answer- a) 626.41
b) 407.48
c) 218.93
d) 2.48
e) -8.60
f) Yes
g) No
h) 0.65
