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A1-ECON2206代写
时间：2024-03-25
Mock In-session test - Solution
1. QUESTION A1
multi
1 point 0.10 penalty Single Shuffle
The following estimated regression model provides evidence on the relationship between
age (age) and log of wage (log(wage)) after controlling for number of siblings (sibs). The
sample size is 935 and R2 = 0.048. Standard errors are presented in brackets ().
“Because of the very low R2 (0.048) there is little evidence of a statistically significant
association between age and log(wage)”. This statement is
(a) True
(b) False (100%)
2. QUESTION A2
multi
1 point 0.10 penalty Single Shuffle
The following regression model studies the effect of time spent in various activities on
CEOs’ wages. CEOs are asked how many hours they spend each week in three activities:
working, leisure, and sleeping. Any activity is put into one of the three categories, so
that for each CEO, the sum of hours in the three activities must be 168.
wage = β0 + β1work + β2leisure+ β3sleep+ u
Does this model violate any Gauss-Markov assumption?
(a) No, the model does not violate any Gauss-Markov assumption.
(b) The model violates the “no perfect collinearity” assumption. (100%)
(c) The model violates the “zero conditional mean” assumption.
(d) The model violates the “normal distribution of the error term” assumption.
3. QUESTION A3
essay
1 point 0.10 penalty editor
The following estimated regression model explains fertility represented by the total num-
ber of children born to a women (kids).
ˆkids = 3.012− 0.236 t educ+ 0.053 t age− 0.016 t agesq,
where t educ refers to education of the women in years minus 13,
t age refers to age of the women in years mius 43,
and t agesq is t age squared.
Interpret the constant term.
1
Answer:
βˆ0 = 3.012: The predicted mean number of children born to a woman aged 43 years old
with 13 years of education is 3 kids. (1 point)
Notes for grader:
4. QUESTION A4
multi
1 point 0.10 penalty Single Shuffle
Suppose you take a random sample of undergraduate students drawn from those enrolled
in the University of New South Wales and you find that students who regularly attend
tutorials get a mark 15% higher in the final exam than those who do not attend regularly.
Which of the following is NOT an appropriate conclusion to be drawn from this finding?
(a) Whether students attend tutorials or not will not be random and thus the finding
will likely to be biased.
(b) The evidence suggests there is a positive correlation between attending tutorials
and final-exam marks.
(c) Because the sample is random, it is likely that the result represents the causal effect
of attending tutorials on final-exam marks. (100%)
(d) Whether students attend tutorial or not is likely to be highly correlated with observ-
able factors such as whether they are a foreign student or not, or whether they are
a hard-working student or not. If these factors were controlled for in the regression,
then the result could possibly be given a causal interpretation.
5. QUESTION A5
essay
1 point 0.10 penalty editor
You have data on all the high school students in Australia on their math score (math)
(scores range 0 to 10) and their school per-student spending (expend) and you are inter-
ested in estimating the following population regression.
math = β0 + β1expend+ u
Suppose that you present your model to your friend, Federico, and he argues that it
is highly unlikely that the error term u is distributed like a normal distribution and
therefore you are not able to use OLS to test whether β > 0.
Is Federico right or wrong? Explain why.
Answer:
The assumption on normal distribution of the error term is required when doing hypoth-
esis testing for small samples. As we have a large sample size, there is no need to be
concerned about the distribution of the error term. We can use the asymptotic theory
to make inferences about OLS estimates. Therefore, Federico is wrong.
Notes for grader:
2
6. PART B
essay
1 point 0.10 penalty editor
The following information will be used for question B1, B2, B3, and B4. You will need
to upload an explanation on how you reached the answer for each of questions in this
part.
The following regression model studies the effect of experience (exper) on log of wage
(log(wage)).
log(wage) = β0 + β1exper + β2exper
2 + β3educ+ u (1)
Using the data from a sample of 82 workers to estimate the model, we get the following
result:
where exper is experience, exper sq is experience squared, and educ is education.
QUESTION B1
Provide one example of an omitted variable that would bias the OLS of β3. Describe in
which direction do you think the bias will go.
QUESTION B2
Using the STATA output above, test whether β1 = −1 against β1 > −1. Perform the
test at the 5% significance level.
QUESTION B3
Using the STATA output above, construct the 95% confidence interval for β3.
QUESTION B4
For this question assume that the Gauss-Markov assumptions from 1 to 4 are satisfied.
3
What is the effect of an extra year of experience on wages for an individual that has 10
years of experience and 12 years of education?
Solutions:
QUESTION B1
One example of an omitted variable that would bias the OLS of β3: ability (IQ), family
income, mother’s education, father’s education, etc.
Ability (IQ)/ family income/ mother’s education/ father’s education, etc. is positively
correlated with education and wage. When one of these variables is omitted from the
regression, some of the estimated effect of educ is actually due to the effect of the omitted
variable. Therefore, we are likely to overestimate the effect of educ on wages, i.e. the
bias is positive.
QUESTION B2
tβˆ1 =
βˆ1 − (−1)
se(βˆ1)
=
−0.0113− (−1)
0.0433
= 22.834
Degrees of freedom (df)= n - k - 1 = 82 - 3 - 1 = 78, thus from the Table, the critical
value is 1.662.
tβˆ1 > 1.662. Therefore, we reject the null that β1 = −1 in favor of the alternative that
β1 > −1 at the 5% significance level.
QUESTION B3
Degrees of freedom (df)= n - k - 1 = 82 - 3 - 1 = 78, thus from the Table, the critical
value is 1.987 (or 2.000).
Therefore, the confidence interval is:
[0.0819 - 1.987*0.0228; 0.0819 + 1.987*0.0228 ] = [0.037; 0.127]
(or [0.0819 - 2.000*0.0228; 0.0819 + 2.000*0.0228 ] = [0.036; 0.128] )
QUESTION B4
The effect of an extra year of experience on log(wage) for an individual with 10 years of
experience is:
−0.0113+2 ∗ 0.0017 ∗ 10 = 0.0227. We can interpret this as a predicted increase in wage
of about 2.27%.
Notes for grader:
Total of marks: 6
1. QUESTION A1
multi
1 point 0.10 penalty Single Shuffle
The following estimated regression model provides evidence on the relationship between
age (age) and log of wage (log(wage)) after controlling for number of siblings (sibs). The
sample size is 935 and R2 = 0.048. Standard errors are presented in brackets ().
“Because of the very low R2 (0.048) there is little evidence of a statistically significant
association between age and log(wage)”. This statement is
(a) True
(b) False (100%)
2. QUESTION A2
multi
1 point 0.10 penalty Single Shuffle
The following regression model studies the effect of time spent in various activities on
CEOs’ wages. CEOs are asked how many hours they spend each week in three activities:
working, leisure, and sleeping. Any activity is put into one of the three categories, so
that for each CEO, the sum of hours in the three activities must be 168.
wage = β0 + β1work + β2leisure+ β3sleep+ u
Does this model violate any Gauss-Markov assumption?
(a) No, the model does not violate any Gauss-Markov assumption.
(b) The model violates the “no perfect collinearity” assumption. (100%)
(c) The model violates the “zero conditional mean” assumption.
(d) The model violates the “normal distribution of the error term” assumption.
3. QUESTION A3
essay
1 point 0.10 penalty editor
The following estimated regression model explains fertility represented by the total num-
ber of children born to a women (kids).
ˆkids = 3.012− 0.236 t educ+ 0.053 t age− 0.016 t agesq,
where t educ refers to education of the women in years minus 13,
t age refers to age of the women in years mius 43,
and t agesq is t age squared.
Interpret the constant term.
1
Answer:
βˆ0 = 3.012: The predicted mean number of children born to a woman aged 43 years old
with 13 years of education is 3 kids. (1 point)
Notes for grader:
4. QUESTION A4
multi
1 point 0.10 penalty Single Shuffle
Suppose you take a random sample of undergraduate students drawn from those enrolled
in the University of New South Wales and you find that students who regularly attend
tutorials get a mark 15% higher in the final exam than those who do not attend regularly.
Which of the following is NOT an appropriate conclusion to be drawn from this finding?
(a) Whether students attend tutorials or not will not be random and thus the finding
will likely to be biased.
(b) The evidence suggests there is a positive correlation between attending tutorials
and final-exam marks.
(c) Because the sample is random, it is likely that the result represents the causal effect
of attending tutorials on final-exam marks. (100%)
(d) Whether students attend tutorial or not is likely to be highly correlated with observ-
able factors such as whether they are a foreign student or not, or whether they are
a hard-working student or not. If these factors were controlled for in the regression,
then the result could possibly be given a causal interpretation.
5. QUESTION A5
essay
1 point 0.10 penalty editor
You have data on all the high school students in Australia on their math score (math)
(scores range 0 to 10) and their school per-student spending (expend) and you are inter-
ested in estimating the following population regression.
math = β0 + β1expend+ u
Suppose that you present your model to your friend, Federico, and he argues that it
is highly unlikely that the error term u is distributed like a normal distribution and
therefore you are not able to use OLS to test whether β > 0.
Is Federico right or wrong? Explain why.
Answer:
The assumption on normal distribution of the error term is required when doing hypoth-
esis testing for small samples. As we have a large sample size, there is no need to be
concerned about the distribution of the error term. We can use the asymptotic theory
to make inferences about OLS estimates. Therefore, Federico is wrong.
Notes for grader:
2
6. PART B
essay
1 point 0.10 penalty editor
The following information will be used for question B1, B2, B3, and B4. You will need
to upload an explanation on how you reached the answer for each of questions in this
part.
The following regression model studies the effect of experience (exper) on log of wage
(log(wage)).
log(wage) = β0 + β1exper + β2exper
2 + β3educ+ u (1)
Using the data from a sample of 82 workers to estimate the model, we get the following
result:
where exper is experience, exper sq is experience squared, and educ is education.
QUESTION B1
Provide one example of an omitted variable that would bias the OLS of β3. Describe in
which direction do you think the bias will go.
QUESTION B2
Using the STATA output above, test whether β1 = −1 against β1 > −1. Perform the
test at the 5% significance level.
QUESTION B3
Using the STATA output above, construct the 95% confidence interval for β3.
QUESTION B4
For this question assume that the Gauss-Markov assumptions from 1 to 4 are satisfied.
3
What is the effect of an extra year of experience on wages for an individual that has 10
years of experience and 12 years of education?
Solutions:
QUESTION B1
One example of an omitted variable that would bias the OLS of β3: ability (IQ), family
income, mother’s education, father’s education, etc.
Ability (IQ)/ family income/ mother’s education/ father’s education, etc. is positively
correlated with education and wage. When one of these variables is omitted from the
regression, some of the estimated effect of educ is actually due to the effect of the omitted
variable. Therefore, we are likely to overestimate the effect of educ on wages, i.e. the
bias is positive.
QUESTION B2
tβˆ1 =
βˆ1 − (−1)
se(βˆ1)
=
−0.0113− (−1)
0.0433
= 22.834
Degrees of freedom (df)= n - k - 1 = 82 - 3 - 1 = 78, thus from the Table, the critical
value is 1.662.
tβˆ1 > 1.662. Therefore, we reject the null that β1 = −1 in favor of the alternative that
β1 > −1 at the 5% significance level.
QUESTION B3
Degrees of freedom (df)= n - k - 1 = 82 - 3 - 1 = 78, thus from the Table, the critical
value is 1.987 (or 2.000).
Therefore, the confidence interval is:
[0.0819 - 1.987*0.0228; 0.0819 + 1.987*0.0228 ] = [0.037; 0.127]
(or [0.0819 - 2.000*0.0228; 0.0819 + 2.000*0.0228 ] = [0.036; 0.128] )
QUESTION B4
The effect of an extra year of experience on log(wage) for an individual with 10 years of
experience is:
−0.0113+2 ∗ 0.0017 ∗ 10 = 0.0227. We can interpret this as a predicted increase in wage
of about 2.27%.
Notes for grader:
Total of marks: 6
