Name: Section #
I attest that I have completed this exam without unauthorized assistance from any person,
materials, or device.
Signature Date
Johns Hopkins University Economics 180.334
Fall 2014
Midterm # 2
Thursday, October 23, 2014
Instructions:
1. Time limit: 70 minutes
2. Total number of points is 70. The number of points for each problem indicates the
approximate time in minutes that should be allocated to the problem
3. The exam is closed book/notes. You are allowed to use a 1-sided, letter size, cheat
sheet
4. You can use a hand calculator. Cellphones/Smartphones are not allowed
5. To receive full credit for your answers, you have to explain your calculations
6. When you conduct a hypothesis test, please state clearly: the null hypothesis and
alternative hypothesis, the formula and value of your test statistics, acceptance or
rejection rules (based on correct critical values), and the outcome of your test
7. A standard normal distribution function and critical values for the χ2q distribution are
included at the back of this booklet.
8. No extra points this time.
Good luck!
1
, 1. Females, it is said, make 70 cents to the dollar in the United States. To investigate this
phenomenon, you collect data on weekly earnings from 1,744 individuals, 850 females
and 894 males. Next, you calculate their average weekly earnings and find that the
females in your sample earned $346.98, while the males made $517.70.
(a) [1] Calculate the female earnings in percent of the male earnings.
Answer: 346.98
517.70
= .67 = 67%
(b) [7] How would you test whether or not this difference is statistically significant
using a regression?
Answer: To test whether or not this difference is statistically significant (meaning
statistically different from zero), I would first define a dummy variable called
f emale. I would define f emale as follows:
(
1, if person i is female
f emalei =
0, if person i is male
Let Yi be the earnings of person i.
I would estimate the equation Yi = β0 + β1 f emale + ui using OLS.
I would then test the hypothesis: H0 : β1 = 0 vs. H1 : β1 6= 0
I would perform this test by either by comparing the p-value to the desired level
of significance, α, and reject when pvalue < α or the test statistic, t, to the
critical value CV (α), and reject when t > CV (α). Intuitively, this hypothesis
test tests whether or not the female earnings are statistically different from the
male earnings since β1 = 0 implies there is no difference.
(c) [10] A peer suggests that this is consistent with the idea that there is discrimi-
nation against females in the labor market. What is your response? Mention at
least two omitted variables that can potentially explain the observed difference in
average earnings. Explain your reasoning for each variable.
Answer: I disagree with my peer’s suggestion. If we interpret the difference in
mean earnings between genders as an estimate of the effect of gender on earnings,
that estimate will almost certainly suffer from omitted variable bias that is biasing
the estimate away from zero. So we cannot be sure that the difference is due to
discrimination.
One such variable that could bias the estimate away from zero is whether or not
the individual works full-time. Clearly, if you only work part-time your weekly
earnings will be less than someone who works full-time on average all else equal.
Furthermore, women are more likely to work part-time, perhaps so that they may
raise their children. If this variable is ignored, the observed effect of gender on
earnings will be further away from zero than the true effect.
Another such variable that could bias the estimate away from zero is the career
choice. It is the case that men are more likely to choose a career path in Science,
2
I attest that I have completed this exam without unauthorized assistance from any person,
materials, or device.
Signature Date
Johns Hopkins University Economics 180.334
Fall 2014
Midterm # 2
Thursday, October 23, 2014
Instructions:
1. Time limit: 70 minutes
2. Total number of points is 70. The number of points for each problem indicates the
approximate time in minutes that should be allocated to the problem
3. The exam is closed book/notes. You are allowed to use a 1-sided, letter size, cheat
sheet
4. You can use a hand calculator. Cellphones/Smartphones are not allowed
5. To receive full credit for your answers, you have to explain your calculations
6. When you conduct a hypothesis test, please state clearly: the null hypothesis and
alternative hypothesis, the formula and value of your test statistics, acceptance or
rejection rules (based on correct critical values), and the outcome of your test
7. A standard normal distribution function and critical values for the χ2q distribution are
included at the back of this booklet.
8. No extra points this time.
Good luck!
1
, 1. Females, it is said, make 70 cents to the dollar in the United States. To investigate this
phenomenon, you collect data on weekly earnings from 1,744 individuals, 850 females
and 894 males. Next, you calculate their average weekly earnings and find that the
females in your sample earned $346.98, while the males made $517.70.
(a) [1] Calculate the female earnings in percent of the male earnings.
Answer: 346.98
517.70
= .67 = 67%
(b) [7] How would you test whether or not this difference is statistically significant
using a regression?
Answer: To test whether or not this difference is statistically significant (meaning
statistically different from zero), I would first define a dummy variable called
f emale. I would define f emale as follows:
(
1, if person i is female
f emalei =
0, if person i is male
Let Yi be the earnings of person i.
I would estimate the equation Yi = β0 + β1 f emale + ui using OLS.
I would then test the hypothesis: H0 : β1 = 0 vs. H1 : β1 6= 0
I would perform this test by either by comparing the p-value to the desired level
of significance, α, and reject when pvalue < α or the test statistic, t, to the
critical value CV (α), and reject when t > CV (α). Intuitively, this hypothesis
test tests whether or not the female earnings are statistically different from the
male earnings since β1 = 0 implies there is no difference.
(c) [10] A peer suggests that this is consistent with the idea that there is discrimi-
nation against females in the labor market. What is your response? Mention at
least two omitted variables that can potentially explain the observed difference in
average earnings. Explain your reasoning for each variable.
Answer: I disagree with my peer’s suggestion. If we interpret the difference in
mean earnings between genders as an estimate of the effect of gender on earnings,
that estimate will almost certainly suffer from omitted variable bias that is biasing
the estimate away from zero. So we cannot be sure that the difference is due to
discrimination.
One such variable that could bias the estimate away from zero is whether or not
the individual works full-time. Clearly, if you only work part-time your weekly
earnings will be less than someone who works full-time on average all else equal.
Furthermore, women are more likely to work part-time, perhaps so that they may
raise their children. If this variable is ignored, the observed effect of gender on
earnings will be further away from zero than the true effect.
Another such variable that could bias the estimate away from zero is the career
choice. It is the case that men are more likely to choose a career path in Science,
2
