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1 Question 1 (25 points total)
Briefly explain after you decide if the statement is True or False. Stating
only if it is True or False is not enough to get points.
• a. (5 points) If an estimator is unbiased, then, for sure it is
consistent as well.
• b. (5 points) The method of least squares is a way to minimize the
sum of squared
esiduals (i.e. prediction e
ors).
• c. (5 points) This is a time series data: The weather temperature of
all states in United States in 07/07/2021.
• d. (5 points) The null hypothesis and its alternative for an estimator
are as follows: H0 :1 =0
Ha :1 6=0 ˆ
If the t statistics for this test is defined as t = 10 and its absolute value is
smaller than ˆ
SE(1 )
1.96, we reject the Null hypothesis and we can conclude that 1 is
statistically significant
and di↵erent than zero at 5 percent significance level.
• e. (5 points) Homoskedasticity is a special case of heteroskedasticity
considering OLS e
ors.
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2 Question 2 (25 points total)
Consider a data set that contains data on births to women in the United
States. Two variables of interest are the dependent variable, infant birth
weight in ounces (bwght), and an explanatory variable, average number
of cigarettes the mother smoked per day during pregnancy (cigs). The
following simple regression was estimated using data on n=1,388 births
(smokers and non-smokers, all of them)::
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• • • •
wght = XXXXXXXXXXcigs
a. (5 points) What is the predicted birth weight when cigs=0? What
about when
d
cigs=20? Comment on the di↵erence.
. (10 points) Does this simple regression necessarily capture a causal
elationship between the child’s birth weight and the mother’s smoking
habits? Explain.
c. (5 points) To predict a birth weight of 125 ounces, what would cigs
have to be? Comment.
d. (5 points) The proportion of women in the sample who do not smoke
while pregnant is about .85. Does this help reconcile your finding from
Part c ?
Question 3 (25 points total)
Consider the following simple linear model:
Yi =0 +1Xi +ui,i=1,...,n ˆ
• a. (15 points) Show that 0 is an unbiased estimator of 0 if OLS (or LSE)
assumptions ˆ
hold (Hint: Use the fact that 1 is unbiased, from the course slides)
• b. (10 points) What happens when we have biased estimators? What
kind of problems we may encounter? Explain.
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Question 4. Empirical (25 points total as Check
Plus(100/100), Check(85/100), Check Minus(65/100), No
Credit(0/100))
Use the data in sleep75 (sleep75.dta) from Biddle and
Hamermesh XXXXXXXXXXto study whether there is a tradeoff
etween the time spent sleeping per week and the time
spent in paid work. We could use either variable as the
dependent variable. For concreteness, estimate the model
sleep =β0 +β1 totwrk +u (1) where sleep is minutes spent
sleeping at night per week and totwrk is total minutes
worked
during the week.
• a. Report your results in equation form along with the
number of observations and R .
2 Are the coefficients for β0 and β1 statistically different
from zero at 5 percent significance
level? How do you conclude? Be specific.
• b. What does the intercept in this equation mean?
Explain.
• c. If totwrk increases by 2 hours, by how much is sleep
estimated to fall? Do you find this to be a large effect?
Explain.