ECON 4400
Prof. Sinanovic
Part 2: Short Questions
1. List assumptions under which the OLS estimator is BLUE? (2pts)
2. What is a random variable? (2pts)
3. What properties do estimators have? (2pts)
4. What is meant by unbiasedness of an estimator? (2pts)
EXAM I-redemption Due October 23
5. How did we obtain the OLS estimators? (Hint: we minimized something?)(2pts)
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ECON 4400 Prof. Sinanovic
PART 3: Long Questions
1. Suppose you were given data on wages for men and women and you would like to test if the average wage is different (not more or less, just different) for men and women. You have 1000 obs of each gender. You use a statistical program to calculate the difference in means and a t-stat for the difference and find men make an average of $2.00 more per hour than women and a t-stat of 2.68 is given for the difference. Suppose that you want to perform this test at 5% level. z- critical value is 1.96. Write out the null and alternative hypotheses, and state the conclusion of the test. (10pts)
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ECON 4400 Prof. Sinanovic
2. Suppose I want to estimate the effect of sleeping on GPA. I collect a random sample of data and for each observation I collect current GPA (variable GPA measured 0-4) and average number of hours slept during a day in any given week (variable sleep in hours).
a) Write down the population regression and all necessary assumptions. (3pts)
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b) Suppose you calculate 𝛽𝛽0 = 4.1, 𝑆𝑆𝑆𝑆�𝛽𝛽0� = 0.2, 𝛽𝛽1 = −0.04., and 𝑆𝑆𝑆𝑆�𝛽𝛽1� = 0.001
Write down the estimated regression. (3pts)
c) Interpret the coefficients from part b. (5pts)
d) What is predicted GPA for individual sleeping 12 hours a day and for individual sleeping 8 hours a day. (3pts)
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ECON 4400
Prof. Sinanovic
e)
Construct 95% confidence interval for both coefficients. (5pts)
f)
Test whether the true effect of sleep on GPA is equal to −0.1. (1pts)
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ECON 4400 Prof. Sinanovic
3. Suppose you are interested in the effects of sector (public vs private) on annual earnings. Below is the STATA output of a regression of private, a dummy variable equal to 1 if individual works in private sector, and 0 if individual works in either federal or state agency, on earnings.
A B
C
a) What is value of box B? (2pts)
b) What is value pf box C? (2pts)
c) Write down the estimated regression. (2pts)
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ECON 4400 Prof. Sinanovic
d) Construct 95% confidence interval for the slope of the regression. (3pts)
e) Interpret ALL coefficients. (Make sure to mention whether they are statistically significant) What do you conclude about which type of jobs on average pay better? (5pts)
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ECON 4400 Prof. Sinanovic
f) Suppose you re-define dummy variable private so that you have a new variable public, a dummy variable equal to 1 if individual works in public sector, and 0 if individual works in private sector, on earnings. Write down this new estimated regression with the estimates for the coefficients. (6pts)
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