Letâ€™s return to the model of problem 2 in assignment 3 of the auction price of iPods on
eBay. In that model, we estimated the following equation:
P RICE i = 109.24 + 54.99N EWi ? 20.44SCRAT CHi + 0.73BIDDERSi
t = 10.28
N = 215
the price at which the ith iPod sold on eBay
equal to 1 if the ith iPod was new, 0 otherwise
equal to 1 if the ith iPod had a minor cosmetic defect, 0 otherwise
the number of bidders on the ith iPod
Letâ€™s suppose that we include a new variable into the equastion: P ERCEN Ti . It measures the percentage of customers of the seller of the ith iPod who gave that seller a positive
rating for quality and reliability in previous transactions. In theory, the higher the rating
of a seller, the more a potential bidder would trust that seller, and the more that potential
bidder would be willing to bid. The new estimated equation is:
P RICE i = 82.67 + 55.42N EWi ? 20.95SCRAT CHi + 0.63BIDDERSi + 0.28P ERCEN Ti
t = 10.38
N = 215
(10%)(1) Do you think we should include BIDDERSi into the equation? Why or why
(10%)(2) Test H0 : ?4
0 v.s. H1 : ?4 > 0 at 5% signi?cance level. Here ?4 is the
coe?cient of P ERCEN Ti .
(10%)(3) Do you think that P ERCEN Ti is an accurate measure of the quality and
reliability of the seller. Why or why not. (Hint: Among other things, consider the case of a
seller with very few previous transactions.)
(10%)(4) What are the pros and cons of including P ERCEN Ti into the equation? (Hint:
Think about the proxy variable we have mentioned in class together with your answer to
NOTE: Though irrelevant, try to compare these four problems with your solution to
problem 2(1) in assignment 3.
Suppose the estimated equation for model:
ln(Income)i = ?0 + ?1 ln(Edu)i + ?2 Genderi + ?3 ln(Edu)i Â· Genderi + ?4 Agei + ?5 Age2 +
ln(Income)i = 10.23+6.17ln(Edu)i +0.62Genderi ?0.22ln(Edu)i Â·Genderi +0.02Agei ?0.13Age2
Incomei = Individual iâ€™s annual income.
Edui = Individual iâ€™s total months of education.
Genderi = 1 if individual i is male and 0 if individual i is female.
Agei = Individual iâ€™s age.
(10%)(1) Interpret ?1 .
(10%)(2) Interpret ?2 .
(10%)(3) Interpret ?3 .
(10%)(4) What does ?5 = ?0.13 mean?
Consider a simple model relating the annual number of crimes on college campuses
(Crimei ) to student enrollment (Enrolli ):
Crimei = ?0 + ?1 ln(Enroll)i +
Suppose we collect data on 97 colleges and universities in the United States for the year
1992. The data come from the FBIâ€™s Uniform Crime Reports, and the average number of
campus crimes in the sample is about 394, while the average enrollment is about 16,076.
Unfortunately, this sample is not a random sample of colleges in the United States,
because many schools in 1992 did not report campus crimes.
(20%)(1) Is there any potential issue of this sample selection procedure? Explain.(Hint:
There can be many correct answers here, just be speci?c as possible.)