# Problem 1 Let’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 (5.34) t = 10.28 (5.11) (0.59) ? 4.00 1.23 N = 215 where: P RICEi = the price at which the ith iPod sold on eBay N EWi = equal to 1 if the ith iPod was new, 0 otherwise SCRAT CHi = equal to 1 if the ith iPod had a minor cosmetic defect, 0 otherwise BIDDERSi = the number of bidders on the ith iPod Let’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: 1 P RICE i = 82.67 + 55.42N EWi ? 20.95SCRAT CHi + 0.63BIDDERSi + 0.28P ERCEN Ti (5.34) t = 10.38 (5.12) (0.59) 1.07 ? 4.10 (0.20) 1.40 N = 215 (10%)(1) Do you think we should include BIDDERSi into the equation? Why or why not. (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 (3).) NOTE: Though irrelevant, try to compare these four problems with your solution to problem 2(1) in assignment 3. 2 Problem 2 Suppose the estimated equation for model: ln(Income)i = ?0 + ?1 ln(Edu)i + ?2 Genderi + ?3 ln(Edu)i · Genderi + ?4 Agei + ?5 Age2 + i i is ln(Income)i = 10.23+6.17ln(Edu)i +0.62Genderi ?0.22ln(Edu)i ·Genderi +0.02Agei ?0.13Age2 i where: Incomei = Individual i’s annual income. Edui = Individual i’s total months of education. Genderi = 1 if individual i is male and 0 if individual i is female. Agei = Individual i’s age. (10%)(1) Interpret ?1 . (10%)(2) Interpret ?2 . (10%)(3) Interpret ?3 . ˆ (10%)(4) What does ?5 = ?0.13 mean? Problem 3 Consider a simple model relating the annual number of crimes on college campuses (Crimei ) to student enrollment (Enrolli ): Crimei = ?0 + ?1 ln(Enroll)i + i Suppose we collect data on 97 colleges and universities in the United States for the year 1992. The data come from the FBI’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.)

Problem 1
Let’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
(5.34)
t = 10.28

(5.11)

(0.59)

? 4.00

1.23

N = 215
where:
P RICEi

=

the price at which the ith iPod sold on eBay

N EWi

=

equal to 1 if the ith iPod was new, 0 otherwise

SCRAT CHi

=

equal to 1 if the ith iPod had a minor cosmetic defect, 0 otherwise

BIDDERSi

=

the number of bidders on the ith iPod

Let’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:

1

P RICE i = 82.67 + 55.42N EWi ? 20.95SCRAT CHi + 0.63BIDDERSi + 0.28P ERCEN Ti
(5.34)
t = 10.38

(5.12)

(0.59)
1.07

? 4.10

(0.20)
1.40

N = 215
(10%)(1) Do you think we should include BIDDERSi into the equation? Why or why
not.
(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:
(3).)
NOTE: Though irrelevant, try to compare these four problems with your solution to
problem 2(1) in assignment 3.

2

Problem 2
Suppose the estimated equation for model:
ln(Income)i = ?0 + ?1 ln(Edu)i + ?2 Genderi + ?3 ln(Edu)i · Genderi + ?4 Agei + ?5 Age2 +
i

i

is
ln(Income)i = 10.23+6.17ln(Edu)i +0.62Genderi ?0.22ln(Edu)i ·Genderi +0.02Agei ?0.13Age2
i
where:
Incomei = Individual i’s annual income.
Edui = Individual i’s total months of education.
Genderi = 1 if individual i is male and 0 if individual i is female.
Agei = Individual i’s age.
(10%)(1) Interpret ?1 .
(10%)(2) Interpret ?2 .
(10%)(3) Interpret ?3 .
ˆ
(10%)(4) What does ?5 = ?0.13 mean?
Problem 3
Consider a simple model relating the annual number of crimes on college campuses
(Crimei ) to student enrollment (Enrolli ):
Crimei = ?0 + ?1 ln(Enroll)i +

i

Suppose we collect data on 97 colleges and universities in the United States for the year
1992. The data come from the FBI’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.)