## Description

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

(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

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:

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 Â· Genderi + ?4 Agei + ?5 Age2 +

i

i

is

ln(Income)i = 10.23+6.17ln(Edu)i +0.62Genderi ?0.22ln(Edu)i Â·Genderi +0.02Agei ?0.13Age2

i

where:

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 .

Ë†

(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 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.)

3

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