Economic Assignment 4

Assignment 4

Due Monday July. 28th Before Class

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:

̂PRICEi = 109.24 + 54.99NEWi − 20.44SCRATCHi + 0.73BIDDERSi

(5.34) (5.11) (0.59)

t = 10.28 − 4.00 1.23

N = 215

where:

PRICEi = the price at which the ith iPod sold on eBay

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

SCRATCHi = 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: PERCENTi. It mea-

sures 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:

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̂PRICEi = 82.67 + 55.42NEWi − 20.95SCRATCHi + 0.63BIDDERSi + 0.28PERCENTi

(5.34) (5.12) (0.59) (0.20)

t = 10.38 − 4.10 1.07 1.40

N = 215

(10%)(1) Do you think we should include BIDDERSi into the equation? Why or why

not.

(10%)(2) Test H0 : β4 6 0 v.s. H1 : β4 > 0 at 5% significance level. Here β4 is the

coefficient of PERCENTi.

(10%)(3) Do you think that PERCENTi 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 PERCENTi 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.

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Problem 2

Suppose the estimated equation for model:

ln(Income)i = β0 + β1ln(Edu)i + β2Genderi + β3ln(Edu)i · Genderi + β4Agei + β5Age2i + �i

is

̂ln(Income)i = 10.23+6.17ln(Edu)i+0.62Genderi−0.22ln(Edu)i·Genderi+0.02Agei−0.13Age 2 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 β1.

(10%)(2) Interpret β2.

(10%)(3) Interpret β3.

(10%)(4) What does β̂5 = −0.13 mean?

Problem 3

Consider a simple model relating the annual number of crimes on college campuses

(Crimei) to student enrollment (Enrolli):

Crimei = β0 + β1ln(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 specific as possible.)

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