Econometrics Sample Paper Questions

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Sample Exam

You have 1 hour and 50 minutes.

There are total of 20 problems, each worth 5 points.

Part 1

Suppose you want to study the following model:

Incomei = 0 + 1Educationi + i

Incomei: Friend i's monthly income after tax.

Educationi: Friend i's years of education after high school.

And you have collected data based on a survey of your three friends:

Incomei 10 2 9

Educationi 7 0 8

(5%)(1) Calculate OLS estimator ^ 1OLS .

(5%)(2) Calculate R2.

(5%)(3) It is common knowledge in economic eld that Assumption III(no endogeneity)

in this model is violated, why? What is the consequence of endogeneity in this model?

Now from the paper we have discussed in class, you know that economists have attempted

using quarter of birth as instrumental variables. Therefore you collect new data of these three

friends for their quarter of birth(QBi):

QBi 1 3 2

(5%)(4) Calculate 2SLS estimator ^ 12SLS .

You know that panel data can also be used to solve endogeneity problem. Therefore ten

years later, you collect data on the same three friends again, now they have changed a bit:

Incomei 12 4 -

Educationi 9 2 -

The last column is missing because you lost contact with the third friend.

(5%)(5) What can you do to x this missing data issue? Is there any problem of your

remedy? Why or why not?

(5%)(6) Calculate standard xed e ects estimator using your remedy.

(5%)(7) Recall that you also learned a plug-in solution for endogeneity problem. There-

fore you decided to use IQ as a proxy for your friends' talent. What are the pros and cons

of including it into the equation?

(5%)(8) Suppose IQi = Talenti + ui, is Assumption III violated? Why or why not.

1

Part 2

Consider the following model of iPod prices on eBay:

PRICEi = 0 + 1NEWi + 2SCRATCHi + 3BIDDERSi + i

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

The estimated equation is:

\ PRICEi = 203:54 + 14:99NEWi

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