Sample ExamYou have 1 hour and 50 minutes.There are total of 20 problems, each worth 5 points.Part 1Suppose you want to study the following model:Incomei = 0 + 1Educationi + iIncomei: 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 9Educationi 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 attemptedusing quarter of birth as instrumental variables. Therefore you collect new data of these threefriends 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 tenyears 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 yourremedy? Why or why not?(5%)(6) Calculate standard xed eects 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 consof including it into the equation?(5%)(8) Suppose IQi = Talenti + ui, is Assumption III violated? Why or why not.1Part 2Consider the following model of iPod prices on eBay:PRICEi = 0 + 1NEWi + 2SCRATCHi + 3BIDDERSi + iwhere:PRICEi = the price at which the ith iPod sold on eBayNEWi = equal to 1 if the ith iPod was new, 0 otherwiseSCRATCHi = equal to 1 if the ith iPod had a minor cosmetic defect, 0 otherwiseBIDDERSi = the number of bidders on the ith iPodThe estimated equation is: PRICEi = 203:54 + 14:99NEWi ???? 10:43SCRATCHi + 0:13BIDDERSi(4:65) (2:34) (0:19)N = 337(5%)(9) Construct a 95% condence interval for 3, test H0 : 3 = 0 v.s. H1 : 3 6= 0with this condence interval.(5%)(10) Propose a testing procedure to check if we should include NEWi and SCRATCHiin the equation.(5%)(11) Propose a testing procedure to check if there is heteroskedasticity in the model.Rewrite the model as:PRICEi = 0 + 1NEWi + 2SCRATCHi + 3BIDDERSi +4BIDDERS2i + 5NEWi REPUTATIONi + i(5%)(12) If the estimated coecient of 4 is negative, what does it imply?(5%)(13) Interpret 5.2Part 3In time series model Yt = 0 +1Xt +t, let the probability distribution of t and Xt be:Pr t=-2 t=0 t=1Xt=1 0.2 0.1 0.4Xt=2 0.1 0 0.2(5%)(14) Is Assumption II violated? Why or why not.(5%)(15) Is Assumption III violated? Why or why not.(5%)(16) Is Assumption V violated? Why or why not.(5%)(17) Suppose Xt = 2Xt????1 + ut, is OLS estimator still consistent? Why or why not?(5%)(18) Suppose there is no inter-temporal relationship between Xt, Yt and t, describethe properties of an OLS estimator.Part 4Bond ratings are letter ratings(Aaa=best) assigned to rms that issue debt. Supposeyou’ve been hired by an arbitrage house that wants to predict one rm’s rating. Your bosswants you to estimate the following model:^ Yi = 0 + 1Pi + 2PVi + 3Di + iwhereYi = 1 if the rating of the ith bond = A, 0 otherwisePi = the prot rate of the rm that issued the ith bondPVi = the standard deviation of Pi over the last ve yearsDi = the ratio of debt to total capitalization of the rm that issued the ith bond(5%)(19) What econometric problems, if any, exist in this equation?(5%)(20) How would you x the issue in (19)?(Briey describe the steps to implement aremedy, you don’t have to use mathematical formulas but they may make your descriptionclearer.)3