Intermediate EconometricsFinal ExamSpring2010Note:(1)You have two hours to complete the exam.(2)You can answer in either English or Chinese.1True or False(20points)Indicate true or false for the following statements.Explain only if the statement is false.2 points each.1.Instrumental variable regression is needed when the residuals are correlated with theregressors.2.Consider the regression modelln(consumption)=0.8(0.2)+3.2(1.1)education+1.4(0.5)education∗f emale+0.9(0.4)ln(income),where education measures years of schooling and female is the dummy if one is a female,and values in brackets are standard errors.This model shows that on average an additional year of education shall increase consumption by3.2%on average,andthis result is significant at5%significance level.3.Consider y=xβ+u,V(ˆβIV)using z as an instrument is always larger than VˆβOLS,so we should avoid using IV whenever x and u are independent.4.Consider the modely1=β0+β1y2+β2z1+u1(1)y2=µ+δ1z1+δ2q1+δ3q2+v,(2) where cov(y2,u1) 0,z1,q1,q2are exogenous variables.Then equation(1)is called the reduced form equation.5.The weakest consistency condition for FGLS for AR(1)is E(u t)=0and E[x k,t−1u t+x kt u t−1]=0for t=1,...,T,k=1,...,K.6.The GLS estimators for correcting heteroskedasticity are one kind of weighted leastsquares estimators.17.When serial correlation exists in the error term,the OLS variance formulaσ2/S S T xoverstates the true variance of the OLS estimator.8.When the error term is AR(1)with the correlation coefficientρ>0,the t statisticsignoring this correlation tends to be smaller than that taking into account of the serial correlation.9.Iflog(y)=xˆβ,then the predicted value of y isˆy=explog(y).10.The heteroskedasticity-robust standard errors are always bigger than the usual stan-dard errors for the linear probability model.2Multiple Choice Questions(50points)One of the choices is correct.Choose the correct one.5points for each question.1.Consider the following four tests:White test,Breusch Pagan test,Chow test,DWtest.How many of them can be used to test for heteroskedasticity?(a)one b)two c)three(d)four2.Which of the following statements is wrong?(a)When the hetereskedasticity is of unknown form,the feasible generalized leastsquare estimator can be unbiased.(b)The FGLS estimator is consistent and is always asymptotically more efficientthan OLS.(c)For large sample sizes,FGLS is an attractive alternative to OLS when there isevidence of heteroskedasticity.(d)We use the FGLS estimates in place of the OLS estimates under heteroskadas-ticity,because they are more efficient and have associated test statistics withthe usual t and F distributions.3.Which of the following statements is not true?(a)It is impossible to see serial correlation in cross-sectional data.(b)The R-squared is still an appropriate measure when there exists serial correla-tion for stationary series.2(c)A t test can be used to test for serial correlation when used appropriately.(d)DW test is used to test whether the error terms are correlated.4.Which of the following is not true?(a)The multiple linear regression with a binary dependent variable is called thelinear probability model.(b)Thefitted values from linear probability model are called predicted probabili-ties.(c)OLS is the efficient estimator for linear probability model.(d)Linear probability model assumes the probability is linearly related to the in-dependent variables.5.In class we discussed the application of Granger Causality on chicken and eggs.Based on those discussions,how many of the following statement(s)is(are)wrong?(a)zero(b)one(c)two(d)three(1)The evidence shows that the lagged values of chickens can predict currentvalues of eggs.(2)If the lagged values of eggs can help predict current values of chickens,then we conclude that in the beginning eggs appeared before chickens.(3)If the lagged values of chickens can help predict current values of eggs,then we conclude that in the beginning chickens appeared before eggs.6.Following our discussions in class about the impact of education on wage,which ofthe following has NOT been used in the literature as an instrument?(a)draft lottery number b)birth quarter c)income d)mother’s education7.Which of the following statements about dealing with endogeneity is WRONG?(a)Let z2be the instrument for y2,then one can test endogeneity of y2throughtesting H0:δ1=0in y1=β0+β1y2+β2z1+δ1ˆy2+error,whereˆy2=ˆπ0+ˆπ1z1+ˆπ2z2.(b)If we canfind suitable proxy variable for the endogenous variable,we can atleast mitigate the endogeneity problem.3(c)Instrumental variable estimation is one of the methods to deal with endogeneitycaused by omitted-variable bias.(d)If we cannotfind good instruments,have panel data at hand,and there is noappropriate proxy,we can use the imperfect OLS estimator but acknowledgingthe problem.8.Consider two modelsy i1=β0+β1x i1+β2x i2+u i1˜y i2=µ0+δ1˜x i1+δ2˜x i2+u i2,where˜y i2=10y i1,˜x i1=2x i1,˜x i2=5x i2.OLS regression for y i1equation givesˆβ1=2.5,ˆβ2=3.Which of the following about the OLS regression of the˜y i2equation istrue?(a)ˆδ1=12.5,ˆδ2=6;b).ˆδ1=0.5,ˆδ2=1.5c).ˆδ1=2.5,ˆδ2=6d).ˆδ1=2.5,ˆδ2=39.Consider the model that evaluate how marriage decisions are affected by variousfactors,where the dependent variable is a dummy that equals to one when one is married.married i=β0+β1x i1+β2x i2+u i1,An OLS regression is done on this equation,then which of the following statement is true?(a)We can assume that u i1is i.i.d.with mean zero and varianceσ2.(b)Because OLS regression usually does not put constraints on the dependentvariables,the predicted values are always meaningful.(c)The usual F statistic for this model no longer has F distribution.(d)It is meaningless to run OLS regressions since the dependent variable is notcontinuous.10.Which of the following statement is true?(a)Because adjusted R squared are positive and don’t increase with additionalexplanatory variables,it is a better measure for goodness offit.(b)The higher the R squared,the better thefit of the regression.(c)We can use adjusted R squared to choose between non-nested models.(d)A higher R squared after estimating the model using2SLS means better good-ness offit.43Analytical Questions(30points)1.A researcher uses the following equation to study return to educationln(wage)=µ+β1edu+β2edu2+β3rural∗edu+β4exp er+β5exp er2+u(3) where the natural log of hourly wage depends on one’s own education(edu),whether he is from rural area(rural),and his/her working experience,u is the error term.(a)(6points)The researcher starts with a simple form of regressionln(wage)=µ+β∗rural+uwith the following summary statistics:ln(wage)mean s.d.rural=11.50.8rural=02.41.6Derive the OLS estimated parameterµandβ.(b)(4points)If all explanatory variables satisfy the exogeneity assumption,pro-vide the BLUE estimator for(3).(c)(5points)This researcher’s work is criticized as he ignores that one’s innateability may be correlated with education.List the requirements for valid in-struments(3).(d)(5points)Based on our discussions in class,list instruments that has beenused in the literature for the identification of return to education equation,anddiscuss when the instruments can be valid.(e)(5points)Suppose your listed instruments are all valid.Write out the stepsyou used to get the consistent estimates for return to education.5。
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