Moshe A Buchinsky Economics 103Department of Economics Introduction to EconometricsUCLA Fall, 2013Mid-Term ExaminationNovember 7, 2013This is an open-book in-class exam. You are allowed to use your text book, your note bookand a calculator.Please answer all the questions below. Please choose the best answer among all availableanswers. Only one answer is the best answer! Please circle one, and only one, answer. If morethan one answer is circled the question will not be counted.Please type you name and your UCLA ID:First NameLast NameUCLA ID #Exam VersionPlease start solving the examinations only when you are instructed to do so.Please stop immediately when instructed to do so.Good Luck!1Part I (each question worth 4 points):Consider the following regression model:yi= 1+ 2xi+ ei;for i = 1; :::; N . Let eijxi0; 2i. That is, conditional on xi, eihas a distribution whose meanis 0 and its variance is 2i. Lets2x=1NNXi=1(xi x)2; where x =1NNXi=1xi: (1)1. One ran a regression of y on x and obtained the following estimates for 1and 2: b1= 4,b2= :5. De…ne x i= 10  xi. If one were to run a regression of y on x the estimates b1andb2would be(a) b1= 4, b2= :5(b) b1= 4, b2= :05(c) b1= :4, b2= :5(d) b1= :4, b2= 52. Under the assumptions SR1-SR5 made in Chapter 2:(a) E (b2) = 2always(b) E (b2) = 2only if the distribution of eiis normal(c) E (b2) = 2only if 2i= 2for all i, i.e., 2iis a constant(d) E (b2) 6= 2always.3. Given the de…nition of s2xin equation (1):(a) The smaller is N s2xthe smaller is the variance of b2.(b) Ns2xprovides no information about the variance of b2.(c) The variance of b2is not a¤ected by the sample variance of x.(d) The larger is N s2xthe smaller is the variance of b2.4. De…ne bei= yi b1 b2xi.(a) It need not be thatPNi=1bei= 0.(b)PNi=1bei= 0 always.(c)PNi=1bei= 0 under assumptions SR1-SR5.(d)PNi=1bei= 0 only if E (ei) = 0:25. Suppose thatPNi=1x2i= 110 andPNi=1xiyi= 90, then(a) b2= 1:054.(b) b2= 0:948.(c) b2= 3:201.(d) It is not possible to compute b2based on the information given.6. Suppose b2= :75, se (b2) = :05, and N = 42. The 90% con…dence interval for b2would be:(a) [:721; :761].(b) [:602; :901].(c) [:666; :834].(d) [:424; 1:194].7. (If ??)The 95% con…dence interval for 2is given by [1:04; 1:46], where N = 20. Then b2,the estimate for 2, is(a) b2= 2:25(b) b2= 1:25(c) b2= 1:50(d) b2= 2:528. Consider the null hypothesis H0: 2= 0 against the alternative hypothesis H1: 2> 0:(a) If one were to reject H0then one will also reject H0: 2= 0 against H1: 26= 0:(b) If one were to reject H0then one will accept H0: 2= 0 against H1: 26= 0:(c) If one were to reject H0then we cannot determine whether he/she will also reject H0:2= 0 against H1: 26= 0:(d) If one were to accept H0then one will also accept H0: 2= 0 against H1: 26= 0:9. Let pvdenote the p-value from testing H0: 2= 0 against H1: 2> 0. Let  denote thesigni…cance level of the test.(a) To reject the null hypothesis we must have the t-statistic (b2 2) =se (b2)(b) If pv>  we will reject the null hypothesis.(c) Only if pv=  can we reject the null hypothesis. ??(d) If pv<  we will reject the null hypothesis.310. Suppose one tested and rejected the null hypothesis H0: 2= 0 against H1: 2= 1 at thesigni…cant level  = 0:01, then one of the following must be true:(a) He will reject H0: 2= 0 against H1: 26= 0.(b) He will reject H0: 2= 0 against H1: 2< 0.(c) He will reject H0: 2= 0 against H1: 2> 0.(d) He will reject H0: 2= 0 against H1: 2< 1.11. If 2i= 2for all i, i.e., 2iis a constant, then:(a) The smaller 2, the smaller the variance of b2.(b) The smaller 2, the smaller the estimated variance of b2.(c) Both (a) and (b) are correct.(d) 2provides no information about the variance of b2.12. The rejection region consists the values of test statistic that have:(a) Low probability of occurring when the null hypothesis is true.(b) High probability of occurring when the null hypothesis is true.(c) Low probability of occurring regardless of whether the null hypothesis is true or not.(d) High probability of occurring regardless of whether the null hypothesis is true or not.4Part II (each question worth 3 points):Consider the following STATA output in which the summary statistics for three variables areprovided, wage (wage), education (educ), and experience (exper). The results of the followingthree linear regressions are also provided. These regressions are:wagei= 1+ 2educi+ eieduci= 1+ 2wagei+ viexperi= 1+ 2educi+ uiSTATA Output 15The following questions refer to this output, namely STATA Output 1. For each of thefollowing questions determine whether it is true, false, or it is not possible to determine (uncertain):1. Since the t-statistic for education in the …rst regression is larger than the t-statistic on wagein the se cond regression, it is indicative that wage a¤ects education as much as educationa¤ects wage.(a) True(b) False(c) Uncertain2. The fact that the p-value for the coe¢ cient on education is zero indicates that the corre-sponding true parameter 2is signi…cantly di¤erent from zero.(a) True(b) False(c) Uncertain3. The 99% con…dence interval for 2is [1:8831; 2:1157].(a) True(b) False(c) Uncertain4. The estimate for 2indicates that education has a negative e¤ect on experience.(a) True(b) False(c) Uncertain5. The R2from the last regression indicates that experience accounts for less than 3% of thevariation in education.(a) True(b) False(c) Uncertain6. If one were to test the null hypothesis H0: 2 1 against H1: 2> 1 at the signi…cant level = :05, then he/she would be able to reject the null hypothesis.(a) True6(b) False(c) Uncertain7. The covariance estimates for 1and 2is negative.(a) True(b) False(c) Uncertain8. A conclusion from the reported results for the three regressions indicates that wage andexperience are uncorrelated.(a) True(b) False(c) Uncertain7Part III (each question worth 4 points):Consider the regression model given byyi= 1+ 2x2i+ 3x3i+ eifor i = 1; :::N .1. It is claimed that group A is being discriminated against, on average, in the market place.Suppose yidenotes wage and x2idenotes education. Assume also that x3itakes the value1 if the individual belongs to group A and take the value 0, otherwise. The null hypothesisthat is most suited to test the assertion about