# UCLA ECON 103 - Econ-103-2013-Midterm-Ver-A (9 pages)

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## Econ-103-2013-Midterm-Ver-A

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- School:
- University of California, Los Angeles
- Course:
- Econ 103 - Introduction to Econometrics

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Moshe A Buchinsky Department of Economics UCLA Economics 103 Introduction to Econometrics Fall 2013 Mid Term Examination November 7 2013 This is an open book in class exam You are allowed to use your text book your note book and a calculator Please answer all the questions below Please choose the best answer among all available answers Only one answer is the best answer Please circle one and only one answer If more than one answer is circled the question will not be counted Please type you name and your UCLA ID First Name Last Name UCLA ID Exam Version Please start solving the examinations only when you are instructed to do so Please stop immediately when instructed to do so Good Luck 1 Part I each question worth 4 points Consider the following regression model yi for i 1 N Let ei jxi 2 i is 0 and its variance is 2 i 0 1 2 xi ei That is conditional on xi ei has a distribution whose mean Let N 1 X xi N s2x x 2 where x i 1 N 1 X xi N 1 One ran a regression of y on x and obtained the following estimates for b2 5 De ne xi 10 a b1 4 b2 5 b b1 4 b2 05 c b1 4 b2 5 d b1 4 b2 5 2 Under the assumptions SR1 SR5 made in Chapter 2 a E b2 2 always b E b2 2 only if the distribution of ei is normal c E b2 2 only if d E b2 6 2 always 2 i 2 for all i i e 2 i is a constant 3 Given the de nition of s2x in equation 1 a The smaller is N s2x the smaller is the variance of b2 b N s2x provides no information about the variance of b2 c The variance of b2 is not a ected by the sample variance of x d The larger is N s2x the smaller is the variance of b2 b1 1 and 2 b1 4 xi If one were to run a regression of y on x the estimates b1 and b2 would be 4 De ne ebi yi 1 i 1 b2 xi P a It need not be that N bi 0 i 1 e PN b bi 0 always i 1 e PN c bi 0 under assumptions SR1 SR5 i 1 e PN d bi 0 only if E ei 0 i 1 e 2 5 Suppose that PN 2 i 1 xi 110 and a b2 1 054 PN i 1 xi yi 90 then b b2 0 948 c b2 3 201 d It is not possible to compute b2 based on the information given 6 Suppose b2 75 se b2 05 and N 42 The 90 con dence interval for b2 would be a 721 761 b 602 901 c 666 834 d 424 1 194 7 If The 95 con dence interval for the estimate for 2 2 is given by 1 04 1 46 where N 20 Then b2 is a b2 2 25 b b2 1 25 c b2 1 50 d b2 2 52 8 Consider the null hypothesis H0 2 0 against the alternative hypothesis H1 a If one were to reject H0 then one will also reject H0 b If one were to reject H0 then one will accept H0 2 2 0 against H1 0 against H1 2 2 2 0 6 0 6 0 c If one were to reject H0 then we cannot determine whether he she will also reject H0 2 0 against H1 2 6 0 d If one were to accept H0 then one will also accept H0 9 Let pv denote the p value from testing H0 2 2 0 against H1 0 against H1 2 0 Let signi cance level of the test a To reject the null hypothesis we must have the t statistic b2 b If pv we will reject the null hypothesis c Only if pv d If pv can we reject the null hypothesis we will reject the null hypothesis 3 2 se b2 2 6 0 denote the 10 Suppose one tested and rejected the null hypothesis H0 signi cant level 2 0 against H1 2 6 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 2 i is a constant then 2 i 2 0 against H1 2 1 at the 0 01 then one of the following must be true a He will reject H0 11 If 2 for all i i e 1 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 2 provides 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 4 Part II each question worth 3 points Consider the following STATA output in which the summary statistics for three variables are provided wage wage education educ and experience exper The results of the following three linear regressions are also provided These regressions are wagei 1 2 educi ei educi 1 2 wagei vi experi 1 2 educi STATA Output 1 5 ui The following questions refer to this output namely STATA Output 1 For each of the following 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 wage in the second regression it is indicative that wage a ects education as much as education a ects wage a True b False c Uncertain 2 The fact that the p value for the coe cient on education is zero indicates that the corresponding true parameter 2 is signi cantly di erent from zero a True b False c Uncertain 3 The 99 con dence interval for 2 is 1 8831 2 1157 a True b False c Uncertain 4 The estimate for 2 indicates that education has a negative e ect on experience a True b False c Uncertain 5 The R2 from the last regression indicates that experience accounts for less than 3 of the variation in education a True b False c Uncertain 6 If one were to test the null hypothesis H0 2 1 against H1 2 05 then he she would be able to reject the null hypothesis a True 6 1 at the signi cant level b False c Uncertain 7 The covariance estimates for 1 and 2 is negative a True b False c Uncertain 8 A conclusion …

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