25/6 Canddates Only January Examnatons 26 Student Number: Desk Number:...... DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR Department Module Code Module Ttle Exam Duraton (n words) Economcs EC2 Introductory Econometrcs hour 3 mnutes CHECK YOU HAVE THE CORRECT QUESTION PAPER Number of Pages 5 Number of Questons 4 Instructons to Canddates Answer ALL questons on THIS exam paper n the space provded after each queston (you do not have to use all of the space provded). You can use the scratch paper at the end of the exam for notes and calculatons. FOR THIS EXAM YOU ARE ALLOWED TO USE THE FOLLOWING: Calculators Books/Statutes provded by the Unversty Are students permtted to brng ther own Books/Statutes/Notes? Permtted calculators are the Caso FX83 and FX85 models No No Addtonal Statonery No Verson Page of 5
25/6 Canddates Only Table. Crtcal Values from N(,) Dstrbuton One-sded Two-sded %.29.645 5%.645.96 % 2.33 2.575 Queston [ ponts] Let X, Y and Z denote three random varables wth: X =. wth probablty one E(Y) =.2 and V(Y) =.6 E(Z) =.8, V(Z) =.8 and cov(y,z) =.2 Defne a new random varable W as a lnear combnaton of these varables, W =.2X+.5Y+.3Z. a) Calculate the mean value of W, E(W). b) Calculate the varance of W, V(W). Verson Page 2 of 5
25/6 Canddates Only Queston 2 [3 ponts] Answer the followng multple choce questons. Crcle only one answer. Each queston s worth 2 ponts. ) The consequence of mperfect multcollnearty s that: A. the estmates of regresson coeffcents are nconsstent B. OLS estmator cannot be computed C. the varance of the coeffcent estmates goes up D. none of the above 2) You know that Y X u E ( u X ) to some x, V ( Y X x), A. depends on the value of u B. s equal to x V ( u X x) C. s equal to V ( X ) V ( u ) D. s equal to V ( u X x) and. The varance of Y gven that X s equal 3) Consder the followng multple regresson models (a) to (d) below. DBlack = f the ndvdual s black, and s zero otherwse; DHspanc s a bnary varable whch takes on the value one f the ndvdual s Hspanc, and s zero otherwse; DWhte s a bnary varable whch s unty for whte ndvduals and s zero otherwse, and DNonWhte s (-DWhte). Regressng weekly earnngs (Earn) on a set of explanatory varables, n whch of the followng cases wll you experence perfect multcollnearty? A. Earn DBlack 2DHspanc u Earn DBlack 2DNonWhte u B. Earn DBlack 2DWhte u C. Earn DWhte 2DNonWhte u D. Y X 4) Consder a regresson model, where Y s a bnary varable equal to one u or zero. Suppose that you estmated ˆ. 3. Ths mples that a unt change n X s predcted to: A. ncrease the probablty of Y= by 3 percentage ponts. B. ncrease the probablty of Y= by 3 percent. C. ncrease Y by.3 unts. D. ncrease Y by 3 percent. Verson Page 3 of 5
25/6 Canddates Only 5) Consder the followng scatterplots of a dependent varable Y aganst an ndependent varable X. Whch of the followng plots shows a clear evdence of heteroskedastcty? Plot Plot 2 Y Y 2 3 4 5 X 2 X 4 6 A. Only Plot B. Only Plot 2 C. Both Plot and Plot 2 D. None of them. Y X X, 6) Consder the followng regresson model, 2 2. You can test the hypothess that 2 the followng procedure: A. Calculate B. Calculate versus the alternatve that 2 bgger than.96. C. Calculate bgger than.96. D. none of the above ˆ ˆ 2 standard error of ˆ u at the 5% sgnfcance level usng t and reject the hypothess f t s bgger than 5%. ˆ ˆ 2 t standard error of ˆ ˆ ˆ 2 t standard error of ˆ 2 and reject the hypothess f absolute value of t s and reject the hypothess f absolute value of t s Verson Page 4 of 5
25/6 Canddates Only 7) You estmated the followng relatonshp between the salary (S) and the length of employment n the retal sector (Ten). The results are as follows Sˆ 235 534.4 Ten (645.8) (524.5) where the standard errors of the estmators are gven n parentheses. Assumng that the estmator has a normal dstrbuton, the 99% confdence nterval for the slope s approxmately: A. [9.9, 258.9] B. [83.82, 2884.99] C. [56.38, 2562.42] D. [67.6, 2397.2] 8) The OLS estmators of the coeffcents n a multvarate regresson model wll be unbased and consstent f the followng set of condtons holds A. expected value of the error term gven the ndependent varables s zero, the varance of the error term does not depend on the values of the ndependent varables, the observatons (Y,X,,X,2,,X k) are..d., large outlers are unlkely B. expected value of the error term gven the ndependent varables s zero, the varance of the error term does not depend on the values of the ndependent varables, there s no perfect multcollnearty between the ndependent varables, the observatons (Y,X,,X,2,,X k ) are..d. C. expected value of the error term gven the ndependent varables s zero, there s no perfect multcollnearty between the ndependent varables, the observatons (Y,X,,X,2,,X k ) are..d., large outlers are unlkely D. the varance of the error term does not depend on the values of the ndependent varables, there s no perfect multcollnearty between the ndependent varables, the observatons (Y,X,,X,2,,X k ) are..d., large outlers are unlkely 9) The nterpretaton of the slope coeffcent n the model Y ln( X ) u s as follows: A. a % change n X s assocated wth a % change n Y. B. a change n X by one unt s assocated wth a % change n Y. C. a % change n X s assocated wth a change n Y of.. D. a change n X by one unt s assocated wth a change n Y. Verson Page 5 of 5
25/6 Canddates Only ) Let TestScore be the average test score and let Income denote the average household ncome n a dstrct n Calforna. Assume that you had estmated the followng regresson model: TestScore 67. 3.8Income. 5Income SCal u where SCal s one for dstrcts n southern parts of Calforna and zero otherwse. If ncome ncreased from to 2 ($, to $2,), then the predcted effect on TestScore n southern Calfornan dstrcts would be A. 3.8 B. 6.6 C. Cannot be calculated because the functon s non-lnear D. 7.6 ) Consder a compettve market where the demand and the supply depend on the current prce of the good. Your data conssts of observatons on quanttes traded and correspondng prces. In order to estmate the demand equaton the correct way to proceed s to: A. ft a lne through the quantty-prce outcomes usng OLS B. ft a lne through the quantty-prce outcomes usng a probt or a logt model C. fnd an nstrument for prce and run an nstrumental varables regresson D. fnd an nstrument for weather and run an nstrumental varables regresson 2) Whch of the followng statements s true? A. Omtted varable bas s never a problem n a regresson wth multple ndependent varables. B. Sample average s always normally dstrbuted n a fnte sample. C. Varance of the OLS estmator of the slope coeffcent n a smple regresson model does not depend on the varance of the regressor. D. All of the above are false. 3) Smultaneous causalty A. means you must run a second regresson of X on Y B. leads to correlaton between the regressor and the error term C. means that a thrd varable affects both Y and X D. cannot be establshed snce regresson analyss only detects correlaton between varables 4) A possble soluton to measurement error bas s to A. use log-log specfcatons B. use a quadratc specfcaton C. use the square root of that varable snce the error becomes smaller D. mtgate the problem through nstrumental varables regresson Verson Page 6 of 5
25/6 Canddates Only 5) In the probt model Pr( Y X, X2,..., Xk) ( X xx2... kxk), A. the s do not have a smple nterpretaton B. the slopes tell you the effect of a unt ncrease n X on the probablty of Y C. cannot be negatve snce probabltes have to le between and D. s the probablty of observng Y when all X s are Verson Page 7 of 5
25/6 Canddates Only Queston 3 [ ponts] Recently Polsh Educaton Research Insttute nvestgated the effect of ntroducng chess lessons n elementary schools on student s performance. The schools appled for partcpaton n the program and pupls test scores were measured after the mplementaton of the program both n schools whch partcpated and those who opted out. Usng these data you estmate the followng regresson model: TestScores Chess u where TestScores s the average score on standardsed test and Chess ndcates f an ndvdual partcpated n the program (Chess=) or not (Chess=). You fnd that ˆ and that the effect of partcpaton n the program s statstcally sgnfcant. We know that schools who appled for the program are more dynamc and provde better qualty of educaton than the other schools. Gven ths nformaton, does ˆ provde an unbased and consstent estmator of the causal effect of the program? If not, what s the drecton of the bas? Explan your answer n detal. Verson Page 8 of 5
25/6 Canddates Only Queston 4 [5 ponts] You estmate a wage regresson, where the dependent varable s the logarthm of wage (lnrwage) and the ndependent varables are: Educaton number of years of educaton Experence years of experence Exp. Squared square of years of experence Black dummy varable ndcatng f a person s black Other Race - dummy varable ndcatng f a person s nether whte nor black and obtaned the followng regresson results n STATA: Table 2 Lnear regresson Number of obs = 6787 F( 5,678) =4327.8 Prob > F =. R-squared =.2553 Root MSE =.4629 ------------------------------------------------------------------------------ Robust lnrwage Coef. Std. Err. t P> t [95% Conf. Interval] -------------+---------------------------------------------------------------- Educaton.85967.2368 363.3..854966.864248 Experence.367624.677 29.27..364338.379 Exp. Squared -.5596 3.74e-6-49.44. -.567 -.5523 Black -.356374.8388-73.76. -.39245 -.32334 Other Race -.452862.3247-4.3. -.55673 -.395 _cons 5.578545.359 593.2. 5.5768 5.58548 ------------------------------------------------------------------------------ (Note that whte people are the base category here.) a) [4 ponts] What s the nterpretaton of the coeffcent on Black? Verson Page 9 of 5
25/6 Canddates Only b) [6 ponts] Interpret the slope coeffcent for Educaton. What s the predcted effect of obtanng 3 more years of educaton? c) [8 ponts] Construct a 99% confdence nterval for the predcted effect of obtanng 3 more years of educaton. d) [8 ponts] What s the predcted effect of accumulatng addtonal years of experence for a person wth 5 years of experence? e) [6 ponts] Is there a (statstcally) sgnfcant dfference between wages of black and non-black pupls? State and test the approprate hypothess at the 5% sgnfcance level. Verson Page of 5
25/6 Canddates Only f) [6 ponts] Test the hypothess that all the slope coeffcents n the regresson are zero at the % sgnfcance level. g) [2 ponts] How would you test that experence has no effect on wages? State the approprate hypothess and dscuss all the necessary steps requred to obtan the result. Verson Page of 5
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