24/5 Canddates Only January Examnatons 25 DO NOT OPEN THE QUESTION PAPER UNTIL INSTRUCTED TO DO SO BY THE CHIEF INVIGILATOR STUDENT CANDIDATE NO.. 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 3 Number of Questons 3 Instructons to Canddates Answer ALL questons on ths exam paper n the space provded after each queston (you do not have to use all of the space provded). For ths exam you are allowed to use the followng Calculators Books/Statutes Addtonal Statonery The Caso FX-83 or Caso FX-85 may be used NOT ALLOWED Not Requred VERSION B Page of 3 Contnued
24/5 Canddates Only Table. Crtcal Values from N(,) Dstrbuton One-sded Two-sded %.29.645 5%.645.96 % 2.33 2.575 Queston [2 ponts] Are the followng statements true or false? Crcle A or B to ndcate whether each statement s true or false.. [2 ponts] Consder the potental outcomes framework dscussed n class. If the data comes from a randomzed experment, then comparng mean outcomes of people who receved a treatment (e.g. medcaton, socal transfer) and those who were not treated wll gve an unbased estmate of the true causal effect of the treatment. 2. [2 ponts] In a smple regresson model Y X u, the ntercept s nterpreted as the mean value of Y for ndvduals wth X =. 3. [2 ponts] A vald nstrumental varable has to be correlated wth the endogenous varable and uncorrelated wth the regresson error term. Y X 4. [2 ponts] Consder a regresson model, where Y s a bnary varable ndcatng f a person was granted a mortgage (Y =) or not (Y =). Suppose that you estmated ˆ.2. Ths mples that a unt change n X s predcted to ncrease the probablty of obtanng a mortgage by 2 percentage ponts. 5. [2 ponts] Omtted varable bas s never a problem n a regresson wth multple ndependent varables. u Page 2 of 3 Contnued
24/5 Canddates Only 6. [2 ponts] Low R 2 n an estmated regresson model ndcates that changes n ndependent varables do not have an mportant effect on the dependent varable. 7. [2 ponts] The consequence of mperfect multcollnearty s that standard errors of the regresson coeffcents are not estmated consstently. 8. [4 ponts] Consder the followng regresson model: Health Drnkng u Health s an ndcator of ndvdual s health. Hgher values of Health ndcate better overall health status. Drnkng ndcates f an ndvdual s drnkng alcohol (Drnkng=) or not (Drnkng=). A researcher uses non-expermental data from a survey and regresses Health aganst Drnkng and fnds that ˆ. We know that people who drnk alcohol also eat less healthy food, n partcular they eat more products wth hgh percentage of saturated fats. Addtonally, hgher percentage of saturated fats has been proven to deterorate person s overall health. Gven ths nformaton, t s lkely the case that. ˆ 9. [2 ponts] Zero correlaton between two varables does not mply that the varables are statstcally ndependent. Page 3 of 3 Contnued
24/5 Canddates Only Queston 2 [3 ponts] Answer the followng multple choce questons. Crcle only one answer. Each queston s worth 2 ponts.. Under mperfect multcollnearty A. the OLS estmator cannot be computed. B. two or more of the regressors are hghly correlated. C. the OLS estmator s based even n samples of n >. D. the error terms are hghly, but not perfectly, correlated. 2. In multple regresson, the R 2 ncreases whenever a regressor s A. added unless the coeffcent on the added regressor s exactly zero B. added C. added unless there s heteroskedastcty D. greater than.96 n absolute value Y ln( X ) ln( X, ) u 3. Consder the followng regresson model, 2 2. You can test the hypothess that versus the alternatve that the followng procedure: A. Calculate B. Calculate bgger than.96. C. Calculate bgger than.96. D. none of the above ˆ standard error of ˆ at the 5% sgnfcance level usng t and reject the hypothess f t s bgger than 5%. ˆ t standard error of ˆ ˆ t standard error of ˆ and reject the hypothess f absolute value of t s and reject the hypothess f absolute value of t s 4. Consder a compettve market where the demand and the supply depend on the current prce of the good. Then fttng a lne through the quantty-prce outcomes wll A. gve you an estmate of the demand curve. B. estmate nether a demand curve nor a supply curve. C. enable you to calculate the prce elastcty of supply. D. gve you the exogenous part of the demand n the frst stage of TSLS. Contnued Page 4 of 3
24/5 Canddates Only 5. Consder the followng multple regresson models (a) to (d) below. DFemme = f the ndvdual s a female, and s zero otherwse; DMale s a bnary varable whch takes on the value one f the ndvdual s male, and s zero otherwse; DMarred s a bnary varable whch s unty for marred ndvduals and s zero otherwse, and DSngle s (-DMarred). Regressng weekly earnngs (Earn) on a set of explanatory varables, you wll experence perfect multcollnearty n all of the followng cases except: Earn DFemme 2DMale u A. Earn DMarred 2DSngle u B. Earn DFemme u C. Earn DFemme DMale DMarred 4DSngle u D. 2 3 Y 6. You know that equal to some x, E( Y X x), A. depends on the value of B. s equal to x X u and E ( u X ) ˆ ˆ C. s equal to x u D. cannot be calculated because we do not know E X ). The expected value of Y gven that X s ( 7. Omtted varable bas A. exsts f the omtted varable s correlated wth the ncluded regressor but s not a determnant of the dependent varable B. exsts f the omtted varable s correlated wth the ncluded regressor and s a determnant of the dependent varable C. exsts f the omtted varable s not correlated wth the ncluded regressor but s a determnant of the dependent varable D. exsts f the omtted varable s not correlated wth the ncluded regressor and s not a determnant of the dependent varable Page 5 of 3 Contnued
24/5 Canddates Only 8. You have obtaned data from UK Jobcenters and estmated the followng relatonshp between the post-unemployment salary (S) and the length of unemployment spell (dur). The results are as follows Sˆ 6345 534.4 dur (345.4) (353.5) where the standard errors of the estmators are gven n parentheses. Assumng that the estmator has a normal dstrbuton, the 9% confdence nterval for the slope s approxmately: A. [8.9, 887.9] B. [78.385, 99.42] C. [-58.46, 227.26] D. [-47., 5.9] 9. The nterpretaton of the slope coeffcent n the model ln( 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.. In a regresson model, endogenous varables A. are correlated wth the error term B. always appear on the left-hand sde of regresson functons C. cannot be regressors D. are uncorrelated wth the error term. 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 Contnued Page 6 of 3
24/5 Canddates Only 2. Assume that you had estmated the followng quadratc regresson model: TestScore 67.3 3.85Income.423Income If ncome ncreased from to ($, to $,), then the predcted effect on TestScores would be A. 3.85 B. 3.85-.423 C. Cannot be calculated because the functon s non-lnear D. 2.96 2 u 3. In the multple regresson model, the adjusted R 2, A. cannot be negatve. B. wll always be greater than the regresson R 2. C. adjusts the standard errors for heteroskedastcty of the error term. D. can decrease when an addtonal explanatory varable s added. 4. Two Stage Least Squares s calculated as follows: n the frst stage A. Y s regressed on the exogenous varables only. The predcted value of Y s then regressed on the nstrumental varables. B. the endogenous varable s regressed on the nstrumental varable, and the predcted values are calculated. In the second stage, Y s regressed on these predcted values and, possbly, on the other exogenous varables. C. the exogenous varables are regressed on the nstruments. The predcted value of the exogenous varables s then used n the second stage, together wth the nstruments, to predct the dependent varable. D. none of the above. Page 7 of 3 Contnued
24/5 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 X 4 5 2 3 4 5 X A. Only Plot B. Only Plot 2 C. Both Plot and Plot 2 D. None of them. Page 8 of 3 Contnued
24/5 Canddates Only Queston 3 [5 ponts] You want to nvestgate a relatonshp between chld s brth weght and hs performance n school. You obtaned data from hosptals and lnked t to prmary school test scores: TS pupl s test score at the end of prmary school MALE a dummy varable ndcatng f a chld s a male (MALE=) and equal zero otherwse MEDU mother s number of years of educaton FEDU father s number of years of educaton BIRTHW - chld s brth weght n klograms and obtaned the followng regresson results n STATA: Table 2 Independent varable: ln(ts) Number of observatons: 354 Varable Coeffcent Standard Error MALE -..23 MEDU.45. FEDU.64.5 BIRTHW.2.6 R-squared.36 F statstc (p-value) 4.74 (.8) where ln denotes natural logarthm. a) [8 ponts] What s the nterpretaton of the coeffcent on BIRTHW? What s the predcted effect of ncreasng BIRTHW from 3.6 kg to 4 kg? Contnued Page 9 of 3
24/5 Canddates Only b) [6 ponts] Interpret the coeffcent on FEDU. c) [6 ponts] Is there a (statstcally) sgnfcant dfference between test scores of male and female pupls? State and test the approprate hypothess at the 5% sgnfcance level. d) [6 ponts] Test the hypothess that all the slope coeffcents n the regresson are zero at the % sgnfcance level. Contnued Page of 3
24/5 Canddates Only e) [2 ponts] Your frend argues that the relatonshp between ln(ts) and BIRTHW s nonlnear. In partcular, he tells you that you should add BIRTHW squared (BIRTHW2) and BIRTHW cubed (BIRTHW3) to the regresson. Explan how you would evaluate hs clam. State all the necessary steps. Contnued Page of 3
24/5 Canddates Only f) [2 ponts] Startng from the model n Table 2, how would you verfy f the effect of brth weght on test scores vares between boys and grls? Descrbe the model that you would estmate to verfy ths clam and state all the necessary steps needed to obtan the answer. Contnued Page 2 of 3
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