ECONOMETRICS - FINAL EXAM, 3rd YEAR (GECO & GADE) May 17, 2016 15:30 Frst famly name: Name: DNI/ID: Moble: Second famly Name: GECO/GADE: Instructor: E-mal: Queston 1 A B C Blank Queston 2 A B C Blank Queston 3 A B C Blank Queston 4 A B C Blank Queston 5 A B C Blank Queston 6 A B C Blank Queston 7 A B C Blank Queston 8 A B C Blank Queston 9 A B C Blank Queston 10 A B C Blank Queston 11 A B C Blank Queston 12 A B C Blank Queston 13 A B C Blank Queston 14 A B C Blank Queston 15 A B C Blank Queston 16 A B C Blank Queston 17 A B C Blank Queston 18 A B C Blank Queston 19 A B C Blank Queston 20 A B C Blank Correct Incorrect Blank Fnal grade - 1 -
INSTRUCTIONS The exam ncludes 20 questons. Choose your answer to each queston by checkng one and only one box per queston n the template that you wll fnd n the frst page. If you want to leave any queston unanswered, check the "Blank" opton. Ths template s the only part of ths exam that wll be graded. A correct answer adds 2 ponts to the fnal grade whle an ncorrect one subtracts 1 pont. A blank answer does not add or subtract. The fnal grade s the number of ponts dvded by 4. Make sure that you checked your optons, ncludng Blank. Do not unclp the sheets. Use the blank space n the followng pages to wrte notes or to do arthmetc calculatons. YOU HAVE ONE HOUR AND FIFTEEN MINUTES TO ANSWER THIS TEST - 2 -
Queston 1. In the standard lnear regresson model, a test for the jont sgnfcance of several parameters: A) Does not allow any of the parameters consdered n the null hypothess to be nonzero. B) Cannot be done usng an F statstc computed on the bass of certan sums of squared resduals. C) Has a margnal sgnfcance level (p-value) whch can always be computed usng a Student t dstrbuton. Queston 2. In the standard lnear regresson model, absence of exact (or perfect ) collnearty requres: A) That the values of the dependent varable are not an exact lnear combnaton of the values of the explanatory varables. B) The explanatory varables values to be lnearly ndependent. C) The sample covarance between each par of explanatory varables to be nonzero. Queston 3. Consder the multple regresson model Y = Xb + U, wth E [ U] = 0 and Var[ U] = s 2 W wth W ¹ I A) The OLS estmator of b s unbased.. Whch of the followng statements s FALSE? B) The covarance matrx of the OLS estmator of b IS s2( XX )-1 C) The covarance matrx of OLS estmator of b IS NOT 2-1 s ( XX ) Queston 4. A set of 20 annual observatons on the Spansh Gross Domestc Product, from 1981 to 2000, s: A) A heteroscedastc stochastc process. B) An annual tme seres. C) A seasonal stochastc process. - 3 -
Queston 5. Choose whch of the followng multple regresson model assumptons s necessary to assure the unbasedness of OLS parameters: A) The errors are not autocorrelated. B) The errors are homoscedastc. C) The expected value of the errors s zero. Questons 6 to 9 correspond to the followng statement: The Table Model 1 dsplays the estmaton results for a model of annual fuel consumpton (n mllons of 1995 dollars) from 1960 to 1995, whch relates the log gas consumpton [LOG(G)] wth: Pg, an ndex of gas prces, Y, dsposable per capta ncome (n thousands of dollars), Pnc, prce ndex of new cars, Puc, prce ndex of used cars, and Ppt, cost ndex of publc transport. Model 1: OLS, usng the observatons 1960-1995 (T = 36) Dependent varable: LOG(G) Coeffcent Std. Error. t-statstc p-value Constant 3.71415 0.0631232 58.8398 <0.00001 Pg -0.0305398 0.0110512-2.7635 0.00968 Y 0.000221807 6.82898e-06 32.4803 <0.00001 Pnc ------------- 0.0790663-1.6052 0.11892 Puc -0.0275409 0.0254615-1.0817 0.28802 Ppt -0.00791789 0.0199616-0.3967 0.69443 Mean of dep. var. 5.392989 S.D. of dep. var. 0.248779 R-squared 0.989930 Adjusted R-squared 0.988252 F(5, 30) ----------- P-value (F) <0.000001 Log-lkelhood 82.27570 Akake crteron -152.5514 Schwarz crteron -143.0503 Hannan-Qunn -149.2353 Queston 6: Accordng to the results n Model 1: A) All the estmated parameters, except for the constant term, can be nterpreted as elastctes and are ndvdually sgnfcant at 1% - 4 -
B) All the estmated parameters, except for the constant term, can be nterpreted as sem-elastctes and are ndvdually sgnfcant at 10% C) Gven the nformaton avalable, t s possble to compute the resdual standard devaton. Queston 7: Accordng to the results n Model 1, the jont hypothess that the coeffcents of Pnc, Puc and Ppt are zero (use all avalable decmals n calculatons): A) Can be tested wth an F statstc, whch value s 7.357 B) Can be tested wth an F statstc, but we do not have enough nformaton to compute ts value. C) Can be tested wth a statstc whch, f the null hypothess s true, follows an F dstrbuton wth 5 degrees of freedom n the numerator and 30 degrees of freedom n the denomnator. Queston 8. Accordng to the results n Model 1 (use all avalable decmals n the calculatons): A) If the prce ndex of new cars, Pnc, decreases by 1 pont, gas consumpton (G) s expected to decrease by 12.69% approx. B) If the prce ndex of new cars, Pnc, ncreases by 1 pont, gas consumpton (G) s expected to decrease by 0.1269% approx. C) If the prce ndex of new cars, Pnc, decreases by 1 pont, gas consumpton (G) s expected to ncrease by 12.69% approx. Queston 9. In order to detect a collnearty problem, we computed the varance nflaton factors (VIF) for all regressors ncluded n Model 1. Varance nflaton factors (VIF) Pg 9.211 Y 7.164 Pnc 120.782 Puc 62.029 Ppt 66.096-5 -
where VIF j = 1/(1 - R j 2 ), where R j 2 denotes the determnaton coeffcent from regressng the j-th regressor on all the other ndependent varables. Accordng to ths nformaton: A) The varables wth the hgher collnearty are the prce ndces Pnc, Puc and Ppt. B) The varables wth the lower collnearty are the prce ndces Pnc, Puc and Ppt. C) There cannot be a hgh degree of collnearty because all the coeffcents n Model 1 (except the constant) are jontly sgnfcant even at a 1% sgnfcance level. Queston 10. Consder the regresson model Y = b + b X + b X + U, where: (a) the matrx 1 2 2 3 3 T X X s dagonal wth the values 100, 280 and 460 n ts man dagonal, and (b) the sample mean of Y s 5. Under these condtons, the pont forecast for Y correspondng to X = = 2 X 3 0 : A) Is equal to 5 B) Cannot be computed wth the avalable nformaton. C) Is equal to 1 Questons 11 to 15 refer to the followng statement: The sales of a fashon clothng company (SALES) depend on an ndex of customer purchasng power (ICAPC) and an ndcator of confdence n the company products (ICONF). Also, t s thought that sales may be seasonal, whch means that the relatonshp between SALES, ICAPC and ICONF may change n dfferent quarters. Tables 1, 2 and 3 summarze the man results of three models estmated by OLS, where Y=LOG(SALES), X1=LOG(ICAPC), X2=LOG(ICONF) and D2, D3 and D4 are 0-1 quarterly dummy varables, whch value s 1 n the correspondng quarters (second, thrd and fourth, respectvely) and 0 otherwse. Use all the decmals n Tables 1,2 and 3 n your calculatons. - 6 -
Queston 11. Accordng to the results n Table 1, the estmated constant term s equal to: A) 17.764886 for the frst quarter. B) 12.75170 for the second quarter. C) -4.658054 for the fourth quarter. Queston 12. Accordng to the results n Table 1, the estmated sales elastcty A) Wth respect to ICONF s 0.933291 for the frst quarter. B) Wth respect to ICAPC s -1.626575 for the second quarter. C) Wth respect to ICONF s -0.930195 for the second quarter. Queston 13. Accordng to the results n Table 2, the expected dfference between the log of sales n the fourth quarter and the log sales n the frst quarter, consderng the same values of ICAPC and ICONF n both quarters: A) Is 0.618763 but s not sgnfcant even at 10% B) Is 0.618763 and s sgnfcant even at 1% C) Is -6.139694 but s not sgnfcant at 1% Queston 14. Accordng to the results n Tables 1 and 2, the F statstc to test the jont hypothess that: (a) the elastcty of sales wth respect to ICAPC s the same n all quarters, and (b) the elastcty of sales wth respect to ICONF s the same n all quarters: A) Is equal to 0.869 B) Is equal to 1.032 C) Cannot be computed wth the avalable nformaton. Queston 15. Accordng to the results n Tables 2 and 3, the F statstc to test the null that the log of sales has no seasonalty,.e. t does not depend on the correspondng quarter: - 7 -
A) Is equal to 48.925 B) Cannot be computed wth the avalable nformaton. C) Is equal to 68.925 Table 1 Dependent varable: Y Sample: 1986:1 to 1992:4 (observatons ncluded: 28) Varable Coeffcent Std. Error t-statstc p-value Constante -13.20387 5.833571-2.263429 0.0379 D2 12.75170 12.06633 1.056800 0.3063 D3 9.671240 8.959647 1.079422 0.2964 D4 8.545816 7.282290 1.173507 0.2578 X1 2.711783 0.841984 3.220704 0.0053 D2*X1-1.626575 1.445855-1.124992 0.2772 D3*X1-1.973991 1.196396-1.649948 0.1184 D4*X1-1.325049 1.069982-1.238385 0.2334 X2 0.933291 0.445010 2.097239 0.0522 D2*X2-0.930195 1.100651-0.845132 0.4105 D3*X2-0.072413 0.754949-0.095918 0.9248 D4*X2-0.345821 0.561278-0.616132 0.5465 Sum of squared resduals = 0.143700 Table 2 Dependent varable: Y Sample: 1986:1 to 1992:4 (observatons ncluded: 28) Varable Coeffcent Std. Error t-statstc p-value Constante -6.139694 2.870911-2.138587 0.0438 D2 0.193198 0.051066 3.783329 0.0010 D3 0.313589 0.051166 6.128849 0.0000 D4 0.618763 0.052318 11.82706 0.0000 X1 1.488666 0.393303 3.785039 0.0010 X2 0.660192 0.240432 2.745860 0.0118-8 -
Sum of squared resduals = 0.199337, R-squared = 0.875514 Table 3 Dependent varable: Y Sample: 1986:1 to 1992:4 (observatons ncluded: 28) Varable Coeffcent Std. Error t-statstc p-value Constante 1.175230 7.073808 0.166138 0.8694 X1 0.774249 0.986040 0.785210 0.4397 X2-0.022716 0.587800-0.038646 R-squared = 0.044989 Questons 16 and 17 refer to the followng statement. The four standardzed plots n Fgure 1 represent the transformatons ndcated at the bottom of each one. All of them are computed from 251 monthly observatons of the Spansh Industral Producton Index (IPI), from January 1975 to November 1995. Queston 16. If ln IPIt = ln IPIt - ln IPI t- 1 and 12 ln IPIt = ln IPIt -ln IPI t-12, where ln stands for the natural logarthm: A) ln IPI t s the ANNUAL log growth rate of IPI. B) 12 ln IPIt s the ANNUAL log growth rate of IPI. C) 12 ln IPIt s the MONTHLY log growth rate of IPI. Queston 17. Accordng to the patterns n Fgure 1: A) ln IPI t s statonary despte ts seasonalty. B) 12 ln IPIt s not statonary because t fluctuates wdely around ts average. C) 12 ln IPIt s not statonary, nor seasonal. - 9 -
Fgure 1 Queston 18. If the errorss U n thee model Y = Xb + U are autocorrelated, the varance-covarance matrx of the OLSS estmator: A) B) Can be adequately estmated usng Whte s estmator. Can be adequately estmated usng Newey-West s estmator. e C) Can be adequately estmatedd usng the expresson sˆ 2 ( X T - X) 1, where sˆ 2 stands for the usual unbased estmator of the errorr varance s 2. Queston 19. Consder the consumpton model stands for the consumpton of the -thh ndvdual, of the -th ndvdual, and C 1 2RTA 3S RTA s ndvdual s male, and 0 otherwse. The Tables Model A U, where 3 the gross dsposable ncome S s a dummy varable takng the value 1 f the -th C and Model B summarze the man OLS estmaton results of two varatons of the ntal model. - 10 -
Model A Dependent varable: Coeffcent C Std. Error Constant 25.18 2.60 RTA 1.61 0.005 S -1.43 0.060 R-squared = 0.80 Model B Dependent varable: C RTA Coeffcent Std. Error Constant 1.61 0.005 1 RTA 21.89 2.10 S RTA -1.42 0.055 R-squared = 0.86 Gven ths nformaton, whch of the followng statements s FALSE? A) Regardless the propertes of the error term, Model B should be preferred to Model A, snce ts goodness of ft s better. B) If the error term s such that Model A. var( U ) RTA, Model B should be preferred to 2 2 C) If the error term s such that var( U ) RTA, the coeffcent assocated wth 2 2 the gross dsposable ncome n Model A corresponds to the constant term n Model B. - 11 -
Queston 20. Choose whch of the followng statements s TRUE? A) To detect nfluental data n a regresson model estmated by OLS t s enough to analyze the correspondng resdual plot. B) In a regresson model one should always remove from the sample the nfluental data, snce ts presence worsens the model R-squared statstc. C) The presence of a few nfluental values n a sample may alter sgnfcantly some OLS estmaton results. CALCULATIONS - 12 -
ECONOMETRICS - FINAL EXAM, 3rd YEAR (GECO & GADE) May 17, 2016 15:30 Frst famly name: Name: DNI/ID: Moble: Second famly Name: ECO/ADE: Instructor: E-mal: Queston 1 A B C Blank Queston 2 A B C Blank Queston 3 A B C Blank Queston 4 A B C Blank Queston 5 A B C Blank Queston 6 A B C Blank Queston 7 A B C Blank Queston 8 A B C Blank Queston 9 A B C Blank Queston 10 A B C Blank Queston 11 A B C Blank Queston 12 A B C Blank Queston 13 A B C Blank Queston 14 A B C Blank Queston 15 A B C Blank Queston 16 A B C Blank Queston 17 A B C Blank Queston 18 A B C Blank Queston 19 A B C Blank Queston 20 A B C Blank Correct Incorrect Blank Fnal grade - 13 -