ECONOMETRICS - FINAL EXAM, 3rd YEAR (GECO & GADE)

ECONOMETRICS - FINAL EXAM, 3rd YEAR (GECO & GADE) June 7, 016 15:30 Frst famly name: Name: DNI/ID: Moble: Second famly Name: GECO/GADE: Instructor: E-mal: Queston 1 A B C Blank Queston 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 1 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 0 A B C Blank Correct Incorrect Blank Fnal grade - 1 -

INSTRUCTIONS The exam ncludes 0 questons. All your answers to the multple choce questons must be marked on the answer sheet that you wll fnd n the frst page. If you want to leave any queston unanswered, choose the "Blank" opton. The answer sheet s the only part of ths exam that wll be graded. A correct answer adds 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 A HALF TO ANSWER THIS TEST REMINDER YOU ARE NOT ALLOWED TO USE DEVICES WITH CONNECTIVITY TO THE INTERNET, INCLUDING MOBILE PHONES, TABLETS, SMART WATCHES OR MP3/4 PLAYERS Possesson of unauthorzed tems s an nfrngement of the regulatons and could result n DISQUALIFICATION from ths examnaton and the overall qualfcaton - -

Questons 1 to 5 correspond to the followng statement. Consder the followng demand functon for chcken meat: Yt = β1 + β Xt + β3xt3 + β4 Xt4 + ut t = 1,...,3 Where Y s the per capta consumpton of chcken (n pounds), X s the real dsposable per capta ncome (n dollars), X 3 s the retal prce of chcken per pound (n cents), X 4 s the retal prce of pork per pound (n cents). The followng OLS results, along wth the estmated varance matrx of the LS estmator, were obtaned usng a sample of US annual data, from 1990 to 013. Model 1: OLS, usng the observatons 1990-013 (T = 3) Dependent varable: Y Coeffcent Std. Error. t-statstc p-value ---------------------------------------------------------------- const 38.647 --------- ------.08e-09 X 0.010876 --------- ------ 0.000 X3-0.541084 --------- ------ 0.008 X4 0.174055 --------- ------ 0.0118 Mean of dep. var 39.66957 S.D. of dependent Var. 7.37950 Sum of squared Resduals 75.75855 S.E. of regresson -------- R-squared 0.936653 Adjusted R-Squared 0.96651 F ------- P-value (F) 1.45e-11 Log-lkelhood -46.3444 Akake crteron 100.6885 Schwarz crteron 105.305 Hannan-Qunn 101.8308 rho 0.56093 Durbn-Watson 0.88813 Covarance Matrx of the LS estmator Const X X3 X4 const 133.196 0.00307994-0.515143 0.098149 X 0.00307994 5,67E-01-1,69E+00-9,00E+00 X3-0.515143-1,69E+00 0.049544-0.00735701 X4 0.098149-9,00E+00-0.00735701 0.00391008 Queston 1. Accordng to the results n Model 1, what s the estmate change n the per capta consumpton of chcken meat f the real dsposable per capta ncome ncreases by $1000 dollars, remanng constant the rest of explanatory varables? (use all avalable decmals n the calculatons): A) Wll ncrease by approxmately 10.87% B) Wll ncrease by approxmately 0.01087 pounds. C) Wll ncrease by approxmately 10.87 pounds. - 3 -

Queston. The LS estmate of the error varance s (use all avalable decmals n the calculatons): A) 75.7585 B) 3.9873 C) 0.967 Queston 3. The test of the null hypothess H 0 : β 4 = 0 aganst the alternatve H1: β4 0 ndcates that: A) The null s not rejected at 1%, 5% and 10% sgnfcance levels. B) The null s rejected at the 5% level, but t s not rejected at 10% C) The null s rejected at the 5% level, but t s not rejected at 1% Queston 4. Testng the null hypothess H0 : β3 = β4 aganst the alternatve H : β β concludes that: (Note: Prob 19.09 = 0.975 and Prob 19 1 3 4.86 = 0.995) A) The null s rejected at the 5% level, but t s not rejected at 1% B) The null s rejected at both, 1% and 5% sgnfcance levels. C) The null s rejected at the 5% level, but t s not rejected at 1% Queston 5. The F statstc for the jont hypothess that all ndependent varables are not nsgnfcant ( H : β β β 0) = = = (use all avalable decmals n the calculatons): 0 3 4 A) Is approxmately equal to 45.91 B) Is approxmately equal to 93.645 C) Is approxmately equal to 73.9303-4 -

Questons 6 to 8 correspond to the followng statement. To fnd out f there s any relatonshp between teacher s pay and per pupl expendture n publc schools, Table 1 shows the LS regresson results of a regresson relatng the average annual teacher salary n thousands of dollars (Salary) as a functon of the spendng on publc schools per pupl n thousands of dollars (Expendture) for the 51 states of the US n 1985. Table 1 Dependent Varable: Salary Least Squares N= 51 Varable Coeffcent Std. Error t-statstc p-value Constant 1.1937 1.197351 10.13017 0.0000 Expendture 3.307585 0.311704 10.6119 0.0000 R-squared 0.696781 Mean of dependent Var 4.356 Sum of squared Resduals 64.85 S.D. of dependent Var 4.17946 F(1,49) 11.5995 p-value (F) 0.000000 Akake crteron 4.563553 Schwarz crteron 4.639311 Lookng for evdence about dfferences between three geographcal regons n the US: Northeast and North Central (1 states), South (17 states) and West (13 states), we defned three dummy varables: D1, whch s equal to 1 f the state s n the West, and equal to 0 otherwse; D whch s equal to 1 f the state s n the Northeast and North Central regon, and equal to 0 otherwse; and D3 whch s equal to 1 f the state s n the South, and equal to 0 otherwse. Addng these varables to the prevous model yelds the results shown n Table. - 5 -

Table Dependent Varable: Salary Least Squares N= 51 Varable Coeffcent Std. Error t-statstc p-value Constant 13.6911 1.395056 9.511530 0.0000 D -1.673514 0.801170 -.088837 0.04 D3-1.144157 0.861118-1.38687 0.1904 Expendture 3.88848 0.31764 10.35393 0.0000 R-squared 0.7665 Mean of dependent Var. 4.356 Sum of squared Resduals 4.188 S.D. of dependent Var. 4.17946 F(3,47) 40.8341 p-value (F) 0.000000 Akake crteron 4.55756 Schwarz crteron 4.70471 Queston 6. Accordng to Tables 1 and, whch of the followng statements s FALSE? A) If the expendture n publc schools s $1000, the estmated Salary of a teacher n the West regon s about $16558, the estmated Salary of a teacher n the Northeast/North Central regon s about $14884 and the estmated Salary of a teacher n the South s about $15414 B) The Salary of the teachers n the South s statstcally dfferent from that of the teachers n the West at the 5% level, but t s not statstcally dfferent at 1%, assumng that Expendture s the same for both regons. C) The value of the statstc computed to test whether the Salary of the teachers n publc schools s the same n the three regons n the US s equal to.19 (roundng to two decmals places). As Prob [ F(, 47) 3.19] = 0.95, the prevous hypothess cannot be rejected at the 5% level of sgnfcance. - 6 -

Queston 7. Accordng to Tables 1 and : A) Table shows that, when Expendture s zero, the estmate Salary of the teachers n the South and the Northeast and North Central regons s negatve, so there mght be a mstake n the model. B) The reward for extra Expendture on publc Schools are much hgher for the teachers n the West regon. C) Assumng that the per pupl expendture n the publc schools s the same, the estmated Salary of the teachers n a state n the Northeast and North Central regon s lower than that of the West regon by $1673.51 Queston 8. Table 3 shows the estmated covarance matrx for the LS parameter estmates n Table : Table 3 Constant D D3 Expendture Constant 1.946-0.4038-0.6514-0.3954 D 0.6419 0.3976 0.0019 D3 0.7415 0.0651 Expendture 0.1009 If Prob [ t(47) 0.690] = 0.4934, Prob [ t(47) 0.4501] = 0.6547 and assumng that the expendture per pupl n the publc schools s the same n the three regons, whch of the followng statements s TRUE? A) The hypothess that the teacher salary on publc schools n the South s not statstcally dfferent from that of teachers n the Northeast and North Central cannot be rejected, nether at 5% nor at 1% level of sgnfcance, because the correspondng t-statstc s 0.690 (roundng at two decmal places). B) The hypothess that the teacher salary on publc schools n the South s not statstcally dfferent from that of teachers n the Northeast and North Central - 7 -

cannot be rejected, nether at 5% nor at 1% level of sgnfcance, because ts t- statstc s 0.4501 (roundng at two decmal places). C) We wll not reject the hypothess that the teacher s salary on publc schools n the West regon s not statstcally dfferent from zero at any level of sgnfcance. Queston 9. Consder the model Y = β1+ βx + U. If the sample means of Y and ( = 1,,..., N) are postve and equal, then the LS estmate of the ntercept would be: A) Equal to zero when the LS estmate of the slope s not equal to one. B) Greater than zero when the LS estmate of the slope s greater than zero and less than one. C) Less than zero when the LS estmate of the slope s less than zero. X Queston 10. Usng a sample of n observatons, y 1, y,..., y n, a researcher wants to descrbe the behavor of the monthly Spansh GDP (Y) usng the model Y = β + β Y + β Y + U ( t = 1,,..., n). If EU [ ] = 0 and t 1 t 1 3 t t T E[ UU ] = σ I, whch of the followng regresson model assumptons s NOT fulflled by the prevous model? A) Errors are not autocorrelated. B) Parameters are constant. C) Regressors are non-random. Queston 11. Consder the model Y = β1+ β X + U, ( = 1,,..., 30), whch fulflls the multple lnear regresson model assumptons. If t s the t-statstc computed to test the hypothess H 0 : β = 1 aganst the alternatve H1: β > 1, whch of the followng statements s TRUE? A) Prob [ t(8) t ] s the margnal level of sgnfcance (p-value) correspondng to the prevous test. B) 1 Prob [ t(8) t ] s the margnal level of sgnfcance (p-value) correspondng to the prevous test. - 8 -

t = ( ˆ β 1) DT, where DT s the standard error (.e. the estmate standard C) devaton) of the LS estmate of b. Queston 1. In the model Yt = b1 + bxt + Ut, assume that U A A A and A t NIID ( 0, s ) 1 t = t + t-1 + t- 3 ( ), A) The error term ( U t ) s heteroscedastc. B) The error term ( U t ) s autocorrelated. A, therefore: C) The expected value of the error s not zero ( E( ) ¹ 0) U. t Queston 13. Whch of the followng statements s TRUE? A) Regresson models relatng non-statonary tme seres may provde spurous results (.e., an emprcal relatonshp whch s complete nonsense). B) There s no specfc problem assocated wth buldng a regresson model relatng non-statonary tme seres. C) Resdual dagnostcs for regresson models relatng non-statonary varables are not sutable tools to detect problems n appled work. Questons 14 to 15 correspond to the followng statement. Fgure M1 shows the tme seres LOG( Y ) (natural logarthm of Y), DLOG( Y ) (the log dfferences of Y), DLOG( Y, 0, 1 ) (seasonal (s=1) log dfferences of Y), and DLOG( Y, 1, 1 ) (the dfferences of the seasonal (s=1) log dfferences of Y). [Note: DLOG( Y ) = lny -lny - 1 DLOG Y, 0, 1 = lny t -lny t - and t t, ( ) 1 ( ) ( ) DLOG(Y, 1, 1) =Ñ ln IPI - ln IPI =Ñ ln IPI -ln IPI t t-1 1 t t-1-9 -

Fgure M1 SERIE LOG( Y ) SERIE DLOG( Y ) 3 1 0-1 - -3 3 1 0-1 - -3 1997 1998 1999 000 001 00 003 004 N = 96 Meda = 4.75 D.T. = 0.6 Jarque-Bera = 1.61 ( p-value = 44.66% ) SERIE DLOG( Y, 0, 1 ) 1997 1998 1999 000 001 00 003 004 N = 95 Meda = 0.007 D.T. = 0.44 Jarque-Bera = 40.50 ( p-value = 0.00% ) SERIE DLOG( Y, 1, 1 ) 3 1 0-1 - -3 3 1 0-1 - -3 1997 1998 1999 000 001 00 003 004 N = 84 Meda = 0.060 D.T. = 0.108 Jarque-Bera = 1.38 ( p-value = 50.% ) 1997 1998 1999 000 001 00 003 004 N = 83 Meda = 0.000 D.T. = 0.085 Jarque-Bera = 1.61 ( p-value = 44.66% ) Queston 14. Whch of the followng statements s FALSE? A) LOG( Y ) s seasonal. B) DLOG( Y, 0, 1 ) s not mean-statonary. C) The seres DLOG( Y ) s mean-statonary. Queston 15. Accordng to Fgure 1, the null hypothess that DLOG( Y, 1, 1 ) follows a normal dstrbuton: A) Cannot be rejected at the 1% level of sgnfcance. B) Is rejected at the 5% level of sgnfcance. C) Is rejected at the 10% level of sgnfcance. Questons 16 to 19 correspond to the followng statement: Gven N=40 cross-sectonal household observatons on weekly food expendture n euros (FoodEx) and weekly household ncome n euros (Inc) the model FoodEx = b1 + binc + U has been estmated. Tables A and B show the results: - 10 -

Table A Dependent varable: FoodEx LS N=40 Varable Coeffcent Std. Error t-statstc p-value Constant 36.69080 19.9479 1.841465 0.0734 Inc 0.1889 0.030539 4.00777 0.000 R-squared 0.317118 Mean. of dep. var. 117.817 Adjusted R-squared 0.99148 S.D. of dep. var. 40.6471 Sum of squared resduals 4399.18 Akake crteron 9.940765 F(1,38) statstc 17.6465 Table B FoodExp versus Inc (wth least squares ft) 50 600 550 500 450 Y = 83.4 + 10.X 00 150 100 50 FoodExp 400 350 300 LS_Resdual 0-50 50-100 00-150 150-00 100 5 10 15 0 5 30-50 5 10 15 0 5 30 Inc Inc Queston 16. The plots n Table B suggest that A) The model error term s homoscedastc. B) The varablty of LS resduals s ndependent of the level of household ncome. C) The varablty of LS resduals ncreases as ncome ncreases. - 11 -

Queston 17. The answer to the prevous queston suggests that a reasonable model for the error varance, Var( U ), would be: A) 1 Inc Var[ U ] = s ( = 1,..., 40) B) Var[ U ] = s ( = 1,..., 40). C) Var[ U ] = s Inc ( = 1,..., 40) Queston 18. The answer to questons 16 and 17 suggests that (ndcate whch statement s TRUE): A) The estmate for b s statstcally sgnfcant at both the 10% and 5% level of confdence B) The standard errors computed for the LS estmates of b 1 and b n Table A are not correct. C) The F-statstc n Table A s sutable to test whether the parameter b s statstcally sgnfcant. Queston 19. Accordng to the answer to prevous questons, whch of the followng statements s TRUE? FoodEx A) In the model 1 = b1 + b + V, the LS estmator s BLUE (Best Inc Inc lnear unbased estmator). B) The Whte heteroscedastcty-consstent standard errors are sutable for estmaton the varances of the LS estmates of b 1 and b n Table A. C) The LS estmator of b 1 and b n FoodEx = b1 + binc + U s based. - 1 -

Queston 0. Whch of the followng statements s TRUE? 1. Effcency of the OLS estmator of b n the General Lnear Model (GLM) mples that there s no other lnear unbased estmator of b wth a smaller varance.. The OLS estmator of b n the GLM s effcent even f the model dsplays approxmate collnearty. 3. The p-value (or margnal sgnfcance level) of the ndvdual sgnfcance test for a parameter n the GLM can be nterpreted as the probablty that the null hypothess s true. 4. It s sad that an observaton n the GLM s outlyng or atypcal f t les far from the center of the sample; n ths stuaton the correspondng resdual s often large. A) TRUE: 1, and 4. FALSE: 3 B) TRUE: 1, 3 and 4. FALSE: C) TRUE: 1, and 3. FALSE: 4-13 -

Calculatons - 14 -