UNIVERSIDAD NACIONAL DE PIURA FACULTAD DE ECONOMIA SOLUCIÓN DE LA PRIMERA PRÁCTICA DE ECONOMETRIA I 1º El investigador especifica los modelos siguientes: CT(t) = a + b SPREAD(t) + c(0) EMI(t) + c1 EMI(t-1) + c2 EMI(t-2)+ .... + u(t) CT(t) = a + b TA(t) + c0 SPREAD(t) + c1 SPREAD(t-1) + ... + c15 SPREAD(t-15) + u(t) Se le pide: 1.1. Estime el primer modelo y obtenga los multiplicadores y el retardo medio. (6 puntos) CT(t) = a + b SPREAD(t) + c(0) EMI(t) + c1 EMI(t-1) + c2 EMI(t-2)+ .... + u(t) Si C(i) = (1-L)Li CT(t) = a + b SPREAD(t) + (1-L) EMI(t) + (1-L)L EMI(t-1) + (1-L)L2 EMI(t-2)+ .... + u(t) (1) retardamos 1 periodo: CT(t-1) = a + b SPREAD(t-1) + (1-L) EMI(t-1) + (1-L)L EMI(t-2) + (1-L)L2 EMI(t-3)+ .... + u(t-1) Multiplicamos por L: LCT(t-1) = aL + bL SPREAD(t-1) + (1-L)L EMI(t-1) + (1-L)L2 EMI(t-2) + (1-L)L3 EMI(t-3)+ .... + L u(t-1) (2) (1) – (2) CT = a(1-L) + b SPREAD(t) - bL SPREAD(t-1) + (1-L) EMI(t) + L CT(t-1) + (u(t)-L u(t-1)) CT = a* + b SPREAD(t) + b* SPREAD(t-1) + L* EMI(t) + L CT(t-1) + u*(t) Dependent Variable: CT Method: Least Squares Sample (adjusted): 2001M02 2009M12 Included observations: 102 after adjustments Variable C Coefficient Std. Error t-Statistic Prob. -1615.517 3924.997 -0.411597 0.6815 SPREAD 49.63791 17.12357 2.898807 0.0046 SPREAD(-1) -37.99468 18.00617 -2.110093 0.0374 EMI 4.504581 0.893980 5.038791 0.0000 CT(-1) 0.914848 0.020171 45.35547 0.0000 R-squared 0.998445 Mean dependent var 578303.5 Adjusted R-squared 0.998381 S.D. dependent var 233710.0 S.E. of regression 9405.187 Akaike info criterion 21.18369 8.58E+09 Schwarz criterion 21.31236 F-statistic 15567.00 Prob(F-statistic) 0.000000 Sum squared resid Log likelihood -1075.368 Durbin-Watson stat 1.629158 Sample: 2001M02 2009M12 Included observations: 102 Autocorrelation Partial Correlation AC PAC Q-Stat Prob . |*. | . |*. | 1 0.158 0.158 2.6223 0.105 .|. | .|. | 2 0.041 0.016 2.8003 0.247 2 Mod1qbp1 = 102*(0.158011072093364^2) = 2.54668488821762 Mod1qbp2 = 102*(0.158011072093364^2+0.040964627589653^2) = 2.71785116100063 Breusch-Godfrey Serial Correlation LM Test: F-statistic 2.752296 Probability 0.100379 2.842811 Probability 0.091783 Obs*R-squared Dependent Variable: RESID Method: Least Squares Variable Coefficient Std. Error t-Statistic Prob. C -169.7478 3891.363 -0.043622 0.9653 SPREAD -4.931046 17.22928 -0.286202 0.7753 SPREAD(-1) 5.740178 18.17802 0.315776 0.7529 EMI 0.146773 0.890419 0.164836 0.8694 CT(-1) -0.003391 0.020095 -0.168767 0.8663 RESID(-1) 0.175546 0.105814 1.659004 0.1004 R-squared 0.027871 Mean dependent var 1.07E-10 Breusch-Godfrey Serial Correlation LM Test: F-statistic 1.362020 Probability 0.261098 Obs*R-squared 2.843232 Probability 0.241324 Dependent Variable: RESID Method: Least Squares Variable Coefficient Std. Error t-Statistic Prob. C -170.2653 3911.867 -0.043525 0.9654 SPREAD -4.862724 17.65124 -0.275489 0.7835 SPREAD(-1) 5.668336 18.62090 0.304407 0.7615 EMI 0.145333 0.897965 0.161847 0.8718 CT(-1) -0.003358 0.020268 -0.165692 0.8688 RESID(-1) 0.175835 0.107340 1.638121 0.1047 RESID(-2) -0.002187 0.108977 -0.020065 0.9840 R-squared 0.027875 Mean dependent var mod1h = mod1rho*sqr(mod1t/(1-mod1t*mod1vb5)) = 1.912769 Dependent Variable: CT Method: Two-Stage Least Squares 1.07E-10 3 Sample (adjusted): 2001M03 2009M12 Included observations: 100 after adjustments Instrument list: C SPREAD SPREAD(-1) SPREAD(-2) EMI EMI(-1) Variable Coefficient Std. Error t-Statistic Prob. C -3216.579 4352.109 -0.739085 0.4617 SPREAD 47.76270 17.99800 2.653779 0.0093 SPREAD(-1) -22.66502 21.68321 -1.045279 0.2985 EMI 7.148063 2.058865 3.471846 0.0008 CT(-1) 0.853912 0.047258 18.06926 0.0000 R-squared 0.998312 Mean dependent var 580597.9 Adjusted R-squared 0.998241 S.D. dependent var 235252.0 S.E. of regression 9866.807 Sum squared resid 9.25E+09 F-statistic 13667.09 Durbin-Watson stat 1.463981 Prob(F-statistic) 0.000000 MOD1MISPREAD = C(2) = 47.7626977023185 MOD1MIEMI = C(4) = 7.1480634098764 MOD1MD1RSPREAD = C(3) + C(2)*C(5) = 18.1201333453488 MOD1MD2RSPREAD = C(3)*C(5) + C(2)*C(5)^2 = 15.4730025877635 MOD1MD1REMI = C(4)*C(5) = 6.1038184173686 MOD1MD2REMI = C(4)*C(5)^2 = 5.21212489815509 MOD1MTSPREAD = (C(3) + C(2))/(1-C(5)) = 171.798592609424 MOD1MTEMI = C(4)/(1-C(5)) = 48.9299071369329 MOD1RMSPREAD = C(3)/(C(2)+C(3)) + C(5)/(1-C(5)) = 4.94212559209028 MOD1RMEMI = C(5)/(1-C(5)) = 5.84519768939473 1.2. Estime el segundo modelo y obtenga los multiplicadores y el retardo medio. (5 puntos) CT(t) = a + b TA(t) + c0 SPREAD(t) + c1 SPREAD(t-1) + ... + c15 SPREAD(t-15) + u(t) Dependent Variable: CT Method: Least Squares Sample (adjusted): 2002M04 2009M12 Included observations: 74 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 2470963. 262045.0 9.429535 0.0000 TA -61901.80 9903.571 -6.250452 0.0000 PDL01 -69.50788 79.55865 -0.873668 0.3855 4 PDL02 -81.21235 56.48055 PDL03 5.490162 PDL04 6.273413 PDL05 PDL06 PDL07 R-squared -1.437882 0.1553 29.57882 0.185611 0.8533 5.407807 1.160066 0.2503 -0.031100 1.609867 -0.019319 0.9846 -0.101708 0.095397 -1.066160 0.2903 -0.000749 0.021397 -0.035027 0.9722 0.831106 Mean dependent var 608250.7 Dependent Variable: CT Method: Least Squares Sample (adjusted): 2002M04 2009M12 Included observations: 74 after adjustments Variable C Coefficient Std. Error t-Statistic Prob. 2471599. 259428.1 9.527108 0.0000 TA -61928.17 9799.900 -6.319266 0.0000 PDL01 -71.89564 40.70745 -1.766154 0.0820 PDL02 -82.53275 41.74026 -1.977293 0.0522 PDL03 6.481457 8.535235 0.759377 0.4503 PDL04 6.410882 3.692151 1.736354 0.0872 PDL05 -0.087022 0.205298 -0.423880 0.6730 PDL06 -0.104275 0.060608 -1.720497 0.0900 R-squared 0.831102 Mean dependent var 608250.7 Dependent Variable: CT Method: Least Squares Sample (adjusted): 2002M04 2009M12 Included observations: 74 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 2528236. 261068.2 9.684197 0.0000 TA -63993.02 9867.379 -6.485311 0.0000 PDL01 -116.8127 31.68691 -3.686464 0.0005 PDL02 -13.46227 11.59298 -1.161244 0.2497 PDL03 17.50606 5.720173 3.060408 0.0032 PDL04 0.092237 0.385280 0.239403 0.8115 PDL05 -0.371801 0.123213 -3.017542 0.0036 R-squared 0.823527 Mean dependent var 608250.7 Adjusted R-squared 0.807724 S.D. dependent var 259759.9 S.E. of regression 113902.9 Akaike info criterion 26.21390 Sum squared resid 8.69E+11 Schwarz criterion 26.43185 5 Log likelihood -962.9142 Lag Distribution of SPREAD * * F-statistic i Coefficient 52.11038 Std. Error t-Statistic *. | 0 -89.1109 106.584 -0.83606 .*| 1 92.4021 30.9568 2.98487 . *| 2 144.245 45.3054 3.18384 .*| 3 116.049 50.6073 2.29313 .* | 4 48.5224 40.1464 1.20864 *. | 5 -26.5506 27.5316 -0.96437 *. | 6 -86.3084 26.3817 -3.27153 * . | 7 -116.813 31.6869 -3.68646 * . | 8 -113.048 32.2243 -3.50817 *. | 9 -78.9239 27.0331 -2.91953 *. | 10 -27.2704 25.4147 -1.07302 * | 11 20.1574 35.6164 0.56596 .* | 12 32.6816 45.8515 0.71277 *. | 13 -29.2987 42.1309 -0.69542 . | 14 -214.308 30.9055 -6.93429 . | 15 -579.794 102.472 -5.65807 -907.368 100.232 -9.05263 Sum of Lags MI TA = -63993.02 MI SPREAD = -89.1109 MD SPREAD1R = 92.4021 = -579.794 MD SPREAD2R = 144.245 ……………….. MD SPREAD15R ML SPREAD = -907.368 mod2rmspread=@sum(i*re)/@sum(re) = 16.983367900646 1.3. En el primer modelo aplique el contraste de Hausman y Wu. (2 puntos) HW = @TRANSPOSE(BMCO-BMC2E)*@INVERSE(VARBMC2E-VARBMCO)*(BMCO-BMC2E) = 2.219990. Acepta la hipótesis nula. 1.4. Elija la mejor estimación y justifique su respuesta. (2 puntos) MODELO 1 MODELO 2 Adjusted R-squared 0.998381 Adjusted R-squared 0.807724 Akaike info criterion 21.18369 Akaike info criterion 26.21390 Sum squared resid 8.58E+09 Sum squared resid 8.69E+11 Schwarz criterion 21.31236 Schwarz criterion 26.43185 6 2º Comente y fundamente su respuesta. (5 puntos) 2.1. Cuando se tiene un modelo con variable retardada no se aplica mínimos cuadrados. 2.2. En todo modelo dinámico se puede obtener el multiplicador total.