UNIVERSIDAD NACIONAL DE PIURA FACULTAD DE ECONOMIA SOLUCIÓN DEL EXAMEN PARCIAL DE ECONOMETRIA I 1º El investigador especifica los modelos siguientes: MODELO 1: IMP(t) = a + b IMP(t-1) + c IPM(t) + u(t) MODELO 2: IMP(t) = a + b(0) PBI(t) + b(1) PBI(t-1) +... + b(9) PBI(t-9) + c IPM(t) + u(t) MODELO 3: IMP(t) = a + b PBI(t)^c + d IPM(t) + u(t) se le pide: 1.1. Estimar el modelo 1. (4 puntos) Sample (adjusted): 1951 2009 Included observations: 59 after adjustments C -1064.516 392.7626-2.710328 0.0089 IPM 41.00726 9.442247 4.342956 0.0001 IMP(-1) 0.675121 0.090937 7.424072 0.0000 R-squared 0.924676 Mean dependent var 4193.805 Adjusted R-squared 0.921986 S.D. dependent var 5563.430 S.E. of regression 1553.922 Akaike info criterion 17.58446 Sum squared resid 1.35E+08 Schwarz criterion 17.69010 Log likelihood -515.7416 F-statistic 343.7274 Durbin-Watson stat 1.500327 Prob(F-statistic) 0.000000 mod1h = mod1rho*sqr(mod1t/(1-mod1t*mod1vb3)) = 2,681667 Sample: 1951 2009 Included observations: 59 Autocorrelation Partial Correlation AC PAC Q-Stat Prob. ***. *** 1 0.444 0.444 12.246 0.000. *... 2 0.170-0.034 14.064 0.001 mod1qbp1 = 59*0.444247104750863^2 = 11,64397 mod1qbp2 = 59*(0.444247104750863^2+0.169694926721249^2) = 13,34296 Breusch-Godfrey Serial Correlation LM Test: F-statistic 14.18760 Probability 0.000405 Obs*R-squared 12.09853 Probability 0.000505 Dependent Variable: RESID C -1359.274 505.0616-2.691303 0.0094 IPM 62.14667 18.55766 3.348843 0.0015
2 IMP(-1) -0.726546 0.209523-3.467629 0.0010 RESID(-1) 1.300835 0.345357 3.766643 0.0004 R-squared 0.205060 Mean dependent var 4.93E-13 Breusch-Godfrey Serial Correlation LM Test: F-statistic 10.57244 Probability 0.000133 Obs*R-squared 16.60190 Probability 0.000248 Dependent Variable: RESID C -2022.020 558.0713-3.623228 0.0006 IPM 85.57564 20.31715 4.211990 0.0001 IMP(-1) -0.932152 0.218609-4.264021 0.0001 RESID(-1) 1.033464 0.349684 2.955417 0.0046 RESID(-2) 1.001108 0.418012 2.394928 0.0201 R-squared 0.281388 Mean dependent var 4.93E-13 BVI R1-4128,224 R2 169,3952 R3-0,700391 Method: Two-Stage Least Squares Sample (adjusted): 1951 2009 Included observations: 59 after adjustments Instrument list: C IPM IPM(-1) C -4128.224 1423.646-2.899755 0.0053 IPM 169.3952 51.33165 3.300014 0.0017 IMP(-1) -0.700391 0.540795-1.295114 0.2006 R-squared 0.616928 Mean dependent var 4193.805 Adjusted R-squared 0.603247 S.D. dependent var 5563.430 S.E. of regression 3504.313 Sum squared resid 6.88E+08 F-statistic 63.00741 Durbin-Watson stat 0.135987 Prob(F-statistic) 0.000000 1.2. Estimar el modelo 2. (4 puntos) Sample (adjusted): 1959 2009 Included observations: 51 after adjustments
3 C -1127.346 682.6739-1.651368 0.1061 IPM 133.6116 11.63569 11.48292 0.0000 PDL01 0.001935 0.021044 0.091931 0.9272 PDL02-0.022419 0.027928-0.802756 0.4266 PDL03-0.018262 0.020928-0.872599 0.3878 PDL04 0.005715 0.007808 0.731984 0.4682 PDL05 0.001894 0.003217 0.588754 0.5592 PDL06-0.000331 0.000403-0.820768 0.4164 PDL07-2.51E-05 0.000124-0.203277 0.8399 R-squared 0.972611 Mean dependent var 4805.639 Sample (adjusted): 1959 2009 Included observations: 51 after adjustments C -1133.645 674.3251-1.681155 0.1000 IPM 133.4893 11.48986 11.61802 0.0000 PDL01-0.001451 0.012720-0.114071 0.9097 PDL02-0.026909 0.016901-1.592121 0.1187 PDL03-0.014283 0.007326-1.949544 0.0578 PDL04 0.007083 0.003915 1.809161 0.0774 PDL05 0.001248 0.000489 2.550883 0.0144 PDL06-0.000404 0.000177-2.287083 0.0272 R-squared 0.972584 Mean dependent var 4805.639 Adjusted R-squared 0.968121 S.D. dependent var 5752.171 S.E. of regression 1027.034 Akaike info criterion 16.84984 Sum squared resid 45356345 Schwarz criterion 17.15287 Log likelihood -421.6709 F-statistic 217.9180 Durbin-Watson stat 0.811361 Prob(F-statistic) 0.000000 Lag Distribution of PBI i Coefficient Std. Error t-statistic. * 0 0.15761 0.02731 5.77140 *. 1-0.04124 0.02809-1.46813 *. 2-0.02853 0.01307-2.18296 * 3 0.00574 0.01672 0.34343 * 4-0.00145 0.01272-0.11407 *. 5-0.03472 0.01296-2.67957 *. 6-0.04870 0.01633-2.98156 *. 7-0.01658 0.01382-1.19987.* 8 0.02141 0.02925 0.73180 *. 9-0.09047 0.03143-2.87829 Sum of Lags -0.07693 0.01731-4.44307 1.3. Estimar el modelo 3 considerando: a=-3000, b=0.00002, c=2, d=80, aplicando mínimos cuadrados no lineales
4 y máxima verosimilitud. (3 puntos) Sample: 1950 2009 Included observations: 60 Convergence achieved after 6 iterations IMP=C(1)+C(2)*PBI^C(3)+C(4)*IPM Coefficient Std. Error t-statistic Prob. C(1) -3000.000 607.9314-4.934767 0.0000 C(2) 1.79E-07 1.40E-06 0.128523 0.8982 C(3) 2.015007 0.623103 3.233826 0.0021 C(4) 79.99951 16.28905 4.911243 0.0000 R-squared 0.893813 Mean dependent var 4126.397 Adjusted R-squared 0.888124 S.D. dependent var 5540.738 S.E. of regression 1853.256 Akaike info criterion 17.95162 Sum squared resid 1.92E+08 Schwarz criterion 18.09124 Log likelihood -534.5485 Durbin-Watson stat 0.403725 System: MOD3MV Estimation Method: Full Information Maximum Likelihood (Marquardt) Sample: 1950 2009 Included observations: 60 Total system (balanced) observations 60 Convergence achieved after 51 iterations Coefficient Std. Error z-statistic Prob. C(1) -3000.000 567.5362-5.286006 0.0000 C(2) 5.28E-08 4.73E-07 0.111576 0.9112 C(3) 2.118593 0.721934 2.934608 0.0033 C(4) 79.99596 16.14503 4.954836 0.0000 Log Likelihood -533.5877 Determinant residual covariance 3104552. Equation: IMP=C(1)+C(2)*PBI^C(3)+C(4)*IPM Observations: 60 R-squared 0.897160 Mean dependent var 4126.397 Adjusted R-squared 0.891650 S.D. dependent var 5540.738 S.E. of regression 1823.816 Sum squared resid 1.86E+08 Durbin-Watson stat 0.408951 1.4. Obtener los multiplicadores del modelo 1 y 2. (3 puntos) MODELO 1: IMP(t) = a + b IMP(t-1) + c IPM(t) + u(t) M. I. IPM = c = 169.3952 M. D. 1R IPM = bc = 169.3952 (-0.700391) = - 118.6428735 M. D. 2R IPM = b^2 c =169.3952 (-0.700391)^2 = 83.09640083
5 M. T. IPM = = 99.62132239 MODELO 2: IMP(t) = a + b(0) PBI(t) + b(1) PBI(t-1) +... + b(9) PBI(t-9) + c IPM(t) + u(t) M. I. IPM = c = 133.4893 M. I. PBI = b(0) = 0.15761 M. D. 1R PBI = b(1) = -0.04124 M. D. 2R PBI = b(2) = -0.02853. M. D. 9R PBI = b(9) = -0.09047 M. T. PBI = -0.07693 1.5. Seleccione la mejor estimación, justifique su respuesta. (3 puntos) 2º Comente y fundamente su respuesta. (3 puntos) Todos los modelos dinámicos requieren de la verificación de autocorelación para determinar el método de estimación adecuado.