UNIVERSIDAD NACIONAL DE PIURA FACULTAD DE ECONOMIA PRIMERA PRÁCTICA CALIFICADA DE ECONOMETRIA I 1º El investigador especifica los modelos siguientes: MODELO 1: INV(t) = a + b(0) PIB(t) + b(1) PIB(t-1) + b(2) PIB(t-2) + .............. + c PPIB(t) + u(t) MODELO 2: INV(t) = a + b PIB(t) + c(0) PPIB(t) + c(1) PPIB(t-1) + c(2) PPIB(t-2) + .... + c(K) PPIB(t-K) + u(t) se le pide: 1.1. Estimar el modelo 1 y obtener los multiplicadores, retardo medio y mediano. (6 puntos) Asumimos bi = (1-d)di INV(t) = a + c PPIB(t) + (1-d) PIB(t) + (1-d)d PIB(t-1) + (1-d)d2 PIB(t-2)+ .... + u(t) Retardando un periodo: INV(t-1) = a + c PPIB(t-1) + (1-d) PIB(t-1) + (1-d)d PIB(t-2) + (1-d)d2 PIB(t-3)+ .... + u(t-1) Multiplica por d: dINV(t-1) = ad + cd PPIB(t-1) + (1-d)d PIB(t-1) + (1-d)d2 PIB(t-2) + (1-d)d3 PIB(t3)+ .... + du(t-1) (2) (1) - (2): INV(t) – d INV(t-1) = a(1-d) + c PPIB(t) - cd PPIB(t-1) + (1-d) PIB(t) + u(t) – d u(t-1) INV(t) = a(1-d) + c PPIB(t) - cd PPIB(t-1) + (1-d) PIB(t) + d INV(t-1) + (u(t) - d u(t-1)) Dependent Variable: INV Method: Least Squares Sample (adjusted): 1947Q2 1995Q1 Included observations: 192 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C PIB PPIB PPIB(-1) INV(-1) -29.01886 0.005659 19.44186 -18.15726 0.790185 7.542270 0.004043 4.172197 4.038261 0.043491 -3.847496 1.399879 4.659862 -4.496306 18.16872 0.0002 0.1632 0.0000 0.0000 0.0000 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 0.995814 0.995724 17.31337 56053.75 -817.3870 1.604041 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) mod1h = mod1rho*sqr(mod1t/(1-mod1t*mod1vb5)) = 3.437629 307.2740 264.7758 8.566531 8.651362 11121.03 0.000000 Sample: 1947Q2 1995Q1 Included observations: 192 Autocorrelation .|* .|. | | Partial Correlation .|* .|. | | AC PAC Q-Stat Prob 1 0.154 0.154 4.6199 0.032 2 0.035 0.011 4.8585 0.088 QBP1 = 192*(0.153915159940832)2 = 4.54845628024548 QBP2 = 192*[(0.153915159940832)2+(0.0348859107024808)2] = 4.78212541922944 Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared 9.753547 9.566524 Probability Probability 0.002076 0.001982 Dependent Variable: RESID Method: Least Squares Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C PIB PPIB PPIB(-1) INV(-1) RESID(-1) -11.10736 0.000976 5.165266 -4.517018 -0.097441 0.284504 8.184813 0.003964 4.400482 4.203597 0.052729 0.091098 -1.357070 0.246279 1.173796 -1.074560 -1.847941 3.123067 0.1764 0.8057 0.2420 0.2840 0.0662 0.0021 Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared 7.224544 13.90944 Probability Probability 0.000953 0.000954 Dependent Variable: RESID Method: Least Squares Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C PIB PPIB PPIB(-1) INV(-1) RESID(-1) RESID(-2) -20.17920 0.001689 9.574113 -8.391759 -0.177261 0.336384 0.194070 9.164722 0.003941 4.828464 4.546509 0.064352 0.093497 0.091370 -2.201834 0.428496 1.982849 -1.845759 -2.754572 3.597820 2.124008 0.0289 0.6688 0.0489 0.0665 0.0065 0.0004 0.0350 Dependent Variable: INV Method: Two-Stage Least Squares Sample (adjusted): 1947Q3 1995Q1 Included observations: 191 after adjustments Instrument list: C PIB PIB(-1) PPIB PPIB(-1) PPIB(-2) Variable Coefficient Std. Error t-Statistic Prob. C PIB PPIB PPIB(-1) INV(-1) -106.8405 0.016805 46.06518 -40.60851 0.145526 22.77485 0.006664 9.175054 8.274035 0.176407 -4.691160 2.521836 5.020699 -4.907946 0.824947 0.0000 0.0125 0.0000 0.0000 0.4105 R-squared Adjusted R-squared S.E. of regression F-statistic 0.990859 0.990663 25.58482 5028.155 Mean dependent var S.D. dependent var Sum squared resid Durbin-Watson stat MIPIB = 0.0168047232136378. 308.6613 264.7711 121752.4 0.467308 MIPPIB = 46.0651844264855. MD1PPIB = -40.6085122056975 + 46.0651844264855 * 0.145526348802223 = -33.9048141092101 MD2PPIB = -40.6085122056975 * 0.145526348802223 + 46.0651844264855 * 0.145526348802223^2 = 4.93404380413144 MD1PIB = 0.0168047232136378 * 0.145526348802223 = 0.00244553001191267 MD2PIB = 0.0168047232136378 * 0.145526348802223^2 = 0.000355889053519908 ………….. MTPPIB = -40.6085122056975 / (1 - 0.145526348802223) + (46.0651844264855 * 0.145526348802223) / (1 0.145526348802223) = -39.679180348842 1.2. MTPIB = = 0.0168047232136378 (1 − 0.145526348802223 ) = 0.0196667541358138 Estimar el modelo 2 y y obtener los multiplicadores, retardo medio y mediano. (6 puntos) ELECCIÓN DEL RETARDO ÓPTIMO k T R2 AJUSTADO AkAIkE SCHWARZ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 193 192 191 190 189 188 187 186 185 184 183 182 181 180 0.984929 0.988240 0.988349 0.988237 0.988134 0.988228 0.988712 0.988975 0.989173 0.989123 0.989099 0.989089 0.989095 0.989132 9.816007 9.573247 9.569068 9.583793 9.597914 9.595344 9.558777 9.540579 9.527765 9.537263 9.544076 9.549648 9.553478 9.554820 9.866722 9.641112 9.654206 9.686331 9.717979 9.733065 9.714285 9.714006 9.719245 9.746932 9.772072 9.796110 9.818547 9.838638 14 15 16 17 18 19 20 21 179 178 177 176 175 174 173 172 0.989250 0.989313 0.989453 0.989797 0.989821 0.989742 0.989600 0.989494 9.548795 9.547965 9.540293 9.512359 9.515432 9.528408 9.547088 9.562122 9.851508 9.869718 9.881236 9.872642 9.895206 9.927828 9.966312 10.00131 K = 18 Dependent Variable: INV Method: Least Squares Sample (adjusted): 1951Q3 1995Q1 Included observations: 175 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C PIB PDL01 PDL02 PDL03 PDL04 PDL05 PDL06 PDL07 -126.1478 0.019281 4.192368 -0.216603 -0.795034 0.121218 0.019737 -0.001894 -0.000115 11.15123 0.007574 2.688550 1.127647 0.705402 0.064983 0.026164 0.000698 0.000231 -11.31245 2.545865 1.559342 -0.192084 -1.127065 1.865386 0.754359 -2.713818 -0.498227 0.0000 0.0118 0.1208 0.8479 0.2613 0.0639 0.4517 0.0074 0.6190 Dependent Variable: INV Method: Least Squares Sample (adjusted): 1951Q3 1995Q1 Included observations: 175 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C PIB PDL01 PDL02 PDL03 PDL04 PDL05 PDL06 -125.9231 0.019004 3.001553 -0.228716 -0.451593 0.121711 0.006741 -0.001898 11.11700 0.007536 1.228358 1.124845 0.149400 0.064829 0.002040 0.000696 -11.32707 2.521755 2.443549 -0.203331 -3.022714 1.877434 3.305079 -2.726051 0.0000 0.0126 0.0156 0.8391 0.0029 0.0622 0.0012 0.0071 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Lag Distribution of 0.990798 0.990412 25.86275 111703.3 -813.4606 0.437453 i Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) 332.4263 264.1248 9.388121 9.532797 2568.651 0.000000 Coefficient t-Statistic Std. Error PPIB . .* * . * . * . * . *. * .* .* .* * * .* .* .* .* * * . *| | | | | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Sum of Lags 36.0403 3.40927 -11.1920 -14.6799 -12.2150 -7.42959 -2.65566 0.84751 2.66560 3.00155 2.44780 1.75857 1.62218 2.43325 4.06507 5.64178 5.31072 0.01466 -14.7359 4.98901 1.68144 3.18198 2.69706 1.62289 1.41741 1.85360 1.91802 1.55218 1.22836 1.48215 1.86119 1.83728 1.38801 1.44052 2.46501 3.01138 1.66596 4.57636 7.22393 2.02759 -3.51730 -5.44294 -7.52669 -5.24167 -1.43270 0.44187 1.71733 2.44355 1.65152 0.94486 0.88292 1.75305 2.82194 2.28874 1.76355 0.00880 -3.22000 6.35018 0.24602 25.8113 K = 17: Dependent Variable: INV Method: Least Squares Sample (adjusted): 1951Q2 1995Q1 Included observations: 176 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C PIB PDL01 PDL02 PDL03 PDL04 PDL05 PDL06 PDL07 -127.6156 0.019846 3.798741 0.762063 -1.181977 0.092928 0.037180 -0.002083 -0.000233 11.03087 0.007528 2.948258 1.559689 0.846730 0.111342 0.035330 0.001503 0.000359 -11.56895 2.636234 1.288469 0.488600 -1.395931 0.834621 1.052367 -1.386093 -0.648254 0.0000 0.0092 0.1994 0.6258 0.1646 0.4051 0.2942 0.1676 0.5177 Dependent Variable: INV Method: Least Squares Sample (adjusted): 1951Q2 1995Q1 Included observations: 176 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C PIB -127.3578 0.019526 11.00466 0.007499 -11.57308 2.603796 0.0000 0.0100 PDL01 PDL02 PDL03 PDL04 PDL05 PDL06 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 2.171313 0.221965 -0.654552 0.138716 0.014429 -0.002770 0.990643 0.990254 26.07661 114238.2 -819.5822 0.441809 Lag Distribution of PPIB . .* * . * . * . *. * * .* .* * * .* .* .* .* * * . i *| | | | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Sum of Lags 1.3. 1.543204 1.316235 0.234105 0.085921 0.004058 0.001064 1.407016 0.168636 -2.795977 1.614473 3.555940 -2.604518 0.1613 0.8663 0.0058 0.1083 0.0005 0.0100 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) 330.9091 264.1371 9.404344 9.548456 2541.055 0.000000 Coefficient Std. Error t-Statistic 37.3569 2.16786 -12.4458 -14.9667 -11.5367 -6.28896 -1.68104 1.17328 2.17131 1.88910 1.24899 1.18721 2.32148 4.61853 7.06176 7.31876 1.40891 -16.6290 5.51708 2.17243 3.70668 2.86438 1.63728 1.77862 2.23700 2.07875 1.54320 1.48592 1.99794 2.20095 1.77000 1.48590 2.61534 3.50415 2.14161 5.09131 6.77114 0.99790 -3.35767 -5.22512 -7.04624 -3.53586 -0.75147 0.56441 1.40702 1.27134 0.62514 0.53941 1.31157 3.10824 2.70013 2.08860 0.65788 -3.26615 6.37587 0.24504 26.0192 Compare los dos modelos estimados y elija la mejor estimación, justifique su respuesta. (3 puntos) Se compara el coeficiente de bondad de ajuste y la suma residual de los dos modelos. 2º Comente y fundamente su respuesta. (5 puntos) 2.1. El modelo de regresión múltiple aleatorio o no aleatorio considera el supuesto caeteris paribus. 2.2. El punto fundamental de la crítica de Lucas se refiere a que las estimaciones econométricas a nivel macroeconómicas consideran que los agentes económicos, como un todo, se basan en expectativas adaptativas para pronosticar la evolución de las variables económicas de interés.