UNIVERSIDAD NACIONAL DE PIURA FACULTAD DE ECONOMIA SOLUCIÓN DEL EXAMEN PARCIAL DE ECONOMETRIA I 1º El investigador especifica los modelos siguientes: MODELO 1: M1(t) = a + b M1(t-1) + c INT(t) + d INT(t-1) + u(t) MODELO 2: M1(t) = a + b PBI(t)^c + d INFL(t) + u(t) se le pide: 1.1. Estimar el modelo 1. (5 puntos) Dependent Variable: M1 Sample (adjusted): 1950Q2 2000Q4 Included observations: 203 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C M1(-1) INT INT(-1) 1.109369 1.004473 -1.718651 2.050277 1.363422 0.001729 0.821977 0.819207 0.813665 581.0437 -2.090876 2.502758 0.4168 0.0000 0.0378 0.0131 R-squared Log likelihood Durbin-Watson stat 0.999446 -721.2551 0.729703 Mean dependent var F-statistic Prob(F-statistic) 455.6147 119636.2 0.000000 mod1h = mod1rho*sqr(mod1t/(1-mod1t*mod1vb2)) = 9.052220 Sample: 1950Q2 2000Q4 Included observations: 203 Autocorrelation Partial Correlation .|***** | .|**** | .|***** | .|* | AC PAC Q-Stat Prob 1 0.608 0.608 76.135 0.000 2 0.492 0.194 126.17 0.000 mod1qb1 = 203*0.607916862159251^2 = 75.0212709934026. mod1qb2 = 203*(0.607916862159251^2+0.491588435897297^2) = 124.078086625917 Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared 134.5715 82.14178 Probability Probability 0.000000 0.000000 Dependent Variable: RESID Variable Coefficient Std. Error t-Statistic Prob. C M1(-1) INT INT(-1) RESID(-1) 0.338277 -0.000632 -0.787294 0.771003 0.645967 1.055067 0.001338 0.639445 0.637167 0.055684 0.320621 -0.471952 -1.231213 1.210049 11.60050 0.7488 0.6375 0.2197 0.2277 0.0000 R-squared 0.404639 Mean dependent var -2.89E-15 Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared 76.74919 88.90247 Probability Probability 0.000000 0.000000 Dependent Variable: RESID Variable Coefficient Std. Error t-Statistic Prob. C M1(-1) INT INT(-1) RESID(-1) RESID(-2) 0.451475 -0.000876 -0.584278 0.561276 0.496126 0.239893 1.028265 0.001306 0.625706 0.623687 0.069754 0.070215 0.439065 -0.670667 -0.933790 0.899933 7.112523 3.416573 0.6611 0.5032 0.3516 0.3693 0.0000 0.0008 R-squared 0.437943 Mean dependent var -2.89E-15 Dependent Variable: M1 Method: Two-Stage Least Squares Sample (adjusted): 1950Q3 2000Q4 Included observations: 202 after adjustments Instrument list: C M1(-1) INT INT(-1) INT(-2) Variable Coefficient Std. Error t-Statistic Prob. C M1(-1) INT INT(-1) 1.116539 1.004470 -1.719064 2.049906 1.378655 0.001735 0.824112 0.821322 0.809875 579.0175 -2.085960 2.495860 0.4190 0.0000 0.0383 0.0134 R-squared Adjusted R-squared S.E. of regression F-statistic 1.2. 0.999443 0.999435 8.554931 118494.8 Mean dependent var S.D. dependent var Sum squared resid Durbin-Watson stat 457.3170 359.8733 14490.99 0.729676 Estimar el modelo 2, aplicando la transformación de Box y Cox (3 decimales). (4 puntos) TRANSFORMACION DE BOX COX BETA 2 SUMA RESIDUAL 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 3650429. 3336571. 3043469. 2772053. 2523088. 2297172. 2094735. 1916040. 1761193. 1630148. 1522720. 1438593. 1377334. 1338407. 1.4 1.5 1.6 1.7 1.8 1.9 2 1321183. 1324957. 1348956. 1392355. 1454286. 1533851. 1630127. Dependent Variable: M1 Sample: 1950Q1 2000Q4 Variable Coefficient C (PBI^1.4-1)/1.4 INFL -64.04202 0.005533 -9.588781 R-squared 0.949705 Std. Error 12.29700 8.99E-05 1.674658 t-Statistic -5.207938 61.54197 -5.725815 Mean dependent var Prob. 0.0000 0.0000 0.0000 453.9215 TRANSFORMACION DE BOX COX BETA 2 SUMA RESIDUAL 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.4 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1335719. 1333247. 1330992. 1328951. 1327125. 1325512. 1324112. 1322924. 1321948. 1321183. 1320628. 1320282. 1320144. 1320215. 1320492. 1320976. 1321665. 1322558. 1323656. Dependent Variable: M1 Sample: 1950Q1 2000Q4 Included observations: 204 Variable Coefficient C (PBI^1.43-1)/1.43 INFL -54.60916 0.004283 -9.305409 R-squared 0.949745 Std. Error 12.18389 6.96E-05 1.673789 t-Statistic -4.482078 61.56746 -5.559487 Mean dependent var Prob. 0.0000 0.0000 0.0000 453.9215 TRANSFORMACION DE BOX COX BETA 2 SUMA RESIDUAL 1.421 1.422 1.423 1.424 1.425 1.426 1.427 1.428 1.429 1.43 1.431 1.432 1.433 1.434 1.435 1.436 1.437 1.438 1.439 1320259. 1320238. 1320219. 1320202. 1320187. 1320174. 1320164. 1320155. 1320149. 1320144. 1320142. 1320142. 1320144. 1320148. 1320154. 1320162. 1320172. 1320184. 1320198. Dependent Variable: M1 Method: Least Squares Sample: 1950Q1 2000Q4 Variable Coefficient C (PBI^1.432-1)/1.432 INFL -53.99549 0.004210 -9.286566 R-squared Adjusted R-squared Log likelihood Durbin-Watson stat 1.3. 0.949745 0.949245 -1184.527 0.119805 Std. Error 12.17688 6.84E-05 1.673774 t-Statistic -4.434263 61.56752 -5.548279 Mean dependent var S.D. dependent var F-statistic Prob(F-statistic) Prob. 0.0000 0.0000 0.0000 453.9215 359.7263 1899.297 0.000000 Obtener los multiplicadores del modelo 1 y 2. (4 puntos) MODELO 1: M1(t) = a + b M1(t-1) + c INT(t) + d INT(t-1) + u(t) M1(t) = a + b (a + b M1(t-2) + c INT(t-1) + d INT(t-2) + u(t-1)) + c INT(t) + d INT(t-1) + u(t) M1(t) = a(1+b) + b2 M1(t-2) + c INT(t) + (d + bc) INT(t-1) + bd INT(t-2) + (u(t) + b u(t-1)) M. I. INT = c = -1.71906351019002 M. D. 1R INT = d + bc = 0.323157951058081 M. D. 2 R INT = bd + b2c = 0.324602541305557 ...................... M. T. INT = c + d + bc + bd + b2c + ... = (c + bc + b2c + .....) + (d + bd + ......) = c (1 + b + b2 + ....) + d (1 + b + .....) Para obtener el multiplicador total requiere que: b<1 y en la estimación b = 1.00447022962841 >1. MODELO 2: M1(t) = a + b PBI(t)^c + d INFL(t) + u(t) M. I. PBI = bc PBI(t)^(c-1) = 0.223476 M. I. INFL = d = -9.28656570062868 2º Comente y fundamente su respuesta. (7 puntos) 2.1. Todos los modelos dinámicos requiere de la verificación de autocorelación para determinar el método de estimación adecuado. 2.2. El sistema de ecuaciones normales de un modelo no lineal no difiere del sistema de ecuaciones normales de un modelo lineal.