UNIVERSIDAD NACIONAL DE PIURA FACULTAD DE ECONOMIA DPTO. ACAD. DE ECONOMIA SOLUCIÄN DE LA PRIMERA PRÅCTICA CALIFICADA DE ECONOMETRIA II 1Ä El investigador especifica el modelo siguiente: Donde: Se le pide: Es el crecimiento de los salarios nominales. Es la tasa de inflaciån. Es la tasa de desempleo. Es el crecimiento del precio de las materias primas, se ha valorado como tal la referencia al precio del petråleo. 1.1. Determine quç tipo de variable es la tasa de desempleo. (2 puntos) u t m t w t p t 2t 1t 2t-1 p t-1 La tasa de desempleo es exågena estricta en la primera ecuaciån. 1.2. Aplique la prueba de exogeneidad en la segunda ecuaciån. (3 puntos) Dependent Variable: W Method: Least Squares after adjustments C 10.46323 6.393120 1.636640 0.1212 U -0.422025 0.249423-1.692006 0.1100 M -0.028987 0.033667-0.861012 0.4020 R 0.441512 0.208313 2.119469 0.0500 R-squared 0.513625 Mean dependent var 7.758611 Adjusted R-squared 0.422429 S.D. dependent var 3.980701 S.E. of regression 3.025256 Akaike info criterion 5.228725 Sum squared resid 146.4348 Schwarz criterion 5.427872 Log likelihood -48.28725 Hannan-Quinn criter. 5.267601 F-statistic 5.632133 Durbin-Watson stat 1.724281 Prob(F-statistic) 0.007870
2 Modified: 1970 2002 // frw.fit(f=na) wf 1980 12.21560 11.74926 10.58991 10.28851 10.07206 1985 8.100807 5.888252 8.127680 6.992032 8.814525 1990 10.82280 10.13459 8.640271 7.327393 3.717374 1995 4.228913 5.123213 5.271588 3.471339 3.596105 Dependent Variable: P Method: Least Squares after adjustments C -3.487888 1.398745-2.493585 0.0248 W 0.575132 0.148303 3.878075 0.0015 M 0.016400 0.018629 0.880342 0.3926 R 0.073428 0.239562 0.306511 0.7634 WF 0.586212 0.380674 1.539932 0.1444 R-squared 0.849878 Mean dependent var 6.444500 Adjusted R-squared 0.809846 S.D. dependent var 4.115477 S.E. of regression 1.794624 Akaike info criterion 4.219786 Sum squared resid 48.31011 Schwarz criterion 4.468719 Log likelihood -37.19786 Hannan-Quinn criter. 4.268380 F-statistic 21.22970 Durbin-Watson stat 1.058339 Prob(F-statistic) 0.000005 1.3. Verifique si la tasa de inflaciån es exågena fuerte. (3 puntos) u t m t w t p t 2t 1t p t-1 y la tasa de inflaciån precede al crecimiento de la tasa de salario, por lo tanto la tasa de inflaciån no es exågena fuerte en la primera ecuaciån. 2Ä El investigador corrige el modelo: Donde: Se le pide: Es el crecimiento del coste del uso del capital. 2.1. Estimar la primera ecuaciån por ménimos cuadrados bietñpicos y verifique si los residuos son ruido blanco. (5 puntos)
3 Dependent Variable: W Method: Two-Stage Least Squares after adjustments Instrument list: C U M R C 1.533198 4.835777 0.317053 0.7551 U 0.039712 0.205056 0.193664 0.8487 P 0.849292 0.191619 4.432204 0.0004 R-squared 0.751371 Mean dependent var 7.758611 Adjusted R-squared 0.722121 S.D. dependent var 3.980701 S.E. of regression 2.098396 Sum squared resid 74.85553 F-statistic 17.36756 Durbin-Watson stat 1.922400 Prob(F-statistic) 0.000078 Second-Stage SSR 148.1256 7 6 5 4 3 2 1 0-4 -3-2 -1 0 1 2 3 4 5 6 Series: Residuals Sample 1980 1999 Observations 20 Mean -2.83e-16 Median -0.040835 Maximum 5.191247 Minimum -3.503014 Std. Dev. 1.984884 Skewness 0.700184 Kurtosis 4.112914 Jarque-Bera 2.666341 Probability 0.263640 Autocorrelation Partial Correlation AC PAC Q-Stat Prob.... 1-0.046-0.046 0.0494 0.824 ***. ***. 2-0.388-0.391 3.7225 0.155 Breusch-Godfrey Serial Correlation LM Test: Obs*R-squared 0.043407 Prob. Chi-Square(1) 0.8350 Breusch-Godfrey Serial Correlation LM Test: Obs*R-squared 3.242490 Prob. Chi-Square(2) 0.1977 Heteroskedasticity Test: White F-statistic 1.046381 Prob. F(2,17) 0.3728 Obs*R-squared 2.192204 Prob. Chi-Square(2) 0.3342 Scaled explained SS 2.465222 Prob. Chi-Square(2) 0.2915
4 Heteroskedasticity Test: White F-statistic 0.633707 Prob. F(5,14) 0.6776 Obs*R-squared 3.691095 Prob. Chi-Square(5) 0.5947 Scaled explained SS 4.150786 Prob. Chi-Square(5) 0.5279 Heteroskedasticity Test: ARCH F-statistic 0.035741 Prob. F(1,17) 0.8523 Obs*R-squared 0.039862 Prob. Chi-Square(1) 0.8418 Heteroskedasticity Test: ARCH F-statistic 0.510804 Prob. F(2,15) 0.6101 Obs*R-squared 1.147758 Prob. Chi-Square(2) 0.5633 Heteroskedasticity Test: Breusch-Pagan-Godfrey F-statistic 1.211177 Prob. F(2,17) 0.3223 Obs*R-squared 2.494398 Prob. Chi-Square(2) 0.2873 Scaled explained SS 2.805051 Prob. Chi-Square(2) 0.2460 Heteroskedasticity Test: Harvey F-statistic 1.148635 Prob. F(2,17) 0.3405 Obs*R-squared 2.380927 Prob. Chi-Square(2) 0.3041 Scaled explained SS 2.683800 Prob. Chi-Square(2) 0.2613 F-statistic 1.028515 Prob. F(1,18) 0.3239 Obs*R-squared 1.081025 Prob. Chi-Square(1) 0.2985 Scaled explained SS 1.251367 Prob. Chi-Square(1) 0.2633 C 3.286724 1.910694 1.720173 0.1025 U -0.100936 0.099527-1.014157 0.3239 R-squared 0.054051 Mean dependent var 1.374987 Adjusted R-squared 0.001499 S.D. dependent var 1.396306 S.E. of regression 1.395260 Akaike info criterion 3.598678 Sum squared resid 35.04150 Schwarz criterion 3.698251 Log likelihood -33.98678 Hannan-Quinn criter. 3.618115 F-statistic 1.028515 Durbin-Watson stat 2.053358 F-statistic 1.774109 Prob. F(1,18) 0.1995 Obs*R-squared 1.794375 Prob. Chi-Square(1) 0.1804 Scaled explained SS 2.077122 Prob. Chi-Square(1) 0.1495
5 C -0.734338 1.612931-0.455282 0.6544 1/U 38.70846 29.06135 1.331957 0.1995 R-squared 0.089719 Mean dependent var 1.374987 Adjusted R-squared 0.039148 S.D. dependent var 1.396306 S.E. of regression 1.368702 Akaike info criterion 3.560243 Sum squared resid 33.72024 Schwarz criterion 3.659816 Log likelihood -33.60243 Hannan-Quinn criter. 3.579681 F-statistic 1.774109 Durbin-Watson stat 2.126010 F-statistic 1.185205 Prob. F(1,18) 0.2907 Obs*R-squared 1.235541 Prob. Chi-Square(1) 0.2663 Scaled explained SS 1.430230 Prob. Chi-Square(1) 0.2317 C 5.327828 3.644155 1.462020 0.1610 SQR(U) -0.911599 0.837350-1.088671 0.2907 R-squared 0.061777 Mean dependent var 1.374987 Adjusted R-squared 0.009654 S.D. dependent var 1.396306 S.E. of regression 1.389550 Akaike info criterion 3.590477 Sum squared resid 34.75530 Schwarz criterion 3.690050 Log likelihood -33.90477 Hannan-Quinn criter. 3.609915 F-statistic 1.185205 Durbin-Watson stat 2.068178 F-statistic 1.561463 Prob. F(1,18) 0.2275 Obs*R-squared 1.596469 Prob. Chi-Square(1) 0.2064 Scaled explained SS 1.848031 Prob. Chi-Square(1) 0.1740 C -2.783317 3.341944-0.832844 0.4158 1/SQR(U) 17.88942 14.31628 1.249585 0.2275 R-squared 0.079823 Mean dependent var 1.374987 Adjusted R-squared 0.028703 S.D. dependent var 1.396306 S.E. of regression 1.376122 Akaike info criterion 3.571055 Sum squared resid 34.08680 Schwarz criterion 3.670628 Log likelihood -33.71055 Hannan-Quinn criter. 3.590493 F-statistic 1.561463 Durbin-Watson stat 2.104572
6 2.2. Determine el mçtodo adecuado de estimaciån. (2 puntos) Covariance Analysis: Ordinary after adjustments Balanced sample (listwise missing value deletion) Correlation t-statistic Probability RESID01 RESID02 RESID01 1.000000 ----- ----- RESID02-0.988551 1.000000-27.79628 ----- 0.0000 ----- W P W 1.000000-0.988551 P -0.988551 1.000000 2Ä Comente y fundamente su respuesta. (5 puntos) 2.1. La prueba de Hausman permite establecer si un modelo presenta Endogeneidad. 2.2. La causalidad Granger se utiliza para establecer la exogeneidad.