UNIVERSIDAD NACIONAL DE PIURA FACULTAD DE ECONOMIA SOLUCIÓN DE LA SEGUNDA PRACTICA CALIFICADA DE ECONOMETRIA I 1º El investigador especifica los modelos: Modelo 1: INVR = a + b INGR + c INT^d + e INT(-1) + u Modelo 2: INVR = f exp(g INGR) + h INT + v Se le pide: 1.1. Estimar el modelo 1 para el periodo 1950:2 - 1998:4 por mínimos cuadrados no lineales y utilizando la transformación de Box y Cox (dos decimales). (6 puntos) Dependent Variable: INVR Method: Least Squares Sample (adjusted): 1950Q2 1998Q4 Included observations: 195 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C INGR INT INT(-1) -129.9682 0.169501 14.32042 -17.56753 11.94188 0.002585 6.062011 6.065603 -10.88340 65.57389 2.362323 -2.896255 0.0000 0.0000 0.0192 0.0042 R-squared 0.965004 Mean dependent var 610.9615 Dependent Variable: INVR Method: Least Squares Sample (adjusted): 1950Q2 1998Q4 Included observations: 195 after adjustments Convergence achieved after 32 iterations INVR =C(1)+C(2)*INGR+C(3)*INT^C(4)+C(5)*INT(-1) C(1) C(2) C(3) C(4) C(5) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Coefficient Std. Error t-Statistic Prob. -107.9619 0.171953 1.811234 1.761024 -17.19042 13.35914 0.002826 3.444937 0.609367 6.118844 -8.081500 60.84580 0.525767 2.889924 -2.809423 0.0000 0.0000 0.5997 0.0043 0.0055 0.965770 0.965049 62.25518 736384.4 -1079.753 0.206084 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) TRANSFORMACIÓN DE BOX Y COX BETA 2 SUMA RESIDUAL 0 0.1 773188.1 774033.5 610.9615 333.0013 11.12567 11.20959 1340.158 0.000000 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 774645.9 774842.6 774399.7 773082.4 770707.9 767232.7 762824.9 757865.7 752851.6 748246.1 744362.9 741333.3 739141.1 737684.7 736829.4 736441.9 736405.5 736625.8 737029.3 Dependent Variable: INVR Method: Least Squares Sample: 1950Q2 1998Q4 Included observations: 195 Variable Coefficient Std. Error t-Statistic Prob. C INGR (INT^1.8-1)/1.8 INT(-1) -106.2917 0.172010 2.891388 -16.93023 13.50313 0.002663 0.915675 4.488140 -7.871635 64.58188 3.157656 -3.772215 0.0000 0.0000 0.0018 0.0002 R-squared Adjusted R-squared 0.965769 0.965231 Mean dependent var S.D. dependent var TRANSFORMACION DE BOX COX BETA 2 SUMA RESIDUAL 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.8 1.81 1.82 736424.1 736409.8 736398.8 736391.0 736386.2 736384.4 736385.6 736389.5 736396.2 736405.5 736417.3 736431.7 610.9615 333.0013 1.83 1.84 1.85 1.86 1.87 1.88 1.89 736448.4 736467.4 736488.6 736512.0 736537.5 736565.0 736594.5 Dependent Variable: INVR Method: Least Squares Sample: 1950Q2 1998Q4 Included observations: 195 Variable Coefficient Std. Error t-Statistic Prob. C INGR (INT^1.76-1)/1.76 INT(-1) -106.1473 0.171951 3.197832 -17.19724 13.52458 0.002658 1.012432 4.565223 -7.848475 64.68756 3.158566 -3.767011 0.0000 0.0000 0.0018 0.0002 R-squared Adjusted R-squared 1.2. 0.965770 0.965232 Mean dependent var S.D. dependent var 610.9615 333.0013 Estimar el modelo 2 para el periodo 1950:2 - 1998:4 por máxima verosimilitud y mediante la serie de Taylor. (6 puntos) Dependent Variable: INVR Method: Least Squares Sample: 1950Q2 1998Q4 Included observations: 195 Variable Coefficient Std. Error t-Statistic Prob. C INT 358.8880 48.01823 45.11622 7.531823 7.954743 6.375380 0.0000 0.0000 R-squared 0.173962 Mean dependent var 610.9615 System: M2MV Estimation Method: Full Information Maximum Likelihood (Marquardt) Sample: 1950Q2 1998Q4 Included observations: 195 Convergence achieved after 31 iterations C(1) C(2) C(3) Coefficient Std. Error z-Statistic Prob. 127.7781 0.000279 17.69937 6.188010 6.28E-06 1.314676 20.64930 44.40979 13.46292 0.0000 0.0000 0.0000 Log Likelihood Determinant residual covariance -1029.213 2248.812 Equation: INVR=C(1)*EXP(C(2)*INGR)+C(3)*INT Observations: 195 R-squared 0.979616 Mean dependent var Adjusted R-squared 0.979403 S.D. dependent var 610.9615 333.0013 APROXIMACIÓN APLICANDO TAYLOR I T R2 AJUSTADO AKAIKE SCHWARZ 1 2 3 4 5 6 7 8 195 195 195 195 195 195 195 195 0.963087 0.999925 0.999926 0.999690 0.998928 0.998041 0.998242 0.998236 11.17025 10.93092 11.25595 10.85552 10.57461 10.58673 10.58680 10.58680 11.22060 10.98127 11.30631 10.90587 10.62497 10.63708 10.63716 10.63716 Dependent Variable: _Y+87.56517733*0.0003400014958*_X *EXP(0.0003400014958*_X) Method: Least Squares Sample: 1950Q2 1998Q4 Included observations: 195 1.3. Variable Coefficient Std. Error t-Statistic Prob. EXP(0.0003400014958*_X) 87.56517733*_X*EXP(0.0003400014958*_ X) INT 123.7778 4.254744 29.09172 0.0000 0.000275 16.95705 5.66E-06 1.474508 48.67463 11.50014 0.0000 0.0000 R-squared Adjusted R-squared 0.998939 0.998928 Mean dependent var S.D. dependent var 1610.471 1450.826 Verifique en ambos modelos si el modelo es no lineal. Fundamente su respuesta. (3 puntos) Wald Test: Equation: M1MCNL Test Statistic F-statistic Chi-square Value 1.559692 1.559692 df (1, 190) 1 Probability 0.2132 0.2117 Wald Test: System: M2MV Test Statistic Chi-square Value 1972.229 df 1 Probability 0.0000 1.4. Determine el modelo que predice mejor. Fundamente su respuesta. (2 puntos) 1700 Forecast: INVRF1 Actual: INVR Forecast sample: 1999Q1 2000Q4 Included observations: 8 1600 1500 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion 1400 1300 265.5589 263.8831 15.33302 0.083747 0.987419 0.010089 0.002492 1200 99Q1 99Q2 99Q3 99Q4 00Q1 00Q2 00Q3 00Q4 INVRF1 Dependent Variable: INVR+87.56517733*0.0003400014958*INGR *EXP(0.0003400014958*INGR) Method: Least Squares Sample: 1950Q2 1998Q4 Included observations: 195 Variable Coefficient Std. Error t-Statistic Prob. EXP(0.0003400014958*INGR) 87.56517733*INGR*EXP(0.0003400014958 *INGR) INT 123.7778 4.254744 29.09172 0.0000 0.000275 16.95705 5.66E-06 1.474508 48.67463 11.50014 0.0000 0.0000 2100 Forecast: INVRF2 Actual: INVR Forecast sample: 1999Q1 2000Q4 Included observations: 8 2000 1900 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion 1800 1700 1600 111.4318 95.77976 5.476860 0.031550 0.704741 0.249452 0.045808 1500 99Q1 99Q2 99Q3 99Q4 00Q1 00Q2 00Q3 00Q4 INVRF2 2º Comente y fundamente su respuesta. (3 puntos) Toda prueba de hipótesis de un modelo no lineal es similar a las pruebas de hipótesis de un modelo lineal; por lo tanto, no existe diferencias entre ambos tipo de modelos.