ECONOMETRÍA II PRÁCTICAS DE ORDENADOR. Práctica 3

ECONOMETRÍA II PRÁCTICAS DE ORDENADOR Práctica 3 Considere la ecuación de inversión RINV t = β 1 +β 2 RPIB t +β 3 r t +u t donde RINV es la inversión real privada, RPIB es el PIB real y r es el tipo de interés real. El fichero invers.wf1 contiene datos sobre el PIB nominal (pib), la inversión nominal privada (invers), el tipo de interés nominal (i) y el deflactor implícito del PIB (def pib) para los Estados Unidos entre los años 1959-90. Con estos datos: a) Estime la ecuación de inversión por MCO. Comente los resultados. b) Contraste la hipótesis nula de ausencia de autocorrelación serial en las perturbaciones utilizando el estadístico de Durbin-Watson. c) Contraste la hipótesis nula de ausencia de autocorrelación serial en las perturbaciones frente a la alternativa de autocorrelación de orden 1, 2 o 3. Realice primero el contraste generando las variables que necesite y efectuando la regresión apropiada. A continuación utilice el comando que proporciona EVIEWS para realizar el contraste de Breusch-Godfrey y compare los resultados obtenidos. d) Estime de nuevo la ecuación de inversión por MCO y calcule los errores estándar válidos bajo autocorrelación de primer orden. Compárelos con los que obtuvo en el apartado a). e) Calcule el estimador de Cochrane-Orcutt y el estimador de Prais-Winsten (utilice la regresión de los residuos sobre el primer retardo de los residuos para estimar ρ). Compare los resultados con los del apartado anterior. f) Suponga ahora que la inversión real depende del Producto Interior Bruto, del tipo de interés nominal y de la inflación, es decir, considere la ecuación de inversión RINV t = α 1 +α 2 RPIB t +α 3 i t +α 4 π t +u t donde π es la inflación. Repita todos los apartados anteriores utilizando este modelo. g) En base a los resultados del apartado f), contraste si la inversión real depende del tipo de interés nominal y de la inflación, o si por el contrario es más adecuado suponer que solo depende del tipo de interés real. 1

Tabla 1 Dependent Variable: RINV Sample (adjusted): 1960 1990 Included observations: 31 after adjustments Práctica 3 C -259.4787 151.4733-1.713032 0.0978 RPIB 0.183682 0.009275 19.80482 0.0000 R -30.24877 16.69145-1.812231 0.0807 R-squared 0.943668 Mean dependent var 2853.475 Adjusted R-squared 0.939644 S.D. dependent var 920.1289 S.E. of regression 226.0515 Akaike info criterion 13.77117 Sum squared resid 1430780. Schwarz criterion 13.90994 Log likelihood -210.4531 F-statistic 234.5272 Durbin-Watson stat 0.785857 Prob(F-statistic) 0.000000 Tabla 2 Dependent Variable: RES Sample (adjusted): 1963 1990 Included observations: 28 after adjustments RES(-1) 0.770839 0.229203 3.363130 0.0028 RES(-2) -0.093031 0.262035-0.355031 0.7259 RES(-3) 0.187040 0.269254 0.694659 0.4945 C 75.82614 166.6597 0.454976 0.6536 RPIB -0.002099 0.009647-0.217600 0.8297 R -21.40617 18.01810-1.188037 0.2475 R-squared 0.383256 Mean dependent var 5.170452 Adjusted R-squared 0.243087 S.D. dependent var 229.3733 S.E. of regression 199.5565 Akaike info criterion 13.61748 Sum squared resid 876101.1 Schwarz criterion 13.90295 Log likelihood -184.6447 F-statistic 2.734242 Durbin-Watson stat 1.787088 Prob(F-statistic) 0.045560

Tabla 3 Breusch-Godfrey Serial Correlation LM Test: F-statistic 5.175111 Probability 0.006411 Obs*R-squared 11.87616 Probability 0.007820 Test Equation: Dependent Variable: RESID C 42.48520 129.7087 0.327543 0.7460 RPIB -0.000343 0.007786-0.044112 0.9652 R -22.18437 16.75853-1.323766 0.1976 RESID(-1) 0.776073 0.215352 3.603734 0.0014 RESID(-2) -0.096817 0.246463-0.392826 0.6978 RESID(-3) 0.181932 0.253042 0.718979 0.4788 R-squared 0.383102 Mean dependent var -7.77E-13 Adjusted R-squared 0.259722 S.D. dependent var 218.3865 S.E. of regression 187.8984 Akaike info criterion 13.48167 Sum squared resid 882645.2 Schwarz criterion 13.75921 Log likelihood -202.9658 F-statistic 3.105066 Durbin-Watson stat 1.774407 Prob(F-statistic) 0.025777 Tabla 4 Dependent Variable: RINV Sample (adjusted): 1960 1990 Included observations: 31 after adjustments Newey-West HAC Standard Errors & Covariance (lag truncation=3) C -259.4787 194.5269-1.333896 0.1930 RPIB 0.183682 0.014329 12.81855 0.0000 R -30.24877 19.87631-1.521850 0.1393 R-squared 0.943668 Mean dependent var 2853.475 Adjusted R-squared 0.939644 S.D. dependent var 920.1289 S.E. of regression 226.0515 Akaike info criterion 13.77117 Sum squared resid 1430780. Schwarz criterion 13.90994 Log likelihood -210.4531 F-statistic 234.5272 Durbin-Watson stat 0.785857 Prob(F-statistic) 0.000000

Tabla 5 Dependent Variable: RES Sample (adjusted): 1961 1990 Included observations: 30 after adjustments RES(-1) 0.632489 0.169941 3.721813 0.0008 R-squared 0.323250 Mean dependent var 0.244031 Adjusted R-squared 0.323250 S.D. dependent var 222.1155 S.E. of regression 182.7230 Akaike info criterion 13.28658 Sum squared resid 968243.2 Schwarz criterion 13.33329 Log likelihood -198.2988 Durbin-Watson stat 1.741808 Tabla 6 Dependent Variable: TRINV Sample (adjusted): 1961 1990 Included observations: 30 after adjustments TC -283.7442 328.4395-0.863916 0.3952 TRPIB 0.188922 0.017419 10.84589 0.0000 TR -69.54738 18.20152-3.820966 0.0007 R-squared 0.815992 Mean dependent var 1120.223 Adjusted R-squared 0.802362 S.D. dependent var 392.4396 S.E. of regression 174.4651 Akaike info criterion 13.25597 Sum squared resid 821827.7 Schwarz criterion 13.39609 Log likelihood -195.8395 Durbin-Watson stat 1.434192

Tabla 7 Dependent Variable: TRINV2 Date: 05/01/06 Time: 16:19 Sample(adjusted): 1960 1990 Included observations: 31 after adjusting endpoints TC2-255.3039 257.6256-0.990988 0.3302 TRPIB2 0.187567 0.014392 13.03267 0.0000 TR2-69.34682 17.82784-3.889805 0.0006 R-squared 0.815865 Mean dependent var 1119.624 Adjusted R-squared 0.802712 S.D. dependent var 385.8580 S.E. of regression 171.3869 Akaike info criterion 13.21749 Sum squared resid 822457.5 Schwarz criterion 13.35626 Log likelihood -201.8711 Durbin-Watson stat 1.444768 Tabla 8 Dependent Variable: RINV Sample (adjusted): 1960 1990 Included observations: 31 after adjustments C -283.3732 153.0542-1.851457 0.0751 RPIB 0.179123 0.010262 17.45477 0.0000 I -23.08662 18.05713-1.278532 0.2119 INFLA 41.88192 20.12159 2.081442 0.0470 R-squared 0.945808 Mean dependent var 2853.475 Adjusted R-squared 0.939787 S.D. dependent var 920.1289 S.E. of regression 225.7848 Akaike info criterion 13.79696 Sum squared resid 1376427. Schwarz criterion 13.98199 Log likelihood -209.8528 F-statistic 157.0764 Durbin-Watson stat 0.904674 Prob(F-statistic) 0.000000

Tabla 9 Dependent Variable: RESF Sample (adjusted): 1963 1990 Included observations: 28 after adjustments RESF(-1) 0.693582 0.244156 2.840730 0.0098 RESF(-2) -0.152754 0.268944-0.567977 0.5761 RESF(-3) 0.018786 0.274799 0.068362 0.9461 C 54.70100 185.5706 0.294772 0.7711 RPIB 0.000749 0.010581 0.070836 0.9442 I -13.56625 20.09957-0.674952 0.5071 INFLA 4.964262 21.80527 0.227663 0.8221 R-squared 0.306518 Mean dependent var 1.583610 Adjusted R-squared 0.108380 S.D. dependent var 225.5730 S.E. of regression 212.9988 Akaike info criterion 13.77277 Sum squared resid 952738.1 Schwarz criterion 14.10582 Log likelihood -185.8188 F-statistic 1.546991 Durbin-Watson stat 1.756010 Prob(F-statistic) 0.211888

Tabla 10 Breusch-Godfrey Serial Correlation LM Test: F-statistic 3.493242 Probability 0.031095 Obs*R-squared 9.422103 Probability 0.024175 Test Equation: Dependent Variable: RESID Presample missing value lagged residuals set to zero. C 26.67516 138.5073 0.192590 0.8489 RPIB 0.001754 0.009122 0.192257 0.8492 I -13.54642 18.74593-0.722633 0.4769 INFLA 6.455705 19.69599 0.327768 0.7459 RESID(-1) 0.691396 0.228877 3.020816 0.0059 RESID(-2) -0.156638 0.251472-0.622884 0.5392 RESID(-3) 0.016553 0.257591 0.064262 0.9493 R-squared 0.303939 Mean dependent var -3.56E-13 Adjusted R-squared 0.129924 S.D. dependent var 214.1983 S.E. of regression 199.7996 Akaike info criterion 13.62819 Sum squared resid 958077.6 Schwarz criterion 13.95199 Log likelihood -204.2369 F-statistic 1.746621 Durbin-Watson stat 1.753871 Prob(F-statistic) 0.153317

Tabla 11 Dependent Variable: RINV Sample (adjusted): 1960 1990 Included observations: 31 after adjustments Newey-West HAC Standard Errors & Covariance (lag truncation=3) C -283.3732 163.0636-1.737807 0.0936 RPIB 0.179123 0.015648 11.44675 0.0000 I -23.08662 17.74204-1.301238 0.2042 INFLA 41.88192 28.32402 1.478672 0.1508 R-squared 0.945808 Mean dependent var 2853.475 Adjusted R-squared 0.939787 S.D. dependent var 920.1289 S.E. of regression 225.7848 Akaike info criterion 13.79696 Sum squared resid 1376427. Schwarz criterion 13.98199 Log likelihood -209.8528 F-statistic 157.0764 Durbin-Watson stat 0.904674 Prob(F-statistic) 0.000000 Tabla 12 Dependent Variable: RESF Sample (adjusted): 1961 1990 Included observations: 30 after adjustments RESF(-1) 0.557528 0.176107 3.165848 0.0036 R-squared 0.256834 Mean dependent var -0.658729 Adjusted R-squared 0.256834 S.D. dependent var 217.8281 S.E. of regression 187.7833 Akaike info criterion 13.34122 Sum squared resid 1022614. Schwarz criterion 13.38793 Log likelihood -199.1183 Durbin-Watson stat 1.676092

Tabla 13 Dependent Variable: TRINV Sample (adjusted): 1961 1990 Included observations: 30 after adjustments TC -280.1221 298.0091-0.939978 0.3559 TRPIB 0.188483 0.015789 11.93737 0.0000 TI -63.89803 19.12394-3.341259 0.0025 TINFLA 63.31845 27.15958 2.331349 0.0278 R-squared 0.848266 Mean dependent var 1331.298 Adjusted R-squared 0.830758 S.D. dependent var 442.9523 S.E. of regression 182.2260 Akaike info criterion 13.37194 Sum squared resid 863364.3 Schwarz criterion 13.55876 Log likelihood -196.5791 Durbin-Watson stat 1.330865 Tabla 14 Dependent Variable: TRINV Sample (adjusted): 1960 1990 Included observations: 31 after adjustments TC -259.8930 237.4739-1.094407 0.2834 TRPIB 0.187657 0.013838 13.56060 0.0000 TI -63.78468 18.74691-3.402410 0.0021 TINFLA 62.58024 25.91998 2.414363 0.0228 R-squared 0.848771 Mean dependent var 1326.440 Adjusted R-squared 0.831967 S.D. dependent var 436.3463 S.E. of regression 178.8661 Akaike info criterion 13.33107 Sum squared resid 863813.1 Schwarz criterion 13.51610 Log likelihood -202.6315 Durbin-Watson stat 1.338892

Tabla 15 Wald Test: Equation: EQ12 Test Statistic Value df Probability F-statistic 0.002826 (1, 27) 0.9580 Chi-square 0.002826 1 0.9576 Null Hypothesis Summary: Normalized Restriction (= 0) Value Std. Err. C(3) + C(4) -1.204435 22.65614 Restrictions are linear in coefficients.