UNIVERSIDAD NACIONAL DE PIURA FACULTAD DE ECONOMIA DPTO. ACAD. DE ECONOMIA

PRIMERA PRCTICA CALIFICADA DE ECONOMETRIA II

1 El investigador especifica el siguiente modelo: INFLA = a + b DEV + c INFLA(-1) + U1 DEV = e + f INFLA + g OM + U2 Se le pide: 1.1. Determinar que tipo de variable es DEV. (3 puntos)

DEV es una variable endgena porque la 1 0; 1 0; 1 = 0. 1.2. Verificar que INFLA se puede tratar como exgena. (3 puntos)

Dependent Variable: INFLA

Method: Least Squares

Sample (adjusted): 1966 1995

Included observations: 30 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. C -82.57999 52.31249 -1.578590 0.1261

OM 1.881879 0.070400 26.73136 0.0000

INFLA(-1) 0.057916 0.036004 1.608608 0.1193

R-squared 0.969493 Mean dependent var 439.0467

Dependent Variable: DEV

Method: Least Squares

Sample (adjusted): 1966 1995

Included observations: 30 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. C 13.78205 68.01619 0.202629 0.8410

INFLA 3.551016 0.196643 18.05815 0.0000

OM -1.196951 1.222981 -0.978716 0.3367

INFLAF -1.798276 0.664943 -2.704408 0.0119

R-squared 0.981510 Mean dependent var 467.7206

Wald Test:

Equation: EQ02

Test Statistic Value df Probability

F-statistic 7.313823 (1, 26) 0.0119

Chi-square 7.313823 1 0.0068

INFLA DEV INFLA(-1) OM

U2 U1

U1(-1)

2

Por lo tanto, INFLA no se puede tratar como exgena (0.0119 < 0.05).

1.3. Determine si DEV precede a INFLA. (2 puntos)

Pairwise Granger Causality Tests

Sample: 1965 1995

Lags: 1

Null Hypothesis: Obs F-Statistic Probability

DEV does not Granger Cause INFLA 30 37.2895 1.6E-06

Lags: 2

DEV does not Granger Cause INFLA 29 96.3697 3.4E-12

Lags: 3

DEV does not Granger Cause INFLA 28 254.866 1.1E-16

Lags: 4

DEV does not Granger Cause INFLA 27 239.977 2.4E-15

Lags: 5

DEV does not Granger Cause INFLA 26 259.265 5.3E-14

Lags: 6

DEV does not Granger Cause INFLA 25 238.378 9.2E-12

Lags: 7

DEV does not Granger Cause INFLA 24 113.790 4.7E-08

Por lo tanto, DEV precede a INFLA.

1.4. Estimar la inflacin por mnimos cuadrados bietpicos y verifique si los residuos son ruido blanco. (5 puntos)

Dependent Variable: INFLA

Method: Two-Stage Least Squares

Sample (adjusted): 1966 1995

Included observations: 30 after adjustments

Instrument list: C INFLA(-1) OM

Variable Coefficient Std. Error t-Statistic Prob. C 34.69346 121.1971 0.286257 0.7769

DEV 0.895496 0.078979 11.33837 0.0000

INFLA(-1) -0.032987 0.088073 -0.374546 0.7109

R-squared 0.830432 Mean dependent var 439.0467

3

Sample: 1966 1995

Included observations: 30

Autocorrelation Partial Correlation AC PAC Q-Stat Prob

******| . | ******| . | 1 -0.706 -0.706 16.478 0.000

. |**. | ****| . | 2 0.260 -0.473 18.799 0.000

Breusch-Godfrey Serial Correlation LM Test:

Obs*R-squared 19.04021 Probability 0.000013

Dependent Variable: RESID

Method: Two-Stage Least Squares

Variable Coefficient Std. Error t-Statistic Prob. C 0.164135 3.965196 0.041394 0.9673

DEV 0.096410 0.059906 1.609353 0.1196

INFLA(-1) 0.061732 0.081109 0.761095 0.4534

RESID(-1) -0.757757 0.182295 -4.156761 0.0003

R-squared 0.634674 Mean dependent var -4.74E-14

Breusch-Godfrey Serial Correlation LM Test:

Obs*R-squared 25.41995 Probability 0.000003

Dependent Variable: RESID

Method: Two-Stage Least Squares

Variable Coefficient Std. Error t-Statistic Prob. C 0.262797 2.614112 0.100530 0.9207

DEV -0.099776 0.051623 -1.932780 0.0647

INFLA(-1) 0.357758 0.073319 4.879495 0.0001

RESID(-1) -1.916799 0.230260 -8.324508 0.0000

RESID(-2) -0.907620 0.153804 -5.901147 0.0000

R-squared 0.847332 Mean dependent var -4.74E-14

White Heteroskedasticity Test:

F-statistic 18.29038 Probability 0.000000

Obs*R-squared 22.35953 Probability 0.000170

Dependent Variable: RESID^2

Method: Least Squares

Sample: 1966 1995

Included observations: 30

4

Variable Coefficient Std. Error t-Statistic Prob. C -404686.6 159624.4 -2.535243 0.0179

DEV 1223.399 498.8658 2.452360 0.0215

DEV^2 -0.209424 0.044965 -4.657488 0.0001

INFLA(-1) 6877.288 1172.786 5.864059 0.0000

INFLA(-1)^2 -0.908351 0.155901 -5.826473 0.0000

R-squared 0.745318 Mean dependent var 353010.9

White Heteroskedasticity Test:

F-statistic 128.9509 Probability 0.000000

Obs*R-squared 28.92337 Probability 0.000024

Dependent Variable: RESID^2

Method: Least Squares

Sample: 1966 1995

Included observations: 30

Variable Coefficient Std. Error t-Statistic Prob. C -166608.2 64244.77 -2.593335 0.0159

DEV 5303.023 387.6539 13.67979 0.0000

DEV^2 -3.261528 0.252905 -12.89626 0.0000

DEV*INFLA(-1) 8.505432 0.703145 12.09628 0.0000

INFLA(-1) -917.8264 785.6013 -1.168311 0.2542

INFLA(-1)^2 0.025842 0.097632 0.264693 0.7935

R-squared 0.964112 Mean dependent var 353010.9

ARCH Test:

F-statistic 5.864728 Probability 0.022439

Obs*R-squared 5.175066 Probability 0.022913

Dependent Variable: RESID^2

Method: Least Squares

Sample (adjusted): 1967 1995

Included observations: 29 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. C 210907.4 236635.2 0.891277 0.3807

RESID^2(-1) 0.422434 0.174435 2.421720 0.0224

R-squared 0.178451 Mean dependent var 365161.7

5

ARCH Test:

F-statistic 3.404235 Probability 0.049257

Obs*R-squared 5.993283 Probability 0.049955

Dependent Variable: RESID^2

Method: Least Squares

Sample (adjusted): 1968 1995

Included observations: 28 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. C 265455.7 248505.6 1.068208 0.2956

RESID^2(-1) 0.509999 0.195457 2.609260 0.0151

RESID^2(-2) -0.211910 0.195458 -1.084170 0.2886

R-squared 0.214046 Mean dependent var 378181.6

Modh = modrho*sqr(modt/(1-modt*modvb3)) = -4.411001

2 Comente y fundamente su respuesta. (7 puntos) 2.1. En todo modelo multiecuacional se puede aplicar la prueba de causalidad y de exogeneidad. 2.2. La superexogeneidad requiere que exista precedencia.

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-2000 -1000 0 1000 2000 3000

Series: Residuals

Sample 1966 1995

Observations 30

Mean -4.74e-14

Median -25.18521

Maximum 2586.527

Minimum -1678.946

Std. Dev. 604.3043

Skewness 1.918302

Kurtosis 14.27546

Jarque-Bera 177.3195

Probability 0.000000