SOLUCIÓN DEL EXAMEN PARCIAL DE ECONOMETRIA II ?· UNIVERSIDAD NACIONAL DE PIURA FACULTAD DE ECONOMIA…

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  • UNIVERSIDAD NACIONAL DE PIURA

    FACULTAD DE ECONOMIA

    DPTO. ACAD. DE ECONOMIA

    SOLUCIN DEL EXAMEN PARCIAL DE ECONOMETRIA II

    1 El investigador especifica el siguiente modelo:

    Se le pide: 1.1. Realice la prueba de exogeneidad en la segunda ecuacin. (3 puntos)

    Dependent Variable: CAG

    Method: Least Squares

    Sample (adjusted): 1993 2005

    Included observations: 13 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C -12.03392 5.137579 -2.342333 0.0517

    CAG(-1) 0.018494 0.407326 0.045404 0.9651

    R 0.127466 0.078025 1.633658 0.1463

    PAO 0.279729 0.095746 2.921558 0.0223

    S(-1) 0.002159 0.005718 0.377661 0.7169

    PP(-1) 0.001482 0.112167 0.013212 0.9898 R-squared 0.939464 Mean dependent var 1.910000

    Modified: 1991 2005 // frcag.fit(f=na) cagf

    1990 NA NA 1.508034 0.259962

    1995 0.737793 0.702714 0.528168 0.616278 1.276703

    2000 1.433483 1.525497 2.912789 3.998291 3.704256

    2005 5.626031

    Dependent Variable: S

    Method: Least Squares

    Sample (adjusted): 1993 2005

    Included observations: 13 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C -1036.393 454.3380 -2.281105 0.0565

    CAG(-1) 46.66760 36.02157 1.295546 0.2362

    R 13.96764 6.900062 2.024277 0.0826

    PAO 20.35668 8.467269 2.404161 0.0472

    S(-1) 0.132446 0.505647 0.261934 0.8009

    PP(-1) -6.676478 9.919396 -0.673073 0.5225 R-squared 0.970661 Mean dependent var 194.7154

    Modified: 1991 2005 // frs.fit(f=na) sf

    1990 NA NA 3.805876 35.58787

    1995 2.209473 44.75248 22.82673 37.49009 106.9751

    2000 156.1114 210.5983 349.8195 473.6552 470.1401

    2005 617.3277

    Dependent Variable: PAG

    Method: Least Squares

    Sample (adjusted): 1993 2005

    Included observations: 13 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 32.71483 5.745066 5.694422 0.0007

  • 2

    CAG 2.573000 1.868245 1.377228 0.2109

    S -0.018198 0.021126 -0.861396 0.4175

    R -0.374703 0.144690 -2.589697 0.0360

    CAGF -1.302921 2.172942 -0.599611 0.5677

    SF 0.019065 0.024680 0.772485 0.4651 R-squared 0.793945 Mean dependent var 18.33692

    Wald Test:

    Equation: MEPAG Test Statistic Value df Probability F-statistic 0.316192 (2, 7) 0.7388

    Chi-square 0.632384 2 0.7289

    Las variables CAG y S se pueden tratar como exgenas. 1.2. Estimar la funcin del precio de aceite de girasol por mnimos cuadrados en dos etapas y obtenga los

    multiplicadores de impacto y dinmicos. (5 puntos)

    Dependent Variable: CAG

    Method: Two-Stage Least Squares

    Sample (adjusted): 1993 2005

    Included observations: 13 after adjustments

    Instrument list: C CAG(-1) R PAO S(-1) PP(-1) Variable Coefficient Std. Error t-Statistic Prob. C -11.98166 5.541744 -2.162074 0.0626

    PAG -0.129451 0.362464 -0.357141 0.7302

    CAG(-1) 0.152649 0.282022 0.541268 0.6031

    R 0.131626 0.067865 1.939537 0.0884

    PAO 0.360569 0.172573 2.089373 0.0701 R-squared 0.915494 Mean dependent var 1.910000

    Adjusted R-squared 0.873241 S.D. dependent var 1.697105

    S.E. of regression 0.604224 Sum squared resid 2.920692

    F-statistic 22.23420 Durbin-Watson stat 1.503953

    Prob(F-statistic) 0.000217 Second-Stage SSR 2.092376

    Dependent Variable: PAG

    Method: Two-Stage Least Squares

    Sample (adjusted): 1993 2005

    Included observations: 13 after adjustments

    Instrument list: C CAG(-1) R PAO S(-1) PP(-1) Variable Coefficient Std. Error t-Statistic Prob. C 32.71483 5.366691 6.095903 0.0002

    CAG 1.270079 1.036573 1.225268 0.2516

    S 0.000867 0.011919 0.072749 0.9436

    R -0.374703 0.135160 -2.772282 0.0217 R-squared 0.768820 Mean dependent var 18.33692

    Adjusted R-squared 0.691760 S.D. dependent var 2.177932

    S.E. of regression 1.209175 Sum squared resid 13.15893

    F-statistic 9.377287 Durbin-Watson stat 1.559705

    Prob(F-statistic) 0.003935 Second-Stage SSR 15.78899

    Dependent Variable: S

  • 3

    Method: Two-Stage Least Squares

    Sample (adjusted): 1993 2005

    Included observations: 13 after adjustments

    Instrument list: C CAG(-1) R PAO S(-1) PP(-1) Variable Coefficient Std. Error t-Statistic Prob. C 92.66438 40.76727 2.273009 0.0491

    CAG 66.07437 17.97751 3.675391 0.0051

    S(-1) 0.555406 0.186232 2.982329 0.0154

    PP(-1) -11.92610 4.425885 -2.694624 0.0246 R-squared 0.985617 Mean dependent var 194.7154

    Adjusted R-squared 0.980822 S.D. dependent var 215.5824

    S.E. of regression 29.85462 Sum squared resid 8021.686

    F-statistic 200.9646 Durbin-Watson stat 3.094825

    Prob(F-statistic) 0.000000 Second-Stage SSR 20350.77

    (%i16) a0:-11.98166335393658;

    (%i17) a1:-0.1294506815323365;

    (%i18) a2:0.1526492830547665;

    (%i19) a3:0.1316257117501045;

    (%i20) a4:0.3605691628840273;

    (%i21) b0:32.71483040789713;

    (%i22) b1:1.270078973095857;

    (%i23) b2:0.0008670782187413609;

    (%i24) b3:-0.3747027108766796;

    (%i25) c0:92.66437759376553;

    (%i26) c1:66.07437063395331;

    (%i27) c2:0.5554062376303326;

    (%i28) c3:-11.92609787064204;

    (%i29) A:matrix([1,-a1,0],[-b1,1,-b2],[-

    c1,0,1]);

    (%i31) B:matrix([a0,a2,a3,a4,0,0],[b0,0,b3,0,0,0],[c0,0,0,0,c2,c3]);

  • 4

    (%i32) FR:invert(A).B;

    (%i33) P[2]:FR[1,2];

    (%i34) P[3]:FR[1,3];

    (%i35) P[4]:FR[1,4];

    (%i49) P[5]:FR[1,5];

    (%i36) P[6]:FR[1,6];

    (%i38) P[8]:FR[2,2];

    (%i39) P[9]:FR[2,3];

    (%i40) P[10]:FR[2,4];

    (%i41) P[11]:FR[2,5];

    (%i42) P[12]:FR[2,6];

    (%i43) P[14]:FR[3,2];

    (%i44) P[15]:FR[3,3];

    (%i45) P[16]:FR[3,4];

    (%i50) P[17]:FR[3,5];

    (%i46) P[18]:FR[3,6];

    (%i2) FRCAG:P[1]+P[2]*CAG[t-1]+P[3]*R[t]+P[4]*PAO[t]+P[5]*S[t-1]+P[6]*PP[t-1]+V1[t];

    (%i3) FRP:P[7]+P[8]*CAG[t-1]+P[9]*R[t]+P[10]*PAO[t]+P[11]*S[t-1]+P[12]*PP[t-1]+V2[t];

    (%i4) FRS:P[13]+P[14]*CAG[t-1]+P[15]*R[t]+P[16]*PAO[t]+P[17]*S[t-1]+P[18]*PP[t-1]+V3[t];

    (%i5) S1:expand(P[7]+P[8]*(P[1]+P[2]*CAG[t-2]+P[3]*R[t-1]+P[4]*PAO[t-1]+P[5]*S[t-2]+P[6]*PP[t-2]+V1[t-

    1])+P[9]*R[t]+P[10]*PAO[t]+P[11]*(P[13]+P[14]*CAG[t-2]+P[15]*R[t-1]+P[16]*PAO[t-1]+P[17]*S[t-

    2]+P[18]*PP[t-2]+V3[t-1])+P[12]*PP[t-1]+V2[t]);

  • 5

    (%i6) S2:expand(P[7]+P[8]*(P[1]+P[2]*(P[1]+P[2]*CAG[t-3]+P[3]*R[t-2]+P[4]*PAO[t-2]+P[5]*S[t-3]+P[6]*PP[t-

    3]+V1[t-2])+P[3]*R[t-1]+P[4]*PAO[t-1]+P[5]*S[t-2]+P[6]*PP[t-2]+V1[t-

    1])+P[9]*R[t]+P[10]*PAO[t]+P[11]*(P[13]+P[14]*(P[1]+P[2]*CAG[t-3]+P[3]*R[t-2]+P[4]*PAO[t-2]+P[5]*S[t-

    3]+P[6]*PP[t-3]+V1[t-2])+P[15]*R[t-1]+P[16]*PAO[t-1]+P[17]*S[t-2]+P[18]*PP[t-2]+V3[t-1])+P[12]*PP[t-

    1]+V2[t]);

    (%i7) MIMPR:diff(S1,R[t]);

    = -0.17066193343684

    (%i8) MIMPPAO:diff(S1,PAO[t]);

    = 0.40842896077476

    (%i9) MIMPPP:diff(S1,PP[t]);

    (%i10) MD1RR:diff(S1,R[t-1]);

    = 0.030753638927022

    (%i11) MD1RPAO:diff(S1,PAO[t-1]);

    = 0.06155963991418

    (%i12) MD1RPP:diff(S1,PP[t-1]);

    = -0.008824546431509

    (%i13) MD2RR:diff(S2,R[t-2]);

    = 0.0040061483436272

    (%i14) MD2RPAO:diff(S2,PAO[t-2]);

    = 0.0080191176745523

    (%i15) MD2RPP:diff(S2,PP[t-2]);

    = -0.0046726648416611

    1.3. En la funcin del consumo de aceite de girasol, verifique si la perturbacin es ruido blanco. (4 puntos)

  • 6

    0

    1

    2

    3

    4

    5

    -1.0 -0.5 0.0 0.5 1.0

    Series: ResidualsSample 1993 2005

    Observations 13

    Mean -2.48e-15

    Median -0.031706

    Maximum 0.969941

    Minimum -0.873880

    Std. Dev. 0.493347

    Skewness 0.243780

    Kurtosis 2.658040

    Jarque-Bera 0.192103

    Probability 0.908417

    Los residuos se distribuyen normal (0.192103 < 5.99 o 0.908417 > 0.05).

    Sample: 1993 2005

    Included observations: 13 Autocorrelation Partial Correlation AC PAC Q-Stat Prob . |** . | . |** . | 1 0.220 0.220 0.7898 0.374

    ****| . | ****| . | 2 -0.491 -0.568 5.0710 0.079

    Los residuos no presentan autocorrelacin de primer orden (0.7898 < 3.84 o 0.374 > 0.05 ) ni de segundo orden

    (5.0710 < 5.99 o 0.079 > 0.05).

    Breusch-Godfrey Serial Correlation LM Test: Obs*R-squared 0.754085 Prob. Chi-Square(1) 0.3852 Dependent Variable: RESID

    Method: Two-Stage Least Squares

    Sample: 1993 2005

    Included observations: 13

    Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C 0.029320 5.750154 0.005099 0.9961

    PAG -0.036718 0.380220 -0.096569 0.9258

    CAG(-1) -0.060265 0.306678 -0.196509 0.8498

    R 0.002701 0.070535 0.038296 0.9705

    PAO 0.022083 0.182189 0.121212 0.9069

    RESID(-1) 0.263110 0.400750 0.656544 0.5325 R-squared 0.058007 Mean dependent var -2.48E-15

    No existe autocorrelacin de primer orden (F = 0.4310531 < F(1,7) = 5.59145).

    Breusch-Godfrey Serial Correlation LM Test: Obs*R-squared 5.895989 Prob. Chi-Square(2) 0.0524 Dependent Variable: RESID

    Method: Two-Stage Least Squares

    Sample: 1993 2005

    Included observations: 13

    Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob.

  • 7

    C 4.105370 5.118936 0.801997 0.4531

    PAG -0.292402 0.336000 -0.870245 0.4176

    CAG(-1) 0.025919 0.255664 0.101380 0.9226

    R -0.042387 0.061930 -0.684444 0.5192

    PAO 0.112136 0.155988 0.718878 0.4992

    RESID(-1) 0.448035 0.341422 1.312264 0.2374

    RESID(-2) -0.721900 0.346411 -2.083943 0.0823 R-squared 0.453538 Mean dependent var -2.48E-15

    No existe autocorrelacin de segundo orden (F = 2.48986023) < F(2,6) = 5.14325).

    Heteroskedasticity Test: White F-statistic 0.517391 Prob. F(4,8) 0.7259

    Obs*R-squared 2.671846 Prob. Chi-Square(4) 0.6142

    Scaled explained SS 0.838822 Prob. Chi-Square(4) 0.9332

    Existe homocedasticidad de los residuos (2.671846 < 9.49 o 0.6142 > 0.05).

    Heteroskedasticity Test: ARCH F-statistic 0.318088 Prob. F(1,10) 0.5852

    Obs*R-squared 0.369938 Prob. Chi-Square(1) 0.5430

    N o Existe heterocedasticidad condicional autoregresiva de primer orden (0.369938 < 3.84 o 0.5430 > 0.05).

    Heteroskedasticity Test: ARCH F-statistic 0.528916 Prob. F(2,8) 0.6085

    Obs*R-squared 1.284651 Prob. Chi-Square(2) 0.5261

    N o Existe heterocedasticidad condicional autoregresiva de segundo orden (1.284651 < 3.84 o 0.5261 > 0.05).

    1.4. Determine la estabilidad del modelo. (3 puntos)

    (%i51) C:matrix([P[2],0,P[5]],[P[8],0,P[11]],[P[14],0,P[17]]);

    (%i53) D:matrix([l,0,0],[0,l,0],[0,0,l]);

    (%i54) E:determinant(D-C);

  • 8

    (%i55) F:allroots(E=0,l);

    El modelo es estable porque las races son menores a uno. 2 Comente y fundamente su respuesta. (5 puntos) 2.1. Todo modelo que pasa la etapa de evaluacin sirve para predecir. 2.2. El test de causalidad de Granger nos sirve para determinar si un modelo es de ecuaciones

    simultneas, es decir, que existe causalidad recproca.

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