UNIVERSIDAD NACIONAL DE PIURA

FACULTAD DE ECONOMIA

SOLUCIN DE LA SEGUNDA PRCTICA DE ECONOMETRIA II

1 Considere el modelo estructural siguiente:

EMI = a + b*CT + c*EMI(-1) + d*SPREAD + U1

CT = e + f*EMI + g*CT(-1) + h*TA + U2

Se le pide:

1.1. Estime el crdito total por mnimos cuadrados trietpicos para el periodo 2001:01 - 2009:04 y

determine los multiplicadores de impacto y dinmicos. (6 Puntos)

System: SYS01

Estimation Method: Three-Stage Least Squares

Sample: 2001M02 2009M04

Included observations: 95

Total system (balanced) observations 190

Coefficient Std. Error t-Statistic Prob.

C(1) 439.5786 256.0881 1.716513 0.0878

C(2) 0.003937 0.001814 2.170431 0.0313

C(3) 0.827046 0.076014 10.88017 0.0000

C(4) -1.268965 0.432851 -2.931643 0.0038

C(5) 9610.406 14843.74 0.647439 0.5182

C(6) 2.831510 0.736906 3.842433 0.0002

C(7) 0.955394 0.019673 48.56422 0.0000

C(8) -412.7446 576.7413 -0.715649 0.4751

Determinant residual covariance 3.32E+13

Equation: EMI = C(1) + C(2)*CT + C(3)*EMI(-1) + C(4)*SPREAD

Instruments: C EMI(-1) SPREAD CT(-1) TA

Observations: 95

R-squared 0.986080 Mean dependent var 10571.08

Adjusted R-squared 0.985621 S.D. dependent var 5184.013

S.E. of regression 621.6341 Sum squared resid 35165036

Durbin-Watson stat 2.564317

Equation: CT = C(5) + C(6)*EMI + C(7)*CT(-1) + C(8)*TA

Instruments: C EMI(-1) SPREAD CT(-1) TA

Observations: 95

R-squared 0.997620 Mean dependent var 539090.3

Adjusted R-squared 0.997541 S.D. dependent var 197718.9

S.E. of regression 9803.930 Sum squared resid 8.75E+09

Durbin-Watson stat 1.424073

EMI = P1 + P2*EMI(-1) + P3*SPREAD + P4*CT(-1) + P5*TA + V1

CT = P6 + P7*EMI(-1) + P8*SPREAD + P9*CT(-1) + P10*TA + V2

CT = P6 + P7*(P1 + P2*EMI(-2) + P3*SPREAD(-1) + P4*CT(-2) + P5*TA(-1) + V1(-1)) +

P8*SPREAD + P9*( P6 + P7*EMI(-2) + P8*SPREAD(-1) + P9*CT(-2) + P10*TA(-1) + V2(-1)) +

2

P10*TA + V2

CT = (P6+P7*P1+P9*P6) + (P7*P2+ P9*P7)*EMI(-2) + (P7*P4+ P9*P9)*CT(-2) + P8*SPREAD +

(P7*P3+P9*P8)*SPREAD(-1) + P10*TA + (P7*P5+P9*P10)*TA(-1) + ( V2+ P7*V1(-1)+P9*V2(-

1))

A

R1 1.000000 -0.003937

R2 -2.831510 1.000000

B

R1 439.5786 0.827046 -1.268965 0.000000 0.000000

R2 9610.406 0.000000 0.000000 0.955394 -412.7446

FR

R1 482.7927 0.836368 -1.283269 0.003803 -1.643137

R2 10977.44 2.368185 -3.633589 0.966163 -417.3971

MISPREAD = P8 = -3.633589

MITA = P10 = -417.3971

MD1RSPREAD = P7*P3+P9*P8 = fr(2,2)*fr(1,3)-fr(2,4)*fr(2,3) = 0.471621726384948

MD1RTA = P7*P5+P9*P10 = fr(2,2)*fr(1,5)-fr(2,4)*fr(2,5) = 399.38249428631

MD2RSPREAD = (P7*P2+ P9*P7)*P3 + (P7*P4+ P9*P9)*P8 = (FR(2,2)*FR(1,2) +

FR(2,4)*FR(2,2))*FR(1,3) + (FR(2,2)*FR(1,4) + FR(2,4)^2)*FR(2,3) = -8.90250552937832

MD2RTA = (P7*P2+ P9*P7)*P5 + (P7*P4+ P9*P9)*P10 = (FR(2,2)*FR(1,2) +

FR(2,4)*FR(2,2))*FR(1,5) + (FR(2,2)*FR(1,4) + FR(2,4)^2)*FR(2,5) = -400.401960169577

1.2. Determin si puede obtener la forma final del modelo. (4 puntos)

1 00 1

2 47 9

= 1 + 3 + 5 +16 + 8 + 10 +2

1 00 1

2 47 9

= 00

!1 00 1 2 47 9! = 0

! 2 47 9! = 0

($ 2)($ 9) 4 7 = 0 $' (2 + 9)$ + (2 9 4 7) = 0

$ = (2 + 9) )(2 + 9)' 4(2 9 4 7)2

landa1 = ((fr(1,2)+fr(2,4))+sqr((fr(1,2)+fr(2,4))^2-4*(fr(1,2)*fr(2,4)-fr(1,4)*fr(2,2))))/2

= 1.01623920866038

Landa2 = ((fr(1,2)+fr(2,4))-sqr((fr(1,2)+fr(2,4))^2-4*(fr(1,2)*fr(2,4)-fr(1,4)*fr(2,2))))/2

= 0.786292261830141

1.3. Verifique la capacidad predictiva del modelo. (3 puntos)

3

obs CT CT_1 EMI EMI_1

2009M05 1025155, 1027041. 19322.59 19985.78

2009M06 1031614, 1040374. 19562.38 20510.36

2009M07 1039102, 1054606. 21123.82 21021.44

2009M08 1033057, 1069872. 20230.00 21559.45

2009M09 1020450, 1085997. 20315.00 22097.14

2009M10 1034674, 1103083. 20528.00 22651.55

2009M11 1053592, 1120918. 20823.00 23172.78

2009M12 1071925, 1139395. 23548.00 23697.06

Rcrememi = sqr(@sum((emi-emi_1)^2/emi)/8) = 9.99175928420032

Rcremct = sqr(@sum((ct-ct_1)^2/ct)/8) = 48.6099202962821

Epmaemi = @sum(abs(emi-emi_1)/emi)/8 = 0.0579615048775339

Epmact = @sum(abs(ct-ct_1)/ct)/8 = 0.0397604876234572

Uemi = sqr(@sumsq(emi-emi_1)/8)/(sqr(@sumsq(emi)/8)+sqr(@sumsq(emi)/8)) =

0.0335631594992726

Uct = sqr(@sumsq(ct-ct__1)/8)/(sqr(@sumsq(ct)/8)+sqr(@sumsq(ct_1)/8)) = 0.0234338171390143

2 Comente y fundamente su respuesta. (7 puntos)

2.1. El comportamiento dinmico de la serie depender del signo y magnitud de las races caractersticas

cuando estas son reales. Pero dependern del mdulo y el perodo de ciclos en caso de ser complejas.

2.2. Los modelos economtricos resultan especialmente tiles cuando se precisa predicciones a medio y

largo plazo, cuando existe un proceso permanente de revisin de predicciones, cuando es importante

poner de manifiesto los condicionantes de la prediccin y siempre que se disponga de informacin

estadstica suficiente de todas las variables implicadas en el modelo.