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.