SOLUCIÓN DEL EXAMEN PARCIAL DE ECONOMETRIA I

UNIVERSIDAD NACIONAL DE PIURA
FACULTAD DE ECONOMIA
SOLUCIÓN DEL EXAMEN PARCIAL DE ECONOMETRIA I
1º
El investigador especifica los modelos siguientes:
MODELO 1: IMP(t) = a + b IMP(t-1) + c IPM(t) + u(t)
MODELO 2: IMP(t) = a + b(0) PBI(t) + b(1) PBI(t-1) + .... + b(9) PBI(t-9) + c IPM(t) + u(t)
MODELO 3: IMP(t) = a + b PBI(t)^c + d IPM(t) + u(t)
se le pide:
1.1.
Estimar el modelo 1. (4 puntos)
Dependent Variable: IMP
Method: Least Squares
Sample (adjusted): 1951 2009
Included observations: 59 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
IPM
IMP(-1)
-1064.516
41.00726
0.675121
392.7626
9.442247
0.090937
-2.710328
4.342956
7.424072
0.0089
0.0001
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.924676
0.921986
1553.922
1.35E+08
-515.7416
1.500327
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
4193.805
5563.430
17.58446
17.69010
343.7274
0.000000
mod1h = mod1rho*sqr(mod1t/(1-mod1t*mod1vb3)) = 2,681667
Sample: 1951 2009
Included observations: 59
Autocorrelation
. |*** |
. |*. |
Partial Correlation
. |*** |
.|. |
AC
PAC
Q-Stat
Prob
1 0.444 0.444 12.246 0.000
2 0.170 -0.034 14.064 0.001
mod1qbp1 = 59*0.444247104750863^2 = 11,64397
mod1qbp2 = 59*(0.444247104750863^2+0.169694926721249^2) = 13,34296
Breusch-Godfrey Serial Correlation LM Test:
F-statistic
Obs*R-squared
14.18760
12.09853
Probability
Probability
0.000405
0.000505
Dependent Variable: RESID
Method: Least Squares
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
IPM
-1359.274
62.14667
505.0616
18.55766
-2.691303
3.348843
0.0094
0.0015
2
IMP(-1)
RESID(-1)
R-squared
-0.726546
1.300835
0.205060
0.209523
0.345357
-3.467629
3.766643
Mean dependent var
0.0010
0.0004
4.93E-13
Breusch-Godfrey Serial Correlation LM Test:
F-statistic
Obs*R-squared
10.57244
16.60190
Probability
Probability
0.000133
0.000248
Dependent Variable: RESID
Method: Least Squares
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
IPM
IMP(-1)
RESID(-1)
RESID(-2)
-2022.020
85.57564
-0.932152
1.033464
1.001108
558.0713
20.31715
0.218609
0.349684
0.418012
-3.623228
4.211990
-4.264021
2.955417
2.394928
0.0006
0.0001
0.0001
0.0046
0.0201
R-squared
0.281388
R1
R2
R3
Mean dependent var
4.93E-13
BVI
-4128,224
169,3952
-0,700391
Dependent Variable: IMP
Method: Two-Stage Least Squares
Sample (adjusted): 1951 2009
Included observations: 59 after adjustments
Instrument list: C IPM IPM(-1)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
IPM
IMP(-1)
-4128.224
169.3952
-0.700391
1423.646
51.33165
0.540795
-2.899755
3.300014
-1.295114
0.0053
0.0017
0.2006
R-squared
Adjusted R-squared
S.E. of regression
F-statistic
Prob(F-statistic)
1.2.
0.616928
0.603247
3504.313
63.00741
0.000000
Mean dependent var
S.D. dependent var
Sum squared resid
Durbin-Watson stat
Estimar el modelo 2. (4 puntos)
Dependent Variable: IMP
Method: Least Squares
Sample (adjusted): 1959 2009
Included observations: 51 after adjustments
4193.805
5563.430
6.88E+08
0.135987
3
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
IPM
PDL01
PDL02
PDL03
PDL04
PDL05
PDL06
PDL07
-1127.346
133.6116
0.001935
-0.022419
-0.018262
0.005715
0.001894
-0.000331
-2.51E-05
682.6739
11.63569
0.021044
0.027928
0.020928
0.007808
0.003217
0.000403
0.000124
-1.651368
11.48292
0.091931
-0.802756
-0.872599
0.731984
0.588754
-0.820768
-0.203277
0.1061
0.0000
0.9272
0.4266
0.3878
0.4682
0.5592
0.4164
0.8399
R-squared
0.972611
Mean dependent var
4805.639
Dependent Variable: IMP
Method: Least Squares
Sample (adjusted): 1959 2009
Included observations: 51 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
IPM
PDL01
PDL02
PDL03
PDL04
PDL05
PDL06
-1133.645
133.4893
-0.001451
-0.026909
-0.014283
0.007083
0.001248
-0.000404
674.3251
11.48986
0.012720
0.016901
0.007326
0.003915
0.000489
0.000177
-1.681155
11.61802
-0.114071
-1.592121
-1.949544
1.809161
2.550883
-2.287083
0.1000
0.0000
0.9097
0.1187
0.0578
0.0774
0.0144
0.0272
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.972584
0.968121
1027.034
45356345
-421.6709
0.811361
Lag Distribution of
PBI
.
* .
*.
*
*
*.
* .
*.
.*
* .
*|
|
|
|
|
|
|
|
|
|
i Coefficient
0
1
2
3
4
5
6
7
8
9
Sum of Lags
1.3.
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
Std. Error
4805.639
5752.171
16.84984
17.15287
217.9180
0.000000
t-Statistic
0.15761
-0.04124
-0.02853
0.00574
-0.00145
-0.03472
-0.04870
-0.01658
0.02141
-0.09047
0.02731
0.02809
0.01307
0.01672
0.01272
0.01296
0.01633
0.01382
0.02925
0.03143
5.77140
-1.46813
-2.18296
0.34343
-0.11407
-2.67957
-2.98156
-1.19987
0.73180
-2.87829
-0.07693
0.01731
-4.44307
Estimar el modelo 3 considerando: a=-3000, b=0.00002, c=2, d=80, aplicando mínimos cuadrados no lineales
4
y máxima verosimilitud. (3 puntos)
Dependent Variable: IMP
Method: Least Squares
Sample: 1950 2009
Included observations: 60
Convergence achieved after 6 iterations
IMP=C(1)+C(2)*PBI^C(3)+C(4)*IPM
C(1)
C(2)
C(3)
C(4)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Coefficient
Std. Error
t-Statistic
Prob.
-3000.000
1.79E-07
2.015007
79.99951
607.9314
1.40E-06
0.623103
16.28905
-4.934767
0.128523
3.233826
4.911243
0.0000
0.8982
0.0021
0.0000
0.893813
0.888124
1853.256
1.92E+08
-534.5485
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Durbin-Watson stat
4126.397
5540.738
17.95162
18.09124
0.403725
System: MOD3MV
Estimation Method: Full Information Maximum Likelihood (Marquardt)
Sample: 1950 2009
Included observations: 60
Total system (balanced) observations 60
Convergence achieved after 51 iterations
C(1)
C(2)
C(3)
C(4)
Coefficient
Std. Error
z-Statistic
Prob.
-3000.000
5.28E-08
2.118593
79.99596
567.5362
4.73E-07
0.721934
16.14503
-5.286006
0.111576
2.934608
4.954836
0.0000
0.9112
0.0033
0.0000
Log Likelihood
Determinant residual covariance
-533.5877
3104552.
Equation: IMP=C(1)+C(2)*PBI^C(3)+C(4)*IPM
Observations: 60
R-squared
0.897160 Mean dependent var
Adjusted R-squared
0.891650 S.D. dependent var
S.E. of regression
1823.816 Sum squared resid
Durbin-Watson stat
0.408951
1.4.
Obtener los multiplicadores del modelo 1 y 2. (3 puntos)
MODELO 1: IMP(t) = a + b IMP(t-1) + c IPM(t) + u(t)
M. I. IPM = c = 169.3952
M. D. 1R IPM = bc = 169.3952 (-0.700391) = - 118.6428735
M. D. 2R IPM = b^2 c =169.3952 (-0.700391)^2 = 83.09640083
4126.397
5540.738
1.86E+08
5
M. T. IPM =
= 99.62132239
MODELO 2: IMP(t) = a + b(0) PBI(t) + b(1) PBI(t-1) + .... + b(9) PBI(t-9) + c IPM(t) + u(t)
M. I. IPM = c = 133.4893
M. I. PBI = b(0) = 0.15761
M. D. 1R PBI = b(1) = -0.04124
M. D. 2R PBI = b(2) = -0.02853
…………………….
M. D. 9R PBI = b(9) = -0.09047
M. T. PBI = -0.07693
1.5.
Seleccione la mejor estimación, justifique su respuesta. (3 puntos)
2º
Comente y fundamente su respuesta. (3 puntos)
Todos los modelos dinámicos requieren de la verificación de autocorelación para determinar el método de
estimación adecuado.