PRIMERA PRÁCTICA CALIFICADA DE ECONOMETRIA II 1° El

UNIVERSIDAD NACIONAL DE PIURA
DPTO. ACAD. DE ECONOMETRIA Y METODOS CUANTITATIVOS
PRIMERA PRÁCTICA CALIFICADA DE ECONOMETRIA II
1°
El investigador especifica el siguiente modelo:
GC = a + b PNB + c GC(-1) + U1
GI = d + e (PNB -PNB(-1)) + f PNB(-1) + g R(-4) + U2
R = h + i PNB + j (PNB - PNB(-1)) + k (M - M(-1)) + l R(-1) + U3
PNB = GC + GI + G
Se le pide:
1.1.
Estimar la función inversión por mínimos cuadrados bietápicos y verifique que la perturbación es ruido blanco. (6
puntos)
Dependent Variable: GI
Method: Two-Stage Least Squares
Sample (adjusted): 1972Q1 2009Q1
Included observations: 149 after adjustments
Instrument list: C GC(-1) PNB(-1) R(-4) M-M(-1) R(-1) G
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PNB-PNB(-1)
PNB(-1)
R(-4)
-62.14682
-1.019254
0.230155
-13.32002
12.47107
0.249664
0.008228
1.896503
-4.983279
-4.082497
27.97321
-7.023462
0.0000
0.0001
0.0000
0.0000
R-squared
Adjusted R-squared
S.E. of regression
F-statistic
0.912906
0.911104
43.06564
543.4915
Mean dependent var
S.D. dependent var
Sum squared resid
Durbin-Watson stat
405.6423
144.4405
268924.1
1.238780
Sample: 1972Q1 2009Q1
Included observations: 149
Autocorrelation
.|***
.|*
Partial Correlation
|
|
.|***
.|.
|
|
AC
PAC
Q-Stat
1 0.372 0.372 21.056 0.000
2 0.125 -0.015 23.454 0.000
24
Series: Residuals
Sample 1972Q1 2009Q1
Observations 149
20
16
12
8
4
0
-150
-100
-50
0
Prob
50
100
150
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
1.43e-14
1.690194
150.9629
-162.4246
42.62693
-0.109658
5.357270
Jarque-Bera
Probability
34.79661
0.000000
Breusch-Godfrey Serial Correlation LM Test:
Obs*R-squared
23.51279
Probability
0.000001
Dependent Variable: RESID
Method: Two-Stage Least Squares
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PNB-PNB(-1)
PNB(-1)
R(-4)
RESID(-1)
2.298957
-0.035066
-0.003044
1.277387
0.348226
2.664835
0.023842
0.003836
1.539668
0.078578
0.862701
-1.470733
-0.793452
0.829651
4.431593
0.3897
0.1435
0.4288
0.4081
0.0000
R-squared
0.157804
Mean dependent var
1.43E-14
Breusch-Godfrey Serial Correlation LM Test:
Obs*R-squared
23.72026
Probability
0.000007
Dependent Variable: RESID
Method: Two-Stage Least Squares
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PNB-PNB(-1)
PNB(-1)
R(-4)
RESID(-1)
RESID(-2)
2.401008
-0.037263
-0.003139
1.328669
0.361925
-0.041370
2.680141
0.024328
0.003852
1.547357
0.083665
0.085012
0.895851
-1.531666
-0.815103
0.858670
4.325893
-0.486643
0.3718
0.1278
0.4164
0.3920
0.0000
0.6273
R-squared
0.159196
Mean dependent var
1.43E-14
4.333282
4.266026
Probability
Probability
0.039120
0.038882
ARCH Test:
F-statistic
Obs*R-squared
Dependent Variable: RESID^2
Method: Least Squares
Sample (adjusted): 1972Q2 2009Q1
Included observations: 148 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
RESID^2(-1)
1489.393
0.169769
341.8062
0.081555
4.357419
2.081654
0.0000
0.0391
R-squared
0.028825
Mean dependent var
1797.016
ARCH Test:
F-statistic
Obs*R-squared
2.205784
4.369608
Probability
Probability
0.113873
0.112500
Dependent Variable: RESID^2
Method: Least Squares
Sample (adjusted): 1972Q3 2009Q1
Included observations: 147 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
RESID^2(-1)
RESID^2(-2)
1429.581
0.163237
0.034230
366.9638
0.083260
0.083283
3.895700
1.960577
0.411011
0.0001
0.0519
0.6817
R-squared
0.029725
Mean dependent var
1786.480
White Heteroskedasticity Test:
F-statistic
Obs*R-squared
38.14019
91.94592
Probability
Probability
0.000000
0.000000
Dependent Variable: RESID^2
Method: Least Squares
Sample: 1972Q1 2009Q1
Included observations: 149
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PNB-PNB(-1)
(PNB-PNB(-1))^2
PNB(-1)
PNB(-1)^2
R(-4)
R(-4)^2
5065.567
-57.37079
1.763680
-4.678255
0.000841
495.6960
-23.75207
2591.431
8.129623
0.128659
2.591239
0.000437
419.2194
22.80827
1.954738
-7.057005
13.70818
-1.805412
1.924253
1.182426
-1.041380
0.0526
0.0000
0.0000
0.0731
0.0563
0.2390
0.2995
R-squared
0.617087
Mean dependent var
1804.860
White Heteroskedasticity Test:
F-statistic
Obs*R-squared
26.31825
93.89767
Probability
Probability
0.000000
0.000000
Dependent Variable: RESID^2
Method: Least Squares
Sample: 1972Q1 2009Q1
Included observations: 149
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PNB-PNB(-1)
(PNB-PNB(-1))^2
(PNB-PNB(-1))*PNB(-1)
(PNB-PNB(-1))*R(-4)
PNB(-1)
PNB(-1)^2
PNB(-1)*R(-4)
R(-4)
R(-4)^2
R-squared
1.2.
4707.116
-46.11173
1.820128
-0.022705
6.763227
-4.663337
0.001205
-0.239730
607.8990
4.203946
0.630186
2705.725
38.01827
0.132682
0.018281
3.176839
3.114289
0.000740
0.297096
715.5028
31.03289
1.739687
-1.212883
13.71802
-1.241959
2.128917
-1.497400
1.628869
-0.806914
0.849611
0.135467
Mean dependent var
0.0841
0.2272
0.0000
0.2163
0.0350
0.1366
0.1056
0.4211
0.3970
0.8924
1804.860
Verifique si PNB se puede tratar como exógena en la función consumo. (3 puntos)
Dependent Variable: PNB
Method: Least Squares
Sample (adjusted): 1972Q1 2009Q1
Included observations: 149 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
GC(-1)
PNB(-1)
R(-4)
M-M(-1)
R(-1)
G
-3.080040
0.468748
0.660678
-6.154040
0.780825
-0.226749
0.334458
14.93192
0.099402
0.077507
2.173091
0.413093
2.023923
0.107842
-0.206272
4.715664
8.524095
-2.831929
1.890192
-0.112035
3.101360
0.8369
0.0000
0.0000
0.0053
0.0608
0.9110
0.0023
R-squared
1972Q1
1973Q1
1974Q1
1975Q1
0.999118
Mean dependent var
2433.421
Modified: 1971Q1 2009Q1 // frpnb.fit(f=actual) pnbf
1253.516
1296.611
1321.031
1340.128
1351.291
1366.054
1376.372
1394.327
1426.753
1450.054
1459.957
1453.699
1434.615
1419.906
1420.061
1436.370
Dependent Variable: GC
Method: Least Squares
Sample (adjusted): 1972Q1 2009Q1
Included observations: 149 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PNB
GC(-1)
PNBF
-1.366045
0.254412
0.978050
-0.235553
4.817074
0.036841
0.026841
0.040999
-0.283584
6.905643
36.43881
-5.745335
0.7771
0.0000
0.0000
0.0000
R-squared
0.999618
Mean dependent var
1493.913
Wald Test:
Equation: FE
Test Statistic
Value
F-statistic
Chi-square
1.3.
33.00888
33.00888
df
Probability
(1, 145)
1
0.0000
0.0000
Determine qué tipo de variable es el PNB en la tasa de interés. (3 puntos)
U1t
GCt-1
Rt-4
GCt
GIt
U3t-4
U2t
Gt
PNBt
PNBt-1
Rt-1
Rt
U3t
U3t-1
Mt-Mt-1
La variable PNB es endógena porque las flechas llegan y se tiene:
E (PNBt u 3t +1 ) = 0
E (PNBt u 3t ) = 0
E (PNBt u 3t −1 ) = 0
E (PNBt u 3t − 4 ) ≠ 0
Por lo tanto, la variable PNB en la tercera ecuación es predeterminada.
1.4.
Verifique la causalidad de Granger entre inversión y tasa de interés. (3 puntos)
Pairwise Granger Causality Tests
Sample: 1971Q1 2009Q1
Lags: 3
Null Hypothesis:
Obs
F-Statistic
Probability
R does not Granger Cause GI
GI does not Granger Cause R
150
8.50310
3.07447
3.1E-05
0.02970
Pairwise Granger Causality Tests
Sample: 1971Q1 2009Q1
Lags: 6
Null Hypothesis:
Obs
F-Statistic
Probability
R does not Granger Cause GI
GI does not Granger Cause R
147
6.92339
3.93928
2.0E-06
0.00117
Null Hypothesis:
Obs
F-Statistic
Probability
R does not Granger Cause GI
GI does not Granger Cause R
144
6.66620
1.59897
9.4E-08
0.12246
Null Hypothesis:
Obs
F-Statistic
Probability
R does not Granger Cause GI
GI does not Granger Cause R
141
6.63880
1.99148
6.1E-09
0.03092
Pairwise Granger Causality Tests
Sample: 1971Q1 2009Q1
Lags: 9
Pairwise Granger Causality Tests
Sample: 1971Q1 2009Q1
Lags: 12
2°
Comente y fundamente su respuesta. (5 puntos)
2.1.
Una variable exógena estricta puede considerarse una variable exógena fuerte y viceversa.
2.2.
La prueba de exogeneidad y la de causalidad de Granger se puede aplicar a todo modelo multuecuacional.