Modelo 1

UNIVERSIDAD NACIONAL DE PIURA
FACULTAD DE ECONOMIA
SOLUCIÓN DE LA SEGUNDA PRACTICA CALIFICADA DE ECONOMETRIA I
1º
El investigador especifica los modelos:
Modelo 1:
INVR = a + b INGR + c INT^d + e INT(-1) + u
Modelo 2:
INVR = f exp(g INGR) + h INT + v
Se le pide:
1.1.
Estimar el modelo 1 para el periodo 1950:2 - 1998:4 por mínimos cuadrados no lineales y utilizando la
transformación de Box y Cox (dos decimales). (6 puntos)
Dependent Variable: INVR
Method: Least Squares
Sample (adjusted): 1950Q2 1998Q4
Included observations: 195 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
INGR
INT
INT(-1)
-129.9682
0.169501
14.32042
-17.56753
11.94188
0.002585
6.062011
6.065603
-10.88340
65.57389
2.362323
-2.896255
0.0000
0.0000
0.0192
0.0042
R-squared
0.965004
Mean dependent var
610.9615
Dependent Variable: INVR
Method: Least Squares
Sample (adjusted): 1950Q2 1998Q4
Included observations: 195 after adjustments
Convergence achieved after 32 iterations
INVR =C(1)+C(2)*INGR+C(3)*INT^C(4)+C(5)*INT(-1)
C(1)
C(2)
C(3)
C(4)
C(5)
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
Coefficient
Std. Error
t-Statistic
Prob.
-107.9619
0.171953
1.811234
1.761024
-17.19042
13.35914
0.002826
3.444937
0.609367
6.118844
-8.081500
60.84580
0.525767
2.889924
-2.809423
0.0000
0.0000
0.5997
0.0043
0.0055
0.965770
0.965049
62.25518
736384.4
-1079.753
0.206084
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
TRANSFORMACIÓN DE BOX Y COX
BETA 2
SUMA RESIDUAL
0
0.1
773188.1
774033.5
610.9615
333.0013
11.12567
11.20959
1340.158
0.000000
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
774645.9
774842.6
774399.7
773082.4
770707.9
767232.7
762824.9
757865.7
752851.6
748246.1
744362.9
741333.3
739141.1
737684.7
736829.4
736441.9
736405.5
736625.8
737029.3
Dependent Variable: INVR
Method: Least Squares
Sample: 1950Q2 1998Q4
Included observations: 195
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
INGR
(INT^1.8-1)/1.8
INT(-1)
-106.2917
0.172010
2.891388
-16.93023
13.50313
0.002663
0.915675
4.488140
-7.871635
64.58188
3.157656
-3.772215
0.0000
0.0000
0.0018
0.0002
R-squared
Adjusted R-squared
0.965769
0.965231
Mean dependent var
S.D. dependent var
TRANSFORMACION DE BOX COX
BETA 2
SUMA RESIDUAL
1.71
1.72
1.73
1.74
1.75
1.76
1.77
1.78
1.79
1.8
1.81
1.82
736424.1
736409.8
736398.8
736391.0
736386.2
736384.4
736385.6
736389.5
736396.2
736405.5
736417.3
736431.7
610.9615
333.0013
1.83
1.84
1.85
1.86
1.87
1.88
1.89
736448.4
736467.4
736488.6
736512.0
736537.5
736565.0
736594.5
Dependent Variable: INVR
Method: Least Squares
Sample: 1950Q2 1998Q4
Included observations: 195
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
INGR
(INT^1.76-1)/1.76
INT(-1)
-106.1473
0.171951
3.197832
-17.19724
13.52458
0.002658
1.012432
4.565223
-7.848475
64.68756
3.158566
-3.767011
0.0000
0.0000
0.0018
0.0002
R-squared
Adjusted R-squared
1.2.
0.965770
0.965232
Mean dependent var
S.D. dependent var
610.9615
333.0013
Estimar el modelo 2 para el periodo 1950:2 - 1998:4 por máxima verosimilitud y mediante la serie de Taylor. (6
puntos)
Dependent Variable: INVR
Method: Least Squares
Sample: 1950Q2 1998Q4
Included observations: 195
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
INT
358.8880
48.01823
45.11622
7.531823
7.954743
6.375380
0.0000
0.0000
R-squared
0.173962
Mean dependent var
610.9615
System: M2MV
Estimation Method: Full Information Maximum Likelihood (Marquardt)
Sample: 1950Q2 1998Q4
Included observations: 195
Convergence achieved after 31 iterations
C(1)
C(2)
C(3)
Coefficient
Std. Error
z-Statistic
Prob.
127.7781
0.000279
17.69937
6.188010
6.28E-06
1.314676
20.64930
44.40979
13.46292
0.0000
0.0000
0.0000
Log Likelihood
Determinant residual covariance
-1029.213
2248.812
Equation: INVR=C(1)*EXP(C(2)*INGR)+C(3)*INT
Observations: 195
R-squared
0.979616 Mean dependent var
Adjusted R-squared
0.979403 S.D. dependent var
610.9615
333.0013
APROXIMACIÓN APLICANDO TAYLOR
I
T
R2 AJUSTADO
AKAIKE
SCHWARZ
1
2
3
4
5
6
7
8
195
195
195
195
195
195
195
195
0.963087
0.999925
0.999926
0.999690
0.998928
0.998041
0.998242
0.998236
11.17025
10.93092
11.25595
10.85552
10.57461
10.58673
10.58680
10.58680
11.22060
10.98127
11.30631
10.90587
10.62497
10.63708
10.63716
10.63716
Dependent Variable: _Y+87.56517733*0.0003400014958*_X
*EXP(0.0003400014958*_X)
Method: Least Squares
Sample: 1950Q2 1998Q4
Included observations: 195
1.3.
Variable
Coefficient
Std. Error
t-Statistic
Prob.
EXP(0.0003400014958*_X)
87.56517733*_X*EXP(0.0003400014958*_
X)
INT
123.7778
4.254744
29.09172
0.0000
0.000275
16.95705
5.66E-06
1.474508
48.67463
11.50014
0.0000
0.0000
R-squared
Adjusted R-squared
0.998939
0.998928
Mean dependent var
S.D. dependent var
1610.471
1450.826
Verifique en ambos modelos si el modelo es no lineal. Fundamente su respuesta. (3 puntos)
Wald Test:
Equation: M1MCNL
Test Statistic
F-statistic
Chi-square
Value
1.559692
1.559692
df
(1, 190)
1
Probability
0.2132
0.2117
Wald Test:
System: M2MV
Test Statistic
Chi-square
Value
1972.229
df
1
Probability
0.0000
1.4.
Determine el modelo que predice mejor. Fundamente su respuesta. (2 puntos)
1700
Forecast: INVRF1
Actual: INVR
Forecast sample: 1999Q1 2000Q4
Included observations: 8
1600
1500
Root Mean Squared Error
Mean Absolute Error
Mean Abs. Percent Error
Theil Inequality Coefficient
Bias Proportion
Variance Proportion
Covariance Proportion
1400
1300
265.5589
263.8831
15.33302
0.083747
0.987419
0.010089
0.002492
1200
99Q1 99Q2 99Q3 99Q4 00Q1 00Q2 00Q3 00Q4
INVRF1
Dependent Variable: INVR+87.56517733*0.0003400014958*INGR
*EXP(0.0003400014958*INGR)
Method: Least Squares
Sample: 1950Q2 1998Q4
Included observations: 195
Variable
Coefficient
Std. Error
t-Statistic
Prob.
EXP(0.0003400014958*INGR)
87.56517733*INGR*EXP(0.0003400014958
*INGR)
INT
123.7778
4.254744
29.09172
0.0000
0.000275
16.95705
5.66E-06
1.474508
48.67463
11.50014
0.0000
0.0000
2100
Forecast: INVRF2
Actual: INVR
Forecast sample: 1999Q1 2000Q4
Included observations: 8
2000
1900
Root Mean Squared Error
Mean Absolute Error
Mean Abs. Percent Error
Theil Inequality Coefficient
Bias Proportion
Variance Proportion
Covariance Proportion
1800
1700
1600
111.4318
95.77976
5.476860
0.031550
0.704741
0.249452
0.045808
1500
99Q1 99Q2 99Q3 99Q4 00Q1 00Q2 00Q3 00Q4
INVRF2
2º
Comente y fundamente su respuesta. (3 puntos)
Toda prueba de hipótesis de un modelo no lineal es similar a las pruebas de hipótesis de un modelo lineal; por lo
tanto, no existe diferencias entre ambos tipo de modelos.