Retardando un periodo: Multiplica por d:

UNIVERSIDAD NACIONAL DE PIURA
FACULTAD DE ECONOMIA
PRIMERA PRÁCTICA CALIFICADA DE ECONOMETRIA I
1º
El investigador especifica los modelos siguientes:
MODELO 1: INV(t) = a + b(0) PIB(t) + b(1) PIB(t-1) + b(2) PIB(t-2) + .............. + c PPIB(t) + u(t)
MODELO 2: INV(t) = a + b PIB(t) + c(0) PPIB(t) + c(1) PPIB(t-1) + c(2) PPIB(t-2) + .... + c(K) PPIB(t-K) + u(t)
se le pide:
1.1.
Estimar el modelo 1 y obtener los multiplicadores, retardo medio y mediano. (6 puntos)
Asumimos bi = (1-d)di
INV(t) = a + c PPIB(t) + (1-d) PIB(t) + (1-d)d PIB(t-1) + (1-d)d2 PIB(t-2)+ .... +
u(t)
Retardando un periodo:
INV(t-1) = a + c PPIB(t-1) + (1-d) PIB(t-1) + (1-d)d PIB(t-2) + (1-d)d2 PIB(t-3)+
.... + u(t-1)
Multiplica por d:
dINV(t-1) = ad + cd PPIB(t-1) + (1-d)d PIB(t-1) + (1-d)d2 PIB(t-2) + (1-d)d3 PIB(t3)+ .... + du(t-1)
(2)
(1) - (2):
INV(t) – d INV(t-1) = a(1-d) + c PPIB(t) - cd PPIB(t-1) + (1-d) PIB(t) + u(t) – d
u(t-1)
INV(t) = a(1-d) + c PPIB(t) - cd PPIB(t-1) + (1-d) PIB(t) + d INV(t-1) + (u(t) - d
u(t-1))
Dependent Variable: INV
Method: Least Squares
Sample (adjusted): 1947Q2 1995Q1
Included observations: 192 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PIB
PPIB
PPIB(-1)
INV(-1)
-29.01886
0.005659
19.44186
-18.15726
0.790185
7.542270
0.004043
4.172197
4.038261
0.043491
-3.847496
1.399879
4.659862
-4.496306
18.16872
0.0002
0.1632
0.0000
0.0000
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
0.995814
0.995724
17.31337
56053.75
-817.3870
1.604041
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
mod1h = mod1rho*sqr(mod1t/(1-mod1t*mod1vb5)) = 3.437629
307.2740
264.7758
8.566531
8.651362
11121.03
0.000000
Sample: 1947Q2 1995Q1
Included observations: 192
Autocorrelation
.|*
.|.
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Partial Correlation
.|*
.|.
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AC
PAC
Q-Stat
Prob
1 0.154 0.154 4.6199 0.032
2 0.035 0.011 4.8585 0.088
QBP1 = 192*(0.153915159940832)2 = 4.54845628024548
QBP2 = 192*[(0.153915159940832)2+(0.0348859107024808)2] = 4.78212541922944
Breusch-Godfrey Serial Correlation LM Test:
F-statistic
Obs*R-squared
9.753547
9.566524
Probability
Probability
0.002076
0.001982
Dependent Variable: RESID
Method: Least Squares
Presample missing value lagged residuals set to zero.
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PIB
PPIB
PPIB(-1)
INV(-1)
RESID(-1)
-11.10736
0.000976
5.165266
-4.517018
-0.097441
0.284504
8.184813
0.003964
4.400482
4.203597
0.052729
0.091098
-1.357070
0.246279
1.173796
-1.074560
-1.847941
3.123067
0.1764
0.8057
0.2420
0.2840
0.0662
0.0021
Breusch-Godfrey Serial Correlation LM Test:
F-statistic
Obs*R-squared
7.224544
13.90944
Probability
Probability
0.000953
0.000954
Dependent Variable: RESID
Method: Least Squares
Presample missing value lagged residuals set to zero.
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PIB
PPIB
PPIB(-1)
INV(-1)
RESID(-1)
RESID(-2)
-20.17920
0.001689
9.574113
-8.391759
-0.177261
0.336384
0.194070
9.164722
0.003941
4.828464
4.546509
0.064352
0.093497
0.091370
-2.201834
0.428496
1.982849
-1.845759
-2.754572
3.597820
2.124008
0.0289
0.6688
0.0489
0.0665
0.0065
0.0004
0.0350
Dependent Variable: INV
Method: Two-Stage Least Squares
Sample (adjusted): 1947Q3 1995Q1
Included observations: 191 after adjustments
Instrument list: C PIB PIB(-1) PPIB PPIB(-1) PPIB(-2)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PIB
PPIB
PPIB(-1)
INV(-1)
-106.8405
0.016805
46.06518
-40.60851
0.145526
22.77485
0.006664
9.175054
8.274035
0.176407
-4.691160
2.521836
5.020699
-4.907946
0.824947
0.0000
0.0125
0.0000
0.0000
0.4105
R-squared
Adjusted R-squared
S.E. of regression
F-statistic
0.990859
0.990663
25.58482
5028.155
Mean dependent var
S.D. dependent var
Sum squared resid
Durbin-Watson stat
MIPIB = 0.0168047232136378.
308.6613
264.7711
121752.4
0.467308
MIPPIB = 46.0651844264855.
MD1PPIB = -40.6085122056975 + 46.0651844264855 * 0.145526348802223 = -33.9048141092101
MD2PPIB = -40.6085122056975 * 0.145526348802223 + 46.0651844264855 * 0.145526348802223^2 = 4.93404380413144
MD1PIB = 0.0168047232136378 * 0.145526348802223 = 0.00244553001191267
MD2PIB = 0.0168047232136378 * 0.145526348802223^2 = 0.000355889053519908
…………..
MTPPIB = -40.6085122056975 / (1 - 0.145526348802223) + (46.0651844264855 * 0.145526348802223) / (1 0.145526348802223) = -39.679180348842
1.2.
MTPIB = = 0.0168047232136378 (1 − 0.145526348802223 ) = 0.0196667541358138
Estimar el modelo 2 y y obtener los multiplicadores, retardo medio y mediano. (6 puntos)
ELECCIÓN DEL RETARDO ÓPTIMO
k
T
R2 AJUSTADO
AkAIkE
SCHWARZ
0
1
2
3
4
5
6
7
8
9
10
11
12
13
193
192
191
190
189
188
187
186
185
184
183
182
181
180
0.984929
0.988240
0.988349
0.988237
0.988134
0.988228
0.988712
0.988975
0.989173
0.989123
0.989099
0.989089
0.989095
0.989132
9.816007
9.573247
9.569068
9.583793
9.597914
9.595344
9.558777
9.540579
9.527765
9.537263
9.544076
9.549648
9.553478
9.554820
9.866722
9.641112
9.654206
9.686331
9.717979
9.733065
9.714285
9.714006
9.719245
9.746932
9.772072
9.796110
9.818547
9.838638
14
15
16
17
18
19
20
21
179
178
177
176
175
174
173
172
0.989250
0.989313
0.989453
0.989797
0.989821
0.989742
0.989600
0.989494
9.548795
9.547965
9.540293
9.512359
9.515432
9.528408
9.547088
9.562122
9.851508
9.869718
9.881236
9.872642
9.895206
9.927828
9.966312
10.00131
K = 18
Dependent Variable: INV
Method: Least Squares
Sample (adjusted): 1951Q3 1995Q1
Included observations: 175 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PIB
PDL01
PDL02
PDL03
PDL04
PDL05
PDL06
PDL07
-126.1478
0.019281
4.192368
-0.216603
-0.795034
0.121218
0.019737
-0.001894
-0.000115
11.15123
0.007574
2.688550
1.127647
0.705402
0.064983
0.026164
0.000698
0.000231
-11.31245
2.545865
1.559342
-0.192084
-1.127065
1.865386
0.754359
-2.713818
-0.498227
0.0000
0.0118
0.1208
0.8479
0.2613
0.0639
0.4517
0.0074
0.6190
Dependent Variable: INV
Method: Least Squares
Sample (adjusted): 1951Q3 1995Q1
Included observations: 175 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PIB
PDL01
PDL02
PDL03
PDL04
PDL05
PDL06
-125.9231
0.019004
3.001553
-0.228716
-0.451593
0.121711
0.006741
-0.001898
11.11700
0.007536
1.228358
1.124845
0.149400
0.064829
0.002040
0.000696
-11.32707
2.521755
2.443549
-0.203331
-3.022714
1.877434
3.305079
-2.726051
0.0000
0.0126
0.0156
0.8391
0.0029
0.0622
0.0012
0.0071
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
Lag Distribution of
0.990798
0.990412
25.86275
111703.3
-813.4606
0.437453
i
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
332.4263
264.1248
9.388121
9.532797
2568.651
0.000000
Coefficient
t-Statistic
Std. Error
PPIB
.
.*
* .
* .
* .
* .
*.
*
.*
.*
.*
*
*
.*
.*
.*
.*
*
* .
*|
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0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Sum of
Lags
36.0403
3.40927
-11.1920
-14.6799
-12.2150
-7.42959
-2.65566
0.84751
2.66560
3.00155
2.44780
1.75857
1.62218
2.43325
4.06507
5.64178
5.31072
0.01466
-14.7359
4.98901
1.68144
3.18198
2.69706
1.62289
1.41741
1.85360
1.91802
1.55218
1.22836
1.48215
1.86119
1.83728
1.38801
1.44052
2.46501
3.01138
1.66596
4.57636
7.22393
2.02759
-3.51730
-5.44294
-7.52669
-5.24167
-1.43270
0.44187
1.71733
2.44355
1.65152
0.94486
0.88292
1.75305
2.82194
2.28874
1.76355
0.00880
-3.22000
6.35018
0.24602
25.8113
K = 17:
Dependent Variable: INV
Method: Least Squares
Sample (adjusted): 1951Q2 1995Q1
Included observations: 176 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PIB
PDL01
PDL02
PDL03
PDL04
PDL05
PDL06
PDL07
-127.6156
0.019846
3.798741
0.762063
-1.181977
0.092928
0.037180
-0.002083
-0.000233
11.03087
0.007528
2.948258
1.559689
0.846730
0.111342
0.035330
0.001503
0.000359
-11.56895
2.636234
1.288469
0.488600
-1.395931
0.834621
1.052367
-1.386093
-0.648254
0.0000
0.0092
0.1994
0.6258
0.1646
0.4051
0.2942
0.1676
0.5177
Dependent Variable: INV
Method: Least Squares
Sample (adjusted): 1951Q2 1995Q1
Included observations: 176 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
PIB
-127.3578
0.019526
11.00466
0.007499
-11.57308
2.603796
0.0000
0.0100
PDL01
PDL02
PDL03
PDL04
PDL05
PDL06
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
Durbin-Watson stat
2.171313
0.221965
-0.654552
0.138716
0.014429
-0.002770
0.990643
0.990254
26.07661
114238.2
-819.5822
0.441809
Lag Distribution of
PPIB
.
.*
* .
* .
* .
*.
*
*
.*
.*
*
*
.*
.*
.*
.*
*
* .
i
*|
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0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Sum of
Lags
1.3.
1.543204
1.316235
0.234105
0.085921
0.004058
0.001064
1.407016
0.168636
-2.795977
1.614473
3.555940
-2.604518
0.1613
0.8663
0.0058
0.1083
0.0005
0.0100
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
F-statistic
Prob(F-statistic)
330.9091
264.1371
9.404344
9.548456
2541.055
0.000000
Coefficient
Std. Error
t-Statistic
37.3569
2.16786
-12.4458
-14.9667
-11.5367
-6.28896
-1.68104
1.17328
2.17131
1.88910
1.24899
1.18721
2.32148
4.61853
7.06176
7.31876
1.40891
-16.6290
5.51708
2.17243
3.70668
2.86438
1.63728
1.77862
2.23700
2.07875
1.54320
1.48592
1.99794
2.20095
1.77000
1.48590
2.61534
3.50415
2.14161
5.09131
6.77114
0.99790
-3.35767
-5.22512
-7.04624
-3.53586
-0.75147
0.56441
1.40702
1.27134
0.62514
0.53941
1.31157
3.10824
2.70013
2.08860
0.65788
-3.26615
6.37587
0.24504
26.0192
Compare los dos modelos estimados y elija la mejor estimación, justifique su respuesta. (3 puntos)
Se compara el coeficiente de bondad de ajuste y la suma residual de los dos modelos.
2º
Comente y fundamente su respuesta. (5 puntos)
2.1.
El modelo de regresión múltiple aleatorio o no aleatorio considera el supuesto caeteris paribus.
2.2.
El punto fundamental de la crítica de Lucas se refiere a que las estimaciones econométricas a nivel
macroeconómicas consideran que los agentes económicos, como un todo, se basan en expectativas adaptativas
para pronosticar la evolución de las variables económicas de interés.