UNIVERSIDAD NACIONAL DE PIURA

UNIVERSIDAD NACIONAL DE PIURA
FACULTAD DE ECONOMIA
SOLUCIÓN DEL EXAMEN PARCIAL DE ECONOMETRIA I
1º
El investigador especifica los modelos siguientes:
MODELO 1: M1(t) = a + b M1(t-1) + c INT(t) + d INT(t-1) + u(t)
MODELO 2: M1(t) = a + b PBI(t)^c + d INFL(t) + u(t)
se le pide:
1.1.
Estimar el modelo 1. (5 puntos)
Dependent Variable: M1
Sample (adjusted): 1950Q2 2000Q4
Included observations: 203 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
M1(-1)
INT
INT(-1)
1.109369
1.004473
-1.718651
2.050277
1.363422
0.001729
0.821977
0.819207
0.813665
581.0437
-2.090876
2.502758
0.4168
0.0000
0.0378
0.0131
R-squared
Log likelihood
Durbin-Watson stat
0.999446
-721.2551
0.729703
Mean dependent var
F-statistic
Prob(F-statistic)
455.6147
119636.2
0.000000
mod1h = mod1rho*sqr(mod1t/(1-mod1t*mod1vb2)) = 9.052220
Sample: 1950Q2 2000Q4
Included observations: 203
Autocorrelation
Partial Correlation
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AC
PAC
Q-Stat
Prob
1 0.608 0.608 76.135 0.000
2 0.492 0.194 126.17 0.000
mod1qb1 = 203*0.607916862159251^2 = 75.0212709934026.
mod1qb2 = 203*(0.607916862159251^2+0.491588435897297^2) = 124.078086625917
Breusch-Godfrey Serial Correlation LM Test:
F-statistic
Obs*R-squared
134.5715
82.14178
Probability
Probability
0.000000
0.000000
Dependent Variable: RESID
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
M1(-1)
INT
INT(-1)
RESID(-1)
0.338277
-0.000632
-0.787294
0.771003
0.645967
1.055067
0.001338
0.639445
0.637167
0.055684
0.320621
-0.471952
-1.231213
1.210049
11.60050
0.7488
0.6375
0.2197
0.2277
0.0000
R-squared
0.404639
Mean dependent var
-2.89E-15
Breusch-Godfrey Serial Correlation LM Test:
F-statistic
Obs*R-squared
76.74919
88.90247
Probability
Probability
0.000000
0.000000
Dependent Variable: RESID
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
M1(-1)
INT
INT(-1)
RESID(-1)
RESID(-2)
0.451475
-0.000876
-0.584278
0.561276
0.496126
0.239893
1.028265
0.001306
0.625706
0.623687
0.069754
0.070215
0.439065
-0.670667
-0.933790
0.899933
7.112523
3.416573
0.6611
0.5032
0.3516
0.3693
0.0000
0.0008
R-squared
0.437943
Mean dependent var
-2.89E-15
Dependent Variable: M1
Method: Two-Stage Least Squares
Sample (adjusted): 1950Q3 2000Q4
Included observations: 202 after adjustments
Instrument list: C M1(-1) INT INT(-1) INT(-2)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
M1(-1)
INT
INT(-1)
1.116539
1.004470
-1.719064
2.049906
1.378655
0.001735
0.824112
0.821322
0.809875
579.0175
-2.085960
2.495860
0.4190
0.0000
0.0383
0.0134
R-squared
Adjusted R-squared
S.E. of regression
F-statistic
1.2.
0.999443
0.999435
8.554931
118494.8
Mean dependent var
S.D. dependent var
Sum squared resid
Durbin-Watson stat
457.3170
359.8733
14490.99
0.729676
Estimar el modelo 2, aplicando la transformación de Box y Cox (3 decimales). (4 puntos)
TRANSFORMACION DE BOX COX
BETA 2
SUMA RESIDUAL
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
3650429.
3336571.
3043469.
2772053.
2523088.
2297172.
2094735.
1916040.
1761193.
1630148.
1522720.
1438593.
1377334.
1338407.
1.4
1.5
1.6
1.7
1.8
1.9
2
1321183.
1324957.
1348956.
1392355.
1454286.
1533851.
1630127.
Dependent Variable: M1
Sample: 1950Q1 2000Q4
Variable
Coefficient
C
(PBI^1.4-1)/1.4
INFL
-64.04202
0.005533
-9.588781
R-squared
0.949705
Std. Error
12.29700
8.99E-05
1.674658
t-Statistic
-5.207938
61.54197
-5.725815
Mean dependent var
Prob.
0.0000
0.0000
0.0000
453.9215
TRANSFORMACION DE BOX COX
BETA 2
SUMA RESIDUAL
1.31
1.32
1.33
1.34
1.35
1.36
1.37
1.38
1.39
1.4
1.41
1.42
1.43
1.44
1.45
1.46
1.47
1.48
1.49
1335719.
1333247.
1330992.
1328951.
1327125.
1325512.
1324112.
1322924.
1321948.
1321183.
1320628.
1320282.
1320144.
1320215.
1320492.
1320976.
1321665.
1322558.
1323656.
Dependent Variable: M1
Sample: 1950Q1 2000Q4
Included observations: 204
Variable
Coefficient
C
(PBI^1.43-1)/1.43
INFL
-54.60916
0.004283
-9.305409
R-squared
0.949745
Std. Error
12.18389
6.96E-05
1.673789
t-Statistic
-4.482078
61.56746
-5.559487
Mean dependent var
Prob.
0.0000
0.0000
0.0000
453.9215
TRANSFORMACION DE BOX COX
BETA 2
SUMA RESIDUAL
1.421
1.422
1.423
1.424
1.425
1.426
1.427
1.428
1.429
1.43
1.431
1.432
1.433
1.434
1.435
1.436
1.437
1.438
1.439
1320259.
1320238.
1320219.
1320202.
1320187.
1320174.
1320164.
1320155.
1320149.
1320144.
1320142.
1320142.
1320144.
1320148.
1320154.
1320162.
1320172.
1320184.
1320198.
Dependent Variable: M1
Method: Least Squares
Sample: 1950Q1 2000Q4
Variable
Coefficient
C
(PBI^1.432-1)/1.432
INFL
-53.99549
0.004210
-9.286566
R-squared
Adjusted R-squared
Log likelihood
Durbin-Watson stat
1.3.
0.949745
0.949245
-1184.527
0.119805
Std. Error
12.17688
6.84E-05
1.673774
t-Statistic
-4.434263
61.56752
-5.548279
Mean dependent var
S.D. dependent var
F-statistic
Prob(F-statistic)
Prob.
0.0000
0.0000
0.0000
453.9215
359.7263
1899.297
0.000000
Obtener los multiplicadores del modelo 1 y 2. (4 puntos)
MODELO 1: M1(t) = a + b M1(t-1) + c INT(t) + d INT(t-1) + u(t)
M1(t) = a + b (a + b M1(t-2) + c INT(t-1) + d INT(t-2) + u(t-1)) + c INT(t) + d INT(t-1) + u(t)
M1(t) = a(1+b) + b2 M1(t-2) + c INT(t) + (d + bc) INT(t-1) + bd INT(t-2) + (u(t) + b u(t-1))
M. I. INT = c = -1.71906351019002
M. D. 1R INT = d + bc = 0.323157951058081
M. D. 2 R INT = bd + b2c = 0.324602541305557
......................
M. T. INT = c + d + bc + bd + b2c + ... = (c + bc + b2c + .....) + (d + bd + ......) = c (1 + b + b2 + ....) + d (1 + b +
.....)
Para obtener el multiplicador total requiere que: b<1 y en la estimación b = 1.00447022962841 >1.
MODELO 2: M1(t) = a + b PBI(t)^c + d INFL(t) + u(t)
M. I. PBI = bc PBI(t)^(c-1) = 0.223476
M. I. INFL = d = -9.28656570062868
2º
Comente y fundamente su respuesta. (7 puntos)
2.1.
Todos los modelos dinámicos requiere de la verificación de autocorelación para determinar el método de
estimación adecuado.
2.2.
El sistema de ecuaciones normales de un modelo no lineal no difiere del sistema de ecuaciones normales de
un modelo lineal.