CT(t)

UNIVERSIDAD NACIONAL DE PIURA
FACULTAD DE ECONOMIA
SOLUCIÓN DE LA PRIMERA PRÁCTICA DE ECONOMETRIA I
1º
El investigador especifica los modelos siguientes:
CT(t) = a + b SPREAD(t) + c(0) EMI(t) + c1 EMI(t-1) + c2 EMI(t-2)+ .... + u(t)
CT(t) = a + b TA(t) + c0 SPREAD(t) + c1 SPREAD(t-1) + ... + c15 SPREAD(t-15) + u(t)
Se le pide:
1.1.
Estime el primer modelo y obtenga los multiplicadores y el retardo medio. (6 puntos)
CT(t) = a + b SPREAD(t) + c(0) EMI(t) + c1 EMI(t-1) + c2 EMI(t-2)+ .... + u(t)
Si C(i) = (1-L)Li
CT(t) = a + b SPREAD(t) + (1-L) EMI(t) + (1-L)L EMI(t-1) + (1-L)L2 EMI(t-2)+ .... + u(t) (1)
retardamos 1 periodo:
CT(t-1) = a + b SPREAD(t-1) + (1-L) EMI(t-1) + (1-L)L EMI(t-2) + (1-L)L2 EMI(t-3)+ .... + u(t-1)
Multiplicamos por L:
LCT(t-1) = aL + bL SPREAD(t-1) + (1-L)L EMI(t-1) + (1-L)L2 EMI(t-2) + (1-L)L3 EMI(t-3)+ .... + L
u(t-1) (2)
(1) – (2)
CT = a(1-L) + b SPREAD(t) - bL SPREAD(t-1) + (1-L) EMI(t) + L CT(t-1) + (u(t)-L u(t-1))
CT = a* + b SPREAD(t) + b* SPREAD(t-1) + L* EMI(t) + L CT(t-1) + u*(t)
Dependent Variable: CT
Method: Least Squares
Sample (adjusted): 2001M02 2009M12
Included observations: 102 after adjustments
Variable
C
Coefficient
Std. Error
t-Statistic
Prob.
-1615.517
3924.997
-0.411597
0.6815
SPREAD
49.63791
17.12357
2.898807
0.0046
SPREAD(-1)
-37.99468
18.00617
-2.110093
0.0374
EMI
4.504581
0.893980
5.038791
0.0000
CT(-1)
0.914848
0.020171
45.35547
0.0000
R-squared
0.998445
Mean dependent var
578303.5
Adjusted R-squared
0.998381
S.D. dependent var
233710.0
S.E. of regression
9405.187
Akaike info criterion
21.18369
8.58E+09
Schwarz criterion
21.31236
F-statistic
15567.00
Prob(F-statistic)
0.000000
Sum squared resid
Log likelihood
-1075.368
Durbin-Watson stat
1.629158
Sample: 2001M02 2009M12
Included observations: 102
Autocorrelation
Partial Correlation
AC
PAC
Q-Stat
Prob
. |*.
|
. |*.
|
1
0.158
0.158
2.6223
0.105
.|.
|
.|.
|
2
0.041
0.016
2.8003
0.247
2
Mod1qbp1 = 102*(0.158011072093364^2) = 2.54668488821762
Mod1qbp2 = 102*(0.158011072093364^2+0.040964627589653^2) = 2.71785116100063
Breusch-Godfrey Serial Correlation LM Test:
F-statistic
2.752296
Probability
0.100379
2.842811
Probability
0.091783
Obs*R-squared
Dependent Variable: RESID
Method: Least Squares
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-169.7478
3891.363
-0.043622
0.9653
SPREAD
-4.931046
17.22928
-0.286202
0.7753
SPREAD(-1)
5.740178
18.17802
0.315776
0.7529
EMI
0.146773
0.890419
0.164836
0.8694
CT(-1)
-0.003391
0.020095
-0.168767
0.8663
RESID(-1)
0.175546
0.105814
1.659004
0.1004
R-squared
0.027871
Mean dependent var
1.07E-10
Breusch-Godfrey Serial Correlation LM Test:
F-statistic
1.362020
Probability
0.261098
Obs*R-squared
2.843232
Probability
0.241324
Dependent Variable: RESID
Method: Least Squares
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-170.2653
3911.867
-0.043525
0.9654
SPREAD
-4.862724
17.65124
-0.275489
0.7835
SPREAD(-1)
5.668336
18.62090
0.304407
0.7615
EMI
0.145333
0.897965
0.161847
0.8718
CT(-1)
-0.003358
0.020268
-0.165692
0.8688
RESID(-1)
0.175835
0.107340
1.638121
0.1047
RESID(-2)
-0.002187
0.108977
-0.020065
0.9840
R-squared
0.027875
Mean dependent var
mod1h = mod1rho*sqr(mod1t/(1-mod1t*mod1vb5)) = 1.912769
Dependent Variable: CT
Method: Two-Stage Least Squares
1.07E-10
3
Sample (adjusted): 2001M03 2009M12
Included observations: 100 after adjustments
Instrument list: C SPREAD SPREAD(-1) SPREAD(-2) EMI EMI(-1)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
-3216.579
4352.109
-0.739085
0.4617
SPREAD
47.76270
17.99800
2.653779
0.0093
SPREAD(-1)
-22.66502
21.68321
-1.045279
0.2985
EMI
7.148063
2.058865
3.471846
0.0008
CT(-1)
0.853912
0.047258
18.06926
0.0000
R-squared
0.998312
Mean dependent var
580597.9
Adjusted R-squared
0.998241
S.D. dependent var
235252.0
S.E. of regression
9866.807
Sum squared resid
9.25E+09
F-statistic
13667.09
Durbin-Watson stat
1.463981
Prob(F-statistic)
0.000000
MOD1MISPREAD = C(2) = 47.7626977023185
MOD1MIEMI = C(4) = 7.1480634098764
MOD1MD1RSPREAD = C(3) + C(2)*C(5) = 18.1201333453488
MOD1MD2RSPREAD = C(3)*C(5) + C(2)*C(5)^2 = 15.4730025877635
MOD1MD1REMI = C(4)*C(5) = 6.1038184173686
MOD1MD2REMI = C(4)*C(5)^2 = 5.21212489815509
MOD1MTSPREAD = (C(3) + C(2))/(1-C(5)) = 171.798592609424
MOD1MTEMI = C(4)/(1-C(5)) = 48.9299071369329
MOD1RMSPREAD = C(3)/(C(2)+C(3)) + C(5)/(1-C(5)) = 4.94212559209028
MOD1RMEMI = C(5)/(1-C(5)) = 5.84519768939473
1.2.
Estime el segundo modelo y obtenga los multiplicadores y el retardo medio. (5 puntos)
CT(t) = a + b TA(t) + c0 SPREAD(t) + c1 SPREAD(t-1) + ... + c15 SPREAD(t-15) + u(t)
Dependent Variable: CT
Method: Least Squares
Sample (adjusted): 2002M04 2009M12
Included observations: 74 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
2470963.
262045.0
9.429535
0.0000
TA
-61901.80
9903.571
-6.250452
0.0000
PDL01
-69.50788
79.55865
-0.873668
0.3855
4
PDL02
-81.21235
56.48055
PDL03
5.490162
PDL04
6.273413
PDL05
PDL06
PDL07
R-squared
-1.437882
0.1553
29.57882
0.185611
0.8533
5.407807
1.160066
0.2503
-0.031100
1.609867
-0.019319
0.9846
-0.101708
0.095397
-1.066160
0.2903
-0.000749
0.021397
-0.035027
0.9722
0.831106
Mean dependent var
608250.7
Dependent Variable: CT
Method: Least Squares
Sample (adjusted): 2002M04 2009M12
Included observations: 74 after adjustments
Variable
C
Coefficient
Std. Error
t-Statistic
Prob.
2471599.
259428.1
9.527108
0.0000
TA
-61928.17
9799.900
-6.319266
0.0000
PDL01
-71.89564
40.70745
-1.766154
0.0820
PDL02
-82.53275
41.74026
-1.977293
0.0522
PDL03
6.481457
8.535235
0.759377
0.4503
PDL04
6.410882
3.692151
1.736354
0.0872
PDL05
-0.087022
0.205298
-0.423880
0.6730
PDL06
-0.104275
0.060608
-1.720497
0.0900
R-squared
0.831102
Mean dependent var
608250.7
Dependent Variable: CT
Method: Least Squares
Sample (adjusted): 2002M04 2009M12
Included observations: 74 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
2528236.
261068.2
9.684197
0.0000
TA
-63993.02
9867.379
-6.485311
0.0000
PDL01
-116.8127
31.68691
-3.686464
0.0005
PDL02
-13.46227
11.59298
-1.161244
0.2497
PDL03
17.50606
5.720173
3.060408
0.0032
PDL04
0.092237
0.385280
0.239403
0.8115
PDL05
-0.371801
0.123213
-3.017542
0.0036
R-squared
0.823527
Mean dependent var
608250.7
Adjusted R-squared
0.807724
S.D. dependent var
259759.9
S.E. of regression
113902.9
Akaike info criterion
26.21390
Sum squared resid
8.69E+11
Schwarz criterion
26.43185
5
Log likelihood
-962.9142
Lag Distribution of
SPREAD
*
*
F-statistic
i
Coefficient
52.11038
Std. Error
t-Statistic
*. |
0
-89.1109
106.584
-0.83606
.*|
1
92.4021
30.9568
2.98487
. *|
2
144.245
45.3054
3.18384
.*|
3
116.049
50.6073
2.29313
.* |
4
48.5224
40.1464
1.20864
*. |
5
-26.5506
27.5316
-0.96437
*. |
6
-86.3084
26.3817
-3.27153
* . |
7
-116.813
31.6869
-3.68646
* . |
8
-113.048
32.2243
-3.50817
*. |
9
-78.9239
27.0331
-2.91953
*. |
10
-27.2704
25.4147
-1.07302
* |
11
20.1574
35.6164
0.56596
.* |
12
32.6816
45.8515
0.71277
*. |
13
-29.2987
42.1309
-0.69542
. |
14
-214.308
30.9055
-6.93429
. |
15
-579.794
102.472
-5.65807
-907.368
100.232
-9.05263
Sum of
Lags
MI TA = -63993.02
MI SPREAD = -89.1109
MD SPREAD1R = 92.4021
= -579.794
MD SPREAD2R = 144.245 ……………….. MD SPREAD15R
ML SPREAD = -907.368
mod2rmspread=@sum(i*re)/@sum(re) = 16.983367900646
1.3.
En el primer modelo aplique el contraste de Hausman y Wu. (2 puntos)
HW = @TRANSPOSE(BMCO-BMC2E)*@INVERSE(VARBMC2E-VARBMCO)*(BMCO-BMC2E)
= 2.219990.
Acepta la hipótesis nula.
1.4.
Elija la mejor estimación y justifique su respuesta. (2 puntos)
MODELO 1
MODELO 2
Adjusted R-squared 0.998381
Adjusted R-squared 0.807724
Akaike info criterion 21.18369
Akaike info criterion 26.21390
Sum squared resid
8.58E+09
Sum squared resid
8.69E+11
Schwarz criterion
21.31236
Schwarz criterion
26.43185
6
2º
Comente y fundamente su respuesta. (5 puntos)
2.1.
Cuando se tiene un modelo con variable retardada no se aplica mínimos cuadrados.
2.2.
En todo modelo dinámico se puede obtener el multiplicador total.