SOLUCIÓN DE LA TERCERA PRÁCTICA CALIFICADA DE

UNIVERSIDAD NACIONAL DE PIURA
FACULTAD DE ECONOMIA
DEPARTAMENTO DE ECONOMIA
SOLUCIÓN DE LA TERCERA PRÁCTICA CALIFICADA DE ECONOMETRIA I
1º
El investigador quiere explicar la participación laboral de la mujer casada (ENFT) considerando las variables: GAMAR, EDUC,
EXPER, EXPER^2, NM6 y NM6Y18. Ayude al investigador a construir un modelo probit para las primeras 700 observaciones.
(8 puntos)
ELECCIÓN DEL MODELO PROBIT
VARIABLE
GAMAR
EDUC
EXPER
EXPER^2
NM6
NM6Y18
SIGNO
BETA
CORRECTO
Z CALCULADO
SIGNIFICAN.
+
+
+/+/-
-0.012755
0.101325
0.062272
0.001538
-0.542059
0.005783
SI
SI
SI
SI
SI
SI
-2.932777
4.644022
9.039912
6.695664
-5.493298
0.157057
ALTA
ALTA
ALTA
ALTA
ALTA
NO
N90 = 1.64485
N95 = 1.95996
GAMAR
EDUC
EXPER
EXPER^2
NM6
GAMAR
1.000000
0.286269
-0.176315
-0.163933
0.039840
R Mc Fadden
0.009268
0.023753
0.098411
0.055329
0.034043
2.64E-05
N99 = 2.57583
EDUC
0.286269
1.000000
0.075238
0.025576
0.108366
EXPER
-0.176315
0.075238
1.000000
0.938095
-0.197885
EXPER^2
-0.163933
0.025576
0.938095
1.000000
-0.184783
NM6
0.039840
0.108366
-0.197885
-0.184783
1.000000
Se elimina EXPER^2.
Dependent Variable: ENFT
Method: ML - Binary Probit (Quadratic hill climbing)
Sample: 1 700
Included observations: 700
Convergence achieved after 4 iterations
Covariance matrix computed using second derivatives
Variable
Coefficient
Std. Error
z-Statistic
Prob.
C
GAMAR
EDUC
EXPER
NM6
-1.499944
-0.016646
0.139782
0.052026
-0.514656
0.297344
0.005066
0.025292
0.007160
0.106570
-5.044477
-3.285810
5.526636
7.266644
-4.829281
0.0000
0.0010
0.0000
0.0000
0.0000
McFadden R-squared
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
LR statistic
Prob(LR statistic)
Obs with Dep=0
Obs with Dep=1
0.152596
0.487774
1.146595
1.179103
1.159162
142.7299
0.000000
272
428
Mean dependent var
S.E. of regression
Sum squared resid
Log likelihood
Restr. log likelihood
Avg. log likelihood
Total obs
Los signos son los correctos y todas las variables son altamente significativas (z > 2.57583).
El modelo en conjunto es significativo (LR = 142.7299 > 9.49 = chi(4)).
0.611429
0.438063
133.3701
-396.3084
-467.6733
-0.566155
700
BAJO
BAJO
BAJO
BAJO
BAJO
BAJO
2
COEFICIENTE DE BONDAD
TIPO
VALOR
R2
EFFRON
MC FADDEN
CRAGG-UHLER
0.198417
0.198056
0.152596
0.250225
El coeficiente de bondad de ajuste es bajo.
Expectation-Prediction Evaluation for Binary Specification
Equation: MODPROB
Success cutoff: C = 0.5
Estimated Equation
Dep=0
Dep=1
Total
P(Dep=1)<=C
P(Dep=1)>C
Total
Correct
% Correct
% Incorrect
Total Gain*
Percent Gain**
137
135
272
137
50.37
49.63
50.37
50.37
77
351
428
351
82.01
17.99
-17.99
NA
Constant Probability
Dep=0
Dep=1
Total
214
486
700
488
69.71
30.29
8.57
22.06
0
272
272
0
0.00
100.00
0
428
428
428
100.00
0.00
0
700
700
428
61.14
38.86
El r2 de conteo es bajo (69.71 %) y el porcentaje de ganancia es de 22.06 %.
Goodness-of-Fit Evaluation for Binary Specification
Andrews and Hosmer-Lemeshow Tests
Equation: MODPROB
Grouping based upon predicted risk (randomize ties)
Quantile of Risk
Low
High
1
2
3
4
5
6
7
8
9
10
0.0108
0.3288
0.4381
0.4984
0.5634
0.6223
0.6726
0.7463
0.8111
0.8780
0.3249
0.4355
0.4983
0.5630
0.6215
0.6709
0.7455
0.8106
0.8764
0.9907
Total
H-L Statistic
Andrews Statistic
Actual
Dep=0
Expect
Actual
Expect
Total
Obs
H-L
Value
55
46
34
38
30
23
14
16
8
8
54.1565
43.4950
36.9734
32.9306
28.5022
24.7711
20.3488
15.4932
11.0070
5.01600
15
24
36
32
40
47
56
54
62
62
15.8435
26.5050
33.0266
37.0694
41.4978
45.2289
49.6512
54.5068
58.9930
64.9840
70
70
70
70
70
70
70
70
70
70
0.05804
0.38101
0.50682
1.47367
0.13278
0.19598
2.79259
0.02129
0.97478
1.91220
272
272.694
428
427.306
700
8.44916
8.4492
9.5909
Dep=1
Prob. Chi-Sq(8)
Prob. Chi-Sq(10)
El Test H-L y Andrews nos confirma que el modelo se comporta y se ajusta bien (Prob > 0.05).
0.3909
0.4771
3
50
Series: Residuals
Sample 1 700
Observations 700
40
30
20
10
0
-1.00
-0.75
-0.50
-0.25
0.00
0.25
0.50
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
0.000991
0.141763
0.896116
-0.987358
0.436807
-0.360305
1.895118
Jarque-Bera
Probability
50.75124
0.000000
0.75
Los residuos no se distribuyen normal (JB = 50.75124 > 5.99 = chi(2)).
Dependent Variable: ENFT
Method: ML - Binary Logit (Quadratic hill climbing)
Sample: 1 700
Included observations: 700
Convergence achieved after 4 iterations
Covariance matrix computed using second derivatives
Variable
Coefficient
Std. Error
z-Statistic
Prob.
C
GAMAR
EDUC
EXPER
NM6
-2.534530
-0.028298
0.231193
0.094066
-0.838567
0.505861
0.008827
0.043385
0.013274
0.177720
-5.010334
-3.205928
5.328822
7.086320
-4.718481
0.0000
0.0013
0.0000
0.0000
0.0000
McFadden R-squared
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
LR statistic
Prob(LR statistic)
Obs with Dep=0
Obs with Dep=1
0.155580
0.487774
1.142608
1.175116
1.155174
145.5211
0.000000
272
428
Mean dependent var
S.E. of regression
Sum squared resid
Log likelihood
Restr. log likelihood
Avg. log likelihood
Total obs
PROBIT
McFadden R-squared
Log likelihood
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Sum squared resid
0.152596
-396.3084
1.146595
1.179103
1.159162
142.7299
0.611429
0.437295
132.9028
-394.9128
-467.6733
-0.564161
700
LOGIT
0.155580
-394.9128
1.142608
1.175116
1.155174
132.9028
El modelo logit es mejor porque tiene los menores criterios de información y los mayores McFadden y log likelihood.
Efmggamar = c(2)*enftf*(1-enftf) = -0.005437144431848025
Efmgeduc=c(3)*enftf*(1-enftf) = 0.04442151277672045
4
Efmgexper =c(4)*enftf*(1-enftf) = 0.01807389054149432
Efmgnm6=c(5)*enftf*(1-enftf) = -0.161122410130612
Obs
701
702
703
704
705
706
707
708
709
710
ENFT
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
ENFTF1
0,552193
0,761846
0,563484
0,942201
0,431336
0,309737
0,485316
0,618318
0,491337
0,316790
ENFTF2
1,000000
1,000000
1,000000
1,000000
0,000000
0,000000
0,000000
1,000000
0,000000
0,000000
Tabulation of ENFT-ENFTF2
Sample: 701 753
Included observations: 53
Number of categories: 2
Value
-1
0
Total
2º
Count
27
26
53
Percent
50.94
49.06
100.00
Estime el modelo siguiente:
HTRAB = F(GAMAR, EDUC, EXPER, EDAD, INGFAM, NM6)) y evalué signos y significancia. (4 puntos)
Dependent Variable: HTRAB
Method: ML - Censored Normal (TOBIT) (Quadratic hill climbing)
Sample: 1 753
Included observations: 753
Left censoring (value) at zero
Convergence achieved after 6 iterations
Covariance matrix computed using second derivatives
Variable
Coefficient
Std. Error
z-Statistic
Prob.
C
GAMAR
EDUC
EXPER
EDAD
INGFAM
NM6
1404.874
-201.8530
-38.23400
25.17984
-26.84469
0.195569
-388.0557
263.6269
9.143016
15.14258
4.664159
4.780045
0.008580
76.78860
5.329023
-22.07729
-2.524934
5.398582
-5.615992
22.79469
-5.053559
0.0000
0.0000
0.0116
0.0000
0.0000
0.0000
0.0000
27.46945
0.0000
Error Distribution
SCALE:C(8)
Mean dependent var
S.E. of regression
Sum squared resid
Log likelihood
Avg. log likelihood
Left censored obs
Uncensored obs
760.4416
740.5764
569.4098
2.42E+08
-3622.857
-4.811231
325
428
27.68318
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Right censored obs
Total obs
871.3142
9.643711
9.692838
9.662637
0
753
5
El signo de educación no es el correcto y todas las variables son altamente significativas.
3º.
Estimar el modelo logit que explique la probablidad de que una familia sea propietaria de una casa para las primeras 8
observaciones, luego evalué la capacidad predictiva del modelo. (4 puntos)
obs
1
2
3
4
5
6
7
8
9
10
1
6
0,156250
0,057190
P
0,200000
0,240000
0,300000
0,350000
0,450000
0,514286
0,600000
0,660000
0,750000
0,800000
INGRESO
6.000000
8.000000
10.00000
13.00000
15.00000
20.00000
25.00000
30.00000
35.00000
40.00000
Modified: 1 10 // varu=1/(nunfam*p*(1-p))
0,109649
0,079365
0,054945
0,064103
0,089127
0,133333
0,040404
0,250000
Dependent Variable: LOG(P/(1-P))
Method: Least Squares
Sample: 1 8
Included observations: 8
Weighting series: 1/SQR(VARU)
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
INGRESO
-1.655593
0.083001
0.142520
0.007899
-11.61653
10.50792
0.0000
0.0000
Weighted Statistics
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
0.948461
0.939871
0.157988
0.149760
4.561135
110.4164
0.000044
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
-0.321000
0.621220
-0.640284
-0.620423
-0.774234
1.303022
Unweighted Statistics
R-squared
Adjusted R-squared
S.E. of regression
0.958869
0.952014
0.161688
Mean dependent var
S.D. dependent var
Sum squared resid
obs
9
10
LF
1,249440
1,664444
P
0,750000
0,800000
PF
0,777203
0,840834
obs
9
EPMAPF
0,043656
RCREMPF
0,039185
UPF
0,021888
4º
Comente y fundamente su respuesta: (4 puntos)
4.1.
4.2.
Los modelos de elección discreta se estiman por máxima verosimilitud.
Todo modelo de elección múltiple se estima por mínimos cuadrados.
-0.385008
0.738111
0.156859