Sunday October 15 10:10:23 2023
Page 1
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Statistics/Data analysis
1 .
name: <unnamed>
log: C:\Users\egevrek\Dropbox\PORTO-econometrics2\Workshops_2023\WS3\Est
> imation_Results.smcl
log type: smcl
opened on:
1 Oct 2023, 17:57:09
2 . import excel "C:\Users\egevrek\Dropbox\PORTO-econometrics2\Workshops_2023\WS3\
> Mroz.xls", sheet("Sheet1") firstrow
(7 vars, 753 obs)
3 . do "C:\Users\egevrek\AppData\Local\Temp\STDb8b0_000000.tmp"
4 . **Part 1. Estimate the linear probability model
5 .
6 .
7 . ** To estimate the linear probability model (LPM) by OLS, we use "reg" command
> .
8 .
9 . reg inlf hincome educ exper age kidslt6 kidsge6
Source
SS
df
MS
Number of obs
F(6, 746)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
753
42.32
0.0000
0.2539
0.2479
.42982
Model
Residual
46.9082357
137.81952
6
746
7.81803929
.184744665
Total
184.727756
752
.245648611
inlf
Coefficient
Std. err.
t
P>|t|
[95% conf. interval]
hincome
educ
exper
age
kidslt6
kidsge6
_cons
-.0033265
.0398189
.0225725
-.017712
-.2718291
.0125301
.7072318
.0014574
.0074006
.0021786
.0024487
.0335715
.0132781
.1504335
-2.28
5.38
10.36
-7.23
-8.10
0.94
4.70
0.023
0.000
0.000
0.000
0.000
0.346
0.000
-.0061876
.0252905
.0182956
-.0225191
-.3377348
-.0135368
.4119083
-.0004654
.0543474
.0268493
-.0129049
-.2059233
.038597
1.002555
10 .
11 . ** Since the error terms are heteroskedastic in the linear probability model (
> LPM), we should obtain heteroskedasticity-robust standard errors.
12 .
13 . **To obtain heteroskedasticity-robust standard errors, we use "reg" command wi
> th "robust" option.
14 .
15 . reg inlf hincome educ exper age kidslt6 kidsge6, robust
Linear regression
Number of obs
F(6, 746)
Prob > F
R-squared
Root MSE
=
=
=
=
=
753
65.55
0.0000
0.2539
.42982
inlf
Coefficient
Robust
std. err.
t
P>|t|
[95% conf. interval]
hincome
educ
exper
age
kidslt6
kidsge6
_cons
-.0033265
.0398189
.0225725
-.017712
-.2718291
.0125301
.7072318
.0015099
.0072073
.0021001
.002273
.0314266
.0136017
.1459241
-2.20
5.52
10.75
-7.79
-8.65
0.92
4.85
0.028
0.000
0.000
0.000
0.000
0.357
0.000
-.0062907
.0256698
.0184497
-.0221743
-.3335241
-.014172
.420761
-.0003623
.053968
.0266952
-.0132497
-.210134
.0392322
.9937025
Sunday October 15 10:10:23 2023
Page 2
16 .
17 . ** All the explanatory variables except for "kidsge6" have a statistically sig
> nificant impact on the probability of being in the labor force (at the 5 perce
> nt significance level).
18 .
19 . **Part 2. Use "predict" command (with "xb" option) to obtain the estimated pro
> babilities.
20 . ** STATA creates a new variable named "probability" whose values are estimated
> probabilities. Note that you can use a different name for the new variable (
> i.e., predict "name of the new variable", xb)
21 .
22 . predict probability, xb
23 .
24 . ** For example, if you want to name the new variable "fittedvalues", then type
> : predict fittedvalues, xb
25 .
26 . ** "summarize" command (or shorcut "sum" command) provides descriptive statist
> ics about a variable.
27 .
28 . **Use "sum" command to find out the number of the estimated probabilities that
> are outside the unit interval.
29 .
30 . sum probability if probability>1 | probability<0
Variable
Obs
Mean
Std. dev.
Min
Max
probability
34
.6666093
.5640637
-.3042662
1.138675
31 .
32 . sum
probability if probability>1
Variable
Obs
Mean
Std. dev.
Min
Max
probability
23
1.04874
.0357447
1.003759
1.138675
33 .
34 . sum
probability if
probability<0
Variable
Obs
Mean
Std. dev.
Min
Max
probability
11
-.1323903
.0951249
-.3042662
-.0003745
35 .
36 . ** Note that 11 of the estimated probabilities are less than zero and 23 of th
> e estimated probabilities are greater than one.
37 .
38 . **Part 4. Use "probit" command to estimate the probit model.
39 .
40 . probit inlf hincome educ exper age kidslt6 kidsge6
Iteration 0:
Iteration 1:
Iteration 2:
Iteration 3:
Iteration 4:
Log likelihood = -514.8732
Log likelihood = -407.11545
Log likelihood = -406.21971
Log likelihood = -406.21886
Log likelihood = -406.21886
Probit regression
Number of obs =
753
LR chi2(6)
= 217.31
Prob > chi2
= 0.0000
Pseudo R2
= 0.2110
Log likelihood = -406.21886
inlf
Coefficient
Std. err.
z
P>|z|
[95% conf. interval]
hincome
educ
exper
age
kidslt6
kidsge6
_cons
-.0115648
.1336902
.0702165
-.0555548
-.8742923
.0345459
.5795817
.0047942
.0251346
.007571
.0083447
.1175098
.0429862
.496205
-2.41
5.32
9.27
-6.66
-7.44
0.80
1.17
0.016
0.000
0.000
0.000
0.000
0.422
0.243
-.0209613
.0844273
.0553775
-.0719101
-1.104607
-.0497055
-.3929623
-.0021684
.1829531
.0850555
-.0391995
-.6439773
.1187974
1.552126
Sunday October 15 10:10:23 2023
Page 3
41 .
42 .
43 . **Part 4 (a). The marginal effect of education on the probability of being in
> the labor force for a woman who is 30 years old, has 14 years of education, 7
> years of labor market experience, a husband with an annual income of $20,000,
> and 2 children who are older than 9 years old?
44 .
45 . ** Use "margins" command with "at" option.
46 .
47 . margins, dydx(educ) at(hincome=20 educ=14 exper=7 age=30 kidslt6=0 kidsge6=2)
Conditional marginal effects
Model VCE: OIM
Number of obs = 753
Expression: Pr(inlf), predict()
dy/dx wrt: educ
At: hincome = 20
educ
= 14
exper
= 7
age
= 30
kidslt6 = 0
kidsge6 = 2
dy/dx
educ
Delta-method
std. err.
z
P>|z|
[95% conf. interval]
.0055782
5.14
0.000
.0177466
.0286796
.0396126
48 .
49 .
50 . **Part 4 (b). The average marginal effect of education on the probability of b
> eing in the labor force
51 . ** Use "margins" command.
52 .
53 . margins, dydx(educ)
Average marginal effects
Model VCE: OIM
Number of obs = 753
Expression: Pr(inlf), predict()
dy/dx wrt: educ
dy/dx
educ
Delta-method
std. err.
z
P>|z|
[95% conf. interval]
.0072785
5.61
0.000
.0265645
.0408301
.0550958
54 .
55 .
56 . **Part 4 (c). The marginal effect of education on the probability of being in
> the labor force for an average individual.
57 . ** Use "margins" command with "atmeans" option.
58 .
59 . margins, dydx(educ) atmeans
Conditional marginal effects
Model VCE: OIM
Expression: Pr(inlf), predict()
dy/dx wrt: educ
At: hincome = 20.12896 (mean)
educ
= 12.28685 (mean)
exper
= 10.63081 (mean)
age
= 42.53785 (mean)
kidslt6 = .2377158 (mean)
kidsge6 = 1.353254 (mean)
Number of obs = 753
Sunday October 15 10:10:23 2023
dy/dx
educ
Page 4
Delta-method
std. err.
z
P>|z|
[95% conf. interval]
.0098013
5.32
0.000
.0329436
.0521537
.0713638
60 .
61 . **Part 5. Use "logit" command to estimate the probit model.
62 .
63 . logit inlf hincome educ exper age kidslt6 kidsge6
Iteration 0:
Iteration 1:
Iteration 2:
Iteration 3:
Iteration 4:
Log likelihood = -514.8732
Log likelihood = -406.91038
Log likelihood = -406.14404
Log likelihood = -406.14318
Log likelihood = -406.14318
Logistic regression
Number of obs =
753
LR chi2(6)
= 217.46
Prob > chi2
= 0.0000
Pseudo R2
= 0.2112
Log likelihood = -406.14318
inlf
Coefficient
Std. err.
z
P>|z|
[95% conf. interval]
hincome
educ
exper
age
kidslt6
kidsge6
_cons
-.0202165
.2269766
.1197458
-.0910884
-1.439393
.0581735
.8379089
.0082637
.0432954
.0136264
.0143207
.2014989
.07338
.8409368
-2.45
5.24
8.79
-6.36
-7.14
0.79
1.00
0.014
0.000
0.000
0.000
0.000
0.428
0.319
-.036413
.1421191
.0930385
-.1191564
-1.834324
-.0856487
-.810297
-.0040199
.3118341
.146453
-.0630204
-1.044462
.2019957
2.486115
64 .
65 .
66 . **Part 5 (a). The marginal effect of labor market experience on the probabilit
> y of being in the labor force for a woman who is 30 years old, has 14 years of
> education, 7 years of labor market experience, a husband with an annual incom
> e of $20,000, and 2 children who are older than 9 years old?
67 .
68 . ** Use "margins" command with "at" option.
69 .
70 . margins, dydx(exper) at(hincome=20 educ=14 exper=7 age=30 kidslt6=0 kidsge6=2)
Conditional marginal effects
Model VCE: OIM
Number of obs = 753
Expression: Pr(inlf), predict()
dy/dx wrt: exper
At: hincome = 20
educ
= 14
exper
= 7
age
= 30
kidslt6 = 0
kidsge6 = 2
dy/dx
exper
.0142325
Delta-method
std. err.
z
P>|z|
[95% conf. interval]
.0026503
5.37
0.000
.0090379
.019427
Sunday October 15 10:10:23 2023
Page 5
71 .
72 .
73 . **Part 5 (b). The average marginal effect of labor market experience on the pr
> obability of being in the labor force
74 . ** Use "margins" command.
75 .
76 . margins, dydx(exper)
Average marginal effects
Model VCE: OIM
Number of obs = 753
Expression: Pr(inlf), predict()
dy/dx wrt: exper
dy/dx
exper
Delta-method
std. err.
z
P>|z|
[95% conf. interval]
.0019897
10.91
0.000
.0177994
.0216992
.025599
77 .
78 .
79 . **Part 5 (c). The marginal effect of labor market experience on the probabilit
> y of being in the labor force for an average individual.
80 . ** Use "margins" command with "atmeans" option.
81 .
82 . margins, dydx(exper) atmeans
Conditional marginal effects
Model VCE: OIM
Number of obs = 753
Expression: Pr(inlf), predict()
dy/dx wrt: exper
At: hincome = 20.12896 (mean)
educ
= 12.28685 (mean)
exper
= 10.63081 (mean)
age
= 42.53785 (mean)
kidslt6 = .2377158 (mean)
kidsge6 = 1.353254 (mean)
dy/dx
exper
Delta-method
std. err.
z
P>|z|
[95% conf. interval]
.003267
8.88
0.000
.0226113
.0290145
.0354177
83 .
84 . **Part 6. Estimate the logit model using "logit" command.
85 .
86 . logit inlf hincome educ exper age kidslt6 kidsge6
Iteration 0:
Iteration 1:
Iteration 2:
Iteration 3:
Iteration 4:
Log likelihood = -514.8732
Log likelihood = -406.91038
Log likelihood = -406.14404
Log likelihood = -406.14318
Log likelihood = -406.14318
Logistic regression
Log likelihood = -406.14318
Number of obs =
753
LR chi2(6)
= 217.46
Prob > chi2
= 0.0000
Pseudo R2
= 0.2112
Sunday October 15 10:10:23 2023
Page 6
inlf
Coefficient
Std. err.
z
P>|z|
[95% conf. interval]
hincome
educ
exper
age
kidslt6
kidsge6
_cons
-.0202165
.2269766
.1197458
-.0910884
-1.439393
.0581735
.8379089
.0082637
.0432954
.0136264
.0143207
.2014989
.07338
.8409368
-2.45
5.24
8.79
-6.36
-7.14
0.79
1.00
0.014
0.000
0.000
0.000
0.000
0.428
0.319
-.036413
.1421191
.0930385
-.1191564
-1.834324
-.0856487
-.810297
-.0040199
.3118341
.146453
-.0630204
-1.044462
.2019957
2.486115
87 .
88 . **Wald Test:
89 .
90 . **Use "test" command to perform Wald Test.
91 .
92 . test educ age
( 1)
( 2)
[inlf]educ = 0
[inlf]age = 0
chi2( 2) =
Prob > chi2 =
72.45
0.0000
93 .
94 . **Likelihood Ratio (LR) Test:
95 .
96 . ** Estimate the unrestricted model using "logit" command and store the estimat
> ion results obtained from the unrestricted model using "estimates store" comma
> nd.
97 .
98 . logit inlf hincome educ exper age kidslt6 kidsge6
Iteration 0:
Iteration 1:
Iteration 2:
Iteration 3:
Iteration 4:
Log likelihood = -514.8732
Log likelihood = -406.91038
Log likelihood = -406.14404
Log likelihood = -406.14318
Log likelihood = -406.14318
Logistic regression
Number of obs =
753
LR chi2(6)
= 217.46
Prob > chi2
= 0.0000
Pseudo R2
= 0.2112
Log likelihood = -406.14318
inlf
Coefficient
Std. err.
z
P>|z|
[95% conf. interval]
hincome
educ
exper
age
kidslt6
kidsge6
_cons
-.0202165
.2269766
.1197458
-.0910884
-1.439393
.0581735
.8379089
.0082637
.0432954
.0136264
.0143207
.2014989
.07338
.8409368
-2.45
5.24
8.79
-6.36
-7.14
0.79
1.00
0.014
0.000
0.000
0.000
0.000
0.428
0.319
-.036413
.1421191
.0930385
-.1191564
-1.834324
-.0856487
-.810297
-.0040199
.3118341
.146453
-.0630204
-1.044462
.2019957
2.486115
99 .
100 . estimates store unrestricted
101 .
102 . ** Estimate the restricted model using "logit" command and store the estimatio
> n results obtained from the restricted model using "estimates store" command.
Sunday October 15 10:10:23 2023
Page 7
103 .
104 . logit inlf hincome exper kidslt6
kidsge6
Iteration 0:
Iteration 1:
Iteration 2:
Iteration 3:
Iteration 4:
Log likelihood = -514.8732
Log likelihood = -450.95875
Log likelihood = -450.24251
Log likelihood = -450.24055
Log likelihood = -450.24055
Logistic regression
Number of obs =
753
LR chi2(4)
= 129.27
Prob > chi2
= 0.0000
Pseudo R2
= 0.1255
Log likelihood = -450.24055
inlf
Coefficient
Std. err.
z
P>|z|
[95% conf. interval]
hincome
exper
kidslt6
kidsge6
_cons
-.0122709
.1053723
-.6853735
.1930941
-.6222555
.0070886
.0126944
.1619961
.0643118
.24754
-1.73
8.30
-4.23
3.00
-2.51
0.083
0.000
0.000
0.003
0.012
-.0261643
.0804918
-1.00288
.0670453
-1.107425
.0016225
.1302527
-.367867
.3191428
-.137086
105 .
106 . estimates store restricted
107 .
108 . ** Note that the command "estimates store" allows us to store the estimation r
> esults from the unrestricted and restricted model.
109 .
110 . ** Use "lrtest" command to perform LR Test.
111 .
112 . lrtest unrestricted restricted
Likelihood-ratio test
Assumption: restricted nested within unrestricted
LR chi2(2) = 88.19
Prob > chi2 = 0.0000
113 .
114 . **Part 7. The percent perfectly predicted in the probit model
115 .
116 . probit inlf hincome educ exper age kidslt6 kidsge6
Iteration 0:
Iteration 1:
Iteration 2:
Iteration 3:
Iteration 4:
Log likelihood = -514.8732
Log likelihood = -407.11545
Log likelihood = -406.21971
Log likelihood = -406.21886
Log likelihood = -406.21886
Probit regression
Number of obs =
753
LR chi2(6)
= 217.31
Prob > chi2
= 0.0000
Pseudo R2
= 0.2110
Log likelihood = -406.21886
inlf
Coefficient
Std. err.
z
P>|z|
[95% conf. interval]
hincome
educ
exper
age
kidslt6
kidsge6
_cons
-.0115648
.1336902
.0702165
-.0555548
-.8742923
.0345459
.5795817
.0047942
.0251346
.007571
.0083447
.1175098
.0429862
.496205
-2.41
5.32
9.27
-6.66
-7.44
0.80
1.17
0.016
0.000
0.000
0.000
0.000
0.422
0.243
-.0209613
.0844273
.0553775
-.0719101
-1.104607
-.0497055
-.3929623
-.0021684
.1829531
.0850555
-.0391995
-.6439773
.1187974
1.552126
Sunday October 15 10:10:24 2023
Page 8
117 .
118 . **Use "predict" command to calculate the estimated probability of being in the
> labor force for each observation.
119 .
120 . predict phat
(option pr assumed; Pr(inlf))
121 .
122 . ** Create a new variable named "p" using "generate" command (or shorcut "gen"
> command)
123 . ** "p" is a dummy variable that takes the value of 1 if the estimated probabil
> ity of being in the labor force is greater than 0.5 and takes the value of 0 o
> therwise.
124 . ** The variable "p" is called predicted outcome.
125 .
126 . gen p=(phat>0.5)
127 .
128 . *** Use "tabulate" command (or shorcut "tab" command) to examine the relations
> hip between the variable "p" (i.e., predicted outcome) and the variable "inlf
> " (i.e, actual outcome)
129 .
130 . tab p inlf
p
inlf
0
1
Total
0
1
213
112
80
348
293
460
Total
325
428
753
131 .
132 . ** The overall percent perfectly predicted is 73.84
133 .
134 . **The percent perfectly predicted for inlf=0 is 65.54
135 .
136 . display (213/325)*100
65.538462
137 .
138 . **The percent perfectly predicted
139 .
140 . display (348/428)*100
81.308411
for inlf=1
is 81.31
141 .
end of do-file
142 . log close
name: <unnamed>
log: C:\Users\egevrek\Dropbox\PORTO-econometrics2\Workshops_2023\WS3\Est
> imation_Results.smcl
log type: smcl
closed on:
1 Oct 2023, 17:58:21