Chapter 15 - Binary Response Models
Examples
------------------------------------------------------------------------------------------
name: SN
log: myReplications\iiexample15.smcl
log type: smcl
opened on: 9 May 2020, 17:51:45
. **********************************************
. * Solomon Negash - Examples
. * Wooldridge (2010). Economic Analysis of Cross-Section and Panel Data. 2nd ed.
. * STATA Program, version 16.1.
. * Chapter 15 - Binary Response Models
. ********************************************
. // Example 15.1 (Married Women's Labor Force Participation)
. bcuse mroz, clear nodesc
. eststo Hetrosced: reg inlf nwifeinc exper expersq educ age kidslt6 kidsge6
Source | SS df MS Number of obs = 753
-------------+---------------------------------- F(7, 745) = 38.22
Model | 48.8080578 7 6.97257968 Prob > F = 0.0000
Residual | 135.919698 745 .182442547 R-squared = 0.2642
-------------+---------------------------------- Adj R-squared = 0.2573
Total | 184.727756 752 .245648611 Root MSE = .42713
------------------------------------------------------------------------------
inlf | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
nwifeinc | -.0034052 .0014485 -2.35 0.019 -.0062488 -.0005616
exper | .0394924 .0056727 6.96 0.000 .0283561 .0506287
expersq | -.0005963 .0001848 -3.23 0.001 -.0009591 -.0002335
educ | .0379953 .007376 5.15 0.000 .023515 .0524756
age | -.0160908 .0024847 -6.48 0.000 -.0209686 -.011213
kidslt6 | -.2618105 .0335058 -7.81 0.000 -.3275875 -.1960335
kidsge6 | .0130122 .013196 0.99 0.324 -.0128935 .0389179
_cons | .5855192 .154178 3.80 0.000 .2828442 .8881943
------------------------------------------------------------------------------
. eststo Robust: reg inlf nwifeinc exper expersq educ age kidslt6 kidsge6, r
Linear regression Number of obs = 753
F(7, 745) = 62.48
Prob > F = 0.0000
R-squared = 0.2642
Root MSE = .42713
------------------------------------------------------------------------------
| Robust
inlf | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
nwifeinc | -.0034052 .0015249 -2.23 0.026 -.0063988 -.0004115
exper | .0394924 .00581 6.80 0.000 .0280864 .0508983
expersq | -.0005963 .00019 -3.14 0.002 -.0009693 -.0002233
educ | .0379953 .007266 5.23 0.000 .023731 .0522596
age | -.0160908 .002399 -6.71 0.000 -.0208004 -.0113812
kidslt6 | -.2618105 .0317832 -8.24 0.000 -.3242058 -.1994152
kidsge6 | .0130122 .0135329 0.96 0.337 -.013555 .0395795
_cons | .5855192 .1522599 3.85 0.000 .2866098 .8844287
------------------------------------------------------------------------------
. estout, cells(b(nostar fmt(4)) se(par fmt(4))) ///
stats(ll r2 r2_p N, fmt(%9.3f %9.0g) labels(Log-Likelihood R-squared Psuedo-R2 N))
--------------------------------------
Hetrosced Robust
b/se b/se
--------------------------------------
nwifeinc -0.0034 -0.0034
(0.0014) (0.0015)
exper 0.0395 0.0395
(0.0057) (0.0058)
expersq -0.0006 -0.0006
(0.0002) (0.0002)
educ 0.0380 0.0380
(0.0074) (0.0073)
age -0.0161 -0.0161
(0.0025) (0.0024)
kidslt6 -0.2618 -0.2618
(0.0335) (0.0318)
kidsge6 0.0130 0.0130
(0.0132) (0.0135)
_cons 0.5855 0.5855
(0.1542) (0.1523)
--------------------------------------
Log-Likeli~d -423.892 -423.892
R-squared .2642162 .2642162
Psuedo-R2
N 753 753
--------------------------------------
. eststo clear
. // Example 15.2 (Married Women's Labor Force Participation
. eststo LPM: reg inlf nwifeinc exper expersq educ age kidslt6 kidsge6
Source | SS df MS Number of obs = 753
-------------+---------------------------------- F(7, 745) = 38.22
Model | 48.8080578 7 6.97257968 Prob > F = 0.0000
Residual | 135.919698 745 .182442547 R-squared = 0.2642
-------------+---------------------------------- Adj R-squared = 0.2573
Total | 184.727756 752 .245648611 Root MSE = .42713
------------------------------------------------------------------------------
inlf | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
nwifeinc | -.0034052 .0014485 -2.35 0.019 -.0062488 -.0005616
exper | .0394924 .0056727 6.96 0.000 .0283561 .0506287
expersq | -.0005963 .0001848 -3.23 0.001 -.0009591 -.0002335
educ | .0379953 .007376 5.15 0.000 .023515 .0524756
age | -.0160908 .0024847 -6.48 0.000 -.0209686 -.011213
kidslt6 | -.2618105 .0335058 -7.81 0.000 -.3275875 -.1960335
kidsge6 | .0130122 .013196 0.99 0.324 -.0128935 .0389179
_cons | .5855192 .154178 3.80 0.000 .2828442 .8881943
------------------------------------------------------------------------------
. eststo Logit: logit inlf nwifeinc exper expersq educ age kidslt6 kidsge6, nolog
Logistic regression Number of obs = 753
LR chi2(7) = 226.22
Prob > chi2 = 0.0000
Log likelihood = -401.76515 Pseudo R2 = 0.2197
------------------------------------------------------------------------------
inlf | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
nwifeinc | -.0213452 .0084214 -2.53 0.011 -.0378509 -.0048394
exper | .2058695 .0320569 6.42 0.000 .1430391 .2686999
expersq | -.0031541 .0010161 -3.10 0.002 -.0051456 -.0011626
educ | .2211704 .0434396 5.09 0.000 .1360303 .3063105
age | -.0880244 .014573 -6.04 0.000 -.116587 -.0594618
kidslt6 | -1.443354 .2035849 -7.09 0.000 -1.842373 -1.044335
kidsge6 | .0601122 .0747897 0.80 0.422 -.086473 .2066974
_cons | .4254524 .8603697 0.49 0.621 -1.260841 2.111746
------------------------------------------------------------------------------
. eststo Probit: probit inlf nwifeinc exper expersq educ age kidslt6 kidsge6, nolog
Probit regression Number of obs = 753
LR chi2(7) = 227.14
Prob > chi2 = 0.0000
Log likelihood = -401.30219 Pseudo R2 = 0.2206
------------------------------------------------------------------------------
inlf | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
nwifeinc | -.0120237 .0048398 -2.48 0.013 -.0215096 -.0025378
exper | .1233476 .0187164 6.59 0.000 .0866641 .1600311
expersq | -.0018871 .0006 -3.15 0.002 -.003063 -.0007111
educ | .1309047 .0252542 5.18 0.000 .0814074 .180402
age | -.0528527 .0084772 -6.23 0.000 -.0694678 -.0362376
kidslt6 | -.8683285 .1185223 -7.33 0.000 -1.100628 -.636029
kidsge6 | .036005 .0434768 0.83 0.408 -.049208 .1212179
_cons | .2700768 .508593 0.53 0.595 -.7267472 1.266901
------------------------------------------------------------------------------
. estout, cells(b(nostar fmt(4)) se(par fmt(4))) stats(ll r2 r2_p N, ///
fmt(%9.3f %9.0g) labels(Log-Likelihood R-squared Psuedo-R2 N)) ///
ti("Table 15.1 LPM, Logit, and Probit Estimates of Labor Force Participation: (inlf)")
Table 15.1 LPM, Logit, and Probit Estimates of Labor Force Participation: (inlf)
---------------------------------------------------
LPM Logit Probit
b/se b/se b/se
---------------------------------------------------
main
nwifeinc -0.0034 -0.0213 -0.0120
(0.0014) (0.0084) (0.0048)
exper 0.0395 0.2059 0.1233
(0.0057) (0.0321) (0.0187)
expersq -0.0006 -0.0032 -0.0019
(0.0002) (0.0010) (0.0006)
educ 0.0380 0.2212 0.1309
(0.0074) (0.0434) (0.0253)
age -0.0161 -0.0880 -0.0529
(0.0025) (0.0146) (0.0085)
kidslt6 -0.2618 -1.4434 -0.8683
(0.0335) (0.2036) (0.1185)
kidsge6 0.0130 0.0601 0.0360
(0.0132) (0.0748) (0.0435)
_cons 0.5855 0.4255 0.2701
(0.1542) (0.8604) (0.5086)
---------------------------------------------------
Log-Likeli~d -423.892 -401.765 -401.302
R-squared .2642162
Psuedo-R2 .2196814 .2205805
N 753 753 753
---------------------------------------------------
. eststo clear
. // Example 15.3 (Testing Exogeneity of Education in the Women's LFP Model) (Page 587)
. reg educ nwifeinc exper expersq age kidslt6 kidsge6 motheduc fatheduc huseduc
Source | SS df MS Number of obs = 753
-------------+---------------------------------- F(9, 743) = 74.07
Model | 1849.07781 9 205.45309 Prob > F = 0.0000
Residual | 2060.96203 743 2.77383853 R-squared = 0.4729
-------------+---------------------------------- Adj R-squared = 0.4665
Total | 3910.03984 752 5.19952106 Root MSE = 1.6655
------------------------------------------------------------------------------
educ | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
nwifeinc | .0156893 .0058267 2.69 0.007 .0042506 .027128
exper | .0577544 .0220604 2.62 0.009 .0144462 .1010625
expersq | -.000784 .000721 -1.09 0.277 -.0021994 .0006314
age | -.0059011 .0098709 -0.60 0.550 -.0252792 .013477
kidslt6 | .1195954 .1307071 0.91 0.360 -.1370038 .3761945
kidsge6 | -.0731404 .0515299 -1.42 0.156 -.174302 .0280212
motheduc | .1300347 .0225669 5.76 0.000 .0857322 .1743373
fatheduc | .0950702 .0214618 4.43 0.000 .0529373 .1372032
huseduc | .3475092 .0235063 14.78 0.000 .3013626 .3936558
_cons | 5.43695 .5873755 9.26 0.000 4.283837 6.590064
------------------------------------------------------------------------------
. predict v2, r
. probit inlf nwifeinc exper expersq educ age kidslt6 kidsge6 v2, nolog
Probit regression Number of obs = 753
LR chi2(8) = 227.90
Prob > chi2 = 0.0000
Log likelihood = -400.92551 Pseudo R2 = 0.2213
------------------------------------------------------------------------------
inlf | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
nwifeinc | -.0102851 .0052347 -1.96 0.049 -.020545 -.0000253
exper | .1262477 .0190256 6.64 0.000 .0889582 .1635373
expersq | -.0019432 .0006032 -3.22 0.001 -.0031254 -.0007609
educ | .1035752 .0403061 2.57 0.010 .0245767 .1825737
age | -.0543808 .0086633 -6.28 0.000 -.0713605 -.0374012
kidslt6 | -.8630859 .1187394 -7.27 0.000 -1.095811 -.630361
kidsge6 | .0313802 .0437901 0.72 0.474 -.0544468 .1172071
v2 | .0433658 .050021 0.87 0.386 -.0546736 .1414051
_cons | .6209105 .6497413 0.96 0.339 -.652559 1.89438
------------------------------------------------------------------------------
. // Example 15.3 (Endogeniety of Nonwife income in the Women's LFP Model) (Page 589)
. reg nwifeinc huseduc educ exper expersq age kidslt6 kidsge6
Source | SS df MS Number of obs = 753
-------------+---------------------------------- F(7, 745) = 27.13
Model | 20676.7702 7 2953.82432 Prob > F = 0.0000
Residual | 81120.3455 745 108.88637 R-squared = 0.2031
-------------+---------------------------------- Adj R-squared = 0.1956
Total | 101797.116 752 135.368505 Root MSE = 10.435
------------------------------------------------------------------------------
nwifeinc | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
huseduc | 1.178155 .1609449 7.32 0.000 .8621956 1.494115
educ | .6746951 .2136829 3.16 0.002 .2552029 1.094187
exper | -.3129878 .1382549 -2.26 0.024 -.5844034 -.0415721
expersq | -.0004776 .0045196 -0.11 0.916 -.0093501 .008395
age | .3401521 .0597084 5.70 0.000 .2229354 .4573687
kidslt6 | .8262718 .8183785 1.01 0.313 -.7803306 2.432874
kidsge6 | .4355289 .3219888 1.35 0.177 -.1965845 1.067642
_cons | -14.72048 3.787326 -3.89 0.000 -22.15559 -7.285382
------------------------------------------------------------------------------
. predict v3, r
. probit inlf nwifeinc exper expersq educ age kidslt6 kidsge6 v3, nolog
Probit regression Number of obs = 753
LR chi2(8) = 229.14
Prob > chi2 = 0.0000
Log likelihood = -400.30301 Pseudo R2 = 0.2225
------------------------------------------------------------------------------
inlf | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
nwifeinc | -.0368641 .0182706 -2.02 0.044 -.0726738 -.0010543
exper | .1163123 .0193312 6.02 0.000 .0784239 .1542007
expersq | -.0019459 .0006009 -3.24 0.001 -.0031235 -.0007682
educ | .1702153 .0376718 4.52 0.000 .0963798 .2440507
age | -.044953 .0101367 -4.43 0.000 -.0648206 -.0250855
kidslt6 | -.8444363 .1198154 -7.05 0.000 -1.07927 -.6096025
kidsge6 | .0477905 .0443204 1.08 0.281 -.0390758 .1346568
v3 | .0267093 .0189352 1.41 0.158 -.0104031 .0638217
_cons | .0171187 .5392914 0.03 0.975 -1.039873 1.07411
------------------------------------------------------------------------------
. margeff
Average marginal effects on Prob(inlf==1) after probit
------------------------------------------------------------------------------
inlf | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
nwifeinc | -.0110576 .0054418 -2.03 0.042 -.0217234 -.0003918
exper | .0348887 .0053903 6.47 0.000 .0243239 .0454535
expersq | -.0005837 .0001767 -3.30 0.001 -.0009299 -.0002374
educ | .0510572 .0108776 4.69 0.000 .0297375 .0723769
age | -.013484 .0029275 -4.61 0.000 -.0192217 -.0077463
kidslt6 | -.2532945 .0324497 -7.81 0.000 -.3168947 -.1896942
kidsge6 | .0143351 .0132656 1.08 0.280 -.0116651 .0403353
v3 | .0080116 .00566 1.42 0.157 -.0030817 .019105
------------------------------------------------------------------------------
. // Example 15.4. (Women's Labor Force Participation and Having More than Two Children)
. u labsup, clear
. g agesq= age^2
. eststo LPM_OLS: reg worked morekids nonmomi educ age agesq black hispan
Source | SS df MS Number of obs = 31,857
-------------+---------------------------------- F(7, 31849) = 405.04
Model | 630.048635 7 90.0069478 Prob > F = 0.0000
Residual | 7077.35169 31,849 .222215821 R-squared = 0.0817
-------------+---------------------------------- Adj R-squared = 0.0815
Total | 7707.40032 31,856 .241945013 Root MSE = .4714
------------------------------------------------------------------------------
worked | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
morekids | -.1091198 .0054742 -19.93 0.000 -.1198495 -.0983901
nonmomi | -.0011675 .0001354 -8.63 0.000 -.0014328 -.0009022
educ | .0206475 .0009053 22.81 0.000 .0188731 .0224219
age | .0562704 .0112458 5.00 0.000 .0342282 .0783125
agesq | -.0007829 .0001932 -4.05 0.000 -.0011616 -.0004041
black | .0176482 .0338829 0.52 0.602 -.0487636 .08406
hispan | -.1285859 .0339362 -3.79 0.000 -.1951022 -.0620696
_cons | -.448645 .1649612 -2.72 0.007 -.7719752 -.1253148
------------------------------------------------------------------------------
. eststo Probit: probit worked morekids nonmomi educ age agesq black hispan, nolog
Probit regression Number of obs = 31,857
LR chi2(7) = 2693.96
Prob > chi2 = 0.0000
Log likelihood = -20218.111 Pseudo R2 = 0.0625
------------------------------------------------------------------------------
worked | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
morekids | -.2986554 .0150511 -19.84 0.000 -.3281551 -.2691558
nonmomi | -.0031412 .0003701 -8.49 0.000 -.0038665 -.0024159
educ | .0554282 .0024978 22.19 0.000 .0505327 .0603237
age | .1479387 .0308452 4.80 0.000 .0874834 .2083941
agesq | -.0020364 .0005305 -3.84 0.000 -.0030763 -.0009966
black | .0412891 .0916525 0.45 0.652 -.1383465 .2209248
hispan | -.3586388 .09188 -3.90 0.000 -.5387203 -.1785574
_cons | -2.496476 .4516554 -5.53 0.000 -3.381704 -1.611247
------------------------------------------------------------------------------
. eststo ProbitAPE: margins, dydx(morekids) post
Average marginal effects Number of obs = 31,857
Model VCE : OIM
Expression : Pr(worked), predict()
dy/dx w.r.t. : morekids
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
morekids | -.1082686 .0053561 -20.21 0.000 -.1187664 -.0977708
------------------------------------------------------------------------------
. eststo LPM_IV: ivreg worked (morekids=samesex) nonmomi educ age agesq black hispan
Instrumental variables (2SLS) regression
Source | SS df MS Number of obs = 31,857
-------------+---------------------------------- F(7, 31849) = 345.86
Model | 567.677514 7 81.0967877 Prob > F = 0.0000
Residual | 7139.72281 31,849 .22417416 R-squared = 0.0737
-------------+---------------------------------- Adj R-squared = 0.0734
Total | 7707.40032 31,856 .241945013 Root MSE = .47347
------------------------------------------------------------------------------
worked | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
morekids | -.200832 .0964721 -2.08 0.037 -.3899211 -.011743
nonmomi | -.00126 .0001671 -7.54 0.000 -.0015874 -.0009325
educ | .0175522 .0033755 5.20 0.000 .0109361 .0241682
age | .0603517 .0120811 5.00 0.000 .0366722 .0840311
agesq | -.0008178 .0001975 -4.14 0.000 -.001205 -.0004307
black | .0168118 .0340432 0.49 0.621 -.0499142 .0835379
hispan | -.1308112 .0341655 -3.83 0.000 -.1977768 -.0638456
_cons | -.454969 .1658195 -2.74 0.006 -.7799816 -.1299564
------------------------------------------------------------------------------
Instrumented: morekids
Instruments: nonmomi educ age agesq black hispan samesex
------------------------------------------------------------------------------
. eststo Biprobit_IV: biprobit (worked morekids nonmomi educ age agesq black hispan) ///
(morekids=samesex nonmomi educ age agesq black hispan)
Seemingly unrelated bivariate probit Number of obs = 31,857
Wald chi2(14) = 5124.29
Log likelihood = -41106.422 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
worked |
morekids | -.7025719 .204014 -3.44 0.001 -1.102432 -.3027119
nonmomi | -.0034903 .000395 -8.84 0.000 -.0042645 -.0027161
educ | .0405621 .0085385 4.75 0.000 .0238271 .0572972
age | .1632256 .0312412 5.22 0.000 .1019939 .2244573
agesq | -.0021524 .0005277 -4.08 0.000 -.0031867 -.001118
black | .0367322 .0909997 0.40 0.686 -.1416239 .2150883
hispan | -.3614826 .0912096 -3.96 0.000 -.5402502 -.182715
_cons | -2.475317 .4496294 -5.51 0.000 -3.356575 -1.59406
-------------+----------------------------------------------------------------
morekids |
samesex | .1446566 .0144319 10.02 0.000 .1163705 .1729427
nonmomi | -.0027063 .0003685 -7.34 0.000 -.0034285 -.0019841
educ | -.0907148 .0024968 -36.33 0.000 -.0956083 -.0858212
age | .1190243 .0307613 3.87 0.000 .0587333 .1793154
agesq | -.001028 .0005284 -1.95 0.052 -.0020636 7.54e-06
black | -.0277804 .0921479 -0.30 0.763 -.208387 .1528263
hispan | -.0690523 .0922843 -0.75 0.454 -.2499262 .1118217
_cons | -1.572557 .4514335 -3.48 0.000 -2.457351 -.6877639
-------------+----------------------------------------------------------------
/athrho | .2599507 .1396201 1.86 0.063 -.0136996 .533601
-------------+----------------------------------------------------------------
rho | .2542495 .1305946 -.0136987 .4881289
------------------------------------------------------------------------------
LR test of rho=0: chi2(1) = 3.33969 Prob > chi2 = 0.0676
. eststo BiprobitAPE: margins, dydx(morekids) post
Average marginal effects Number of obs = 31,857
Model VCE : OIM
Expression : Pr(worked=1,morekids=1), predict()
dy/dx w.r.t. : morekids
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
morekids | -.1163742 .0287226 -4.05 0.000 -.1726695 -.0600788
------------------------------------------------------------------------------
. eststo Biprobit: biprobit (worked morekids nonmomi educ age agesq black hispan) ///
(morekids nonmomi educ age agesq black hispan)
Seemingly unrelated bivariate probit Number of obs = 31,857
Wald chi2(13) = 5878.97
Log likelihood = -41157.989 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
worked |
morekids | -.9663993 .243112 -3.98 0.000 -1.44289 -.4899086
nonmomi | -.0036516 .0003815 -9.57 0.000 -.0043994 -.0029039
educ | .0292476 .0114284 2.56 0.010 .0068483 .0516469
age | .1701076 .0305804 5.56 0.000 .1101711 .2300441
agesq | -.0021836 .0005188 -4.21 0.000 -.0032005 -.0011668
black | .0325432 .0897866 0.36 0.717 -.1434353 .2085216
hispan | -.3550572 .0904013 -3.93 0.000 -.5322405 -.177874
_cons | -2.403905 .4506848 -5.33 0.000 -3.287231 -1.520579
-------------+----------------------------------------------------------------
morekids |
nonmomi | -.0026773 .000368 -7.28 0.000 -.0033985 -.001956
educ | -.090503 .0024904 -36.34 0.000 -.095384 -.085622
age | .1204846 .030709 3.92 0.000 .0602961 .180673
agesq | -.0010565 .0005275 -2.00 0.045 -.0020903 -.0000227
black | -.02663 .0920542 -0.29 0.772 -.2070529 .153793
hispan | -.0667949 .092191 -0.72 0.469 -.247486 .1138962
_cons | -1.522285 .4506283 -3.38 0.001 -2.4055 -.6390698
-------------+----------------------------------------------------------------
/athrho | .4545144 .1974215 2.30 0.021 .0675755 .8414534
-------------+----------------------------------------------------------------
rho | .4256028 .161661 .0674728 .6865781
------------------------------------------------------------------------------
LR test of rho=0: chi2(1) = 3.70365 Prob > chi2 = 0.0543
. eststo Biprobit_APE: margins, dydx(morekids) post
Average marginal effects Number of obs = 31,857
Model VCE : OIM
Expression : Pr(worked=1,morekids=1), predict()
dy/dx w.r.t. : morekids
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
morekids | -.1507563 .0293686 -5.13 0.000 -.2083177 -.0931949
------------------------------------------------------------------------------
. estout LPM_OLS Probit LPM_IV Biprobit_IV Biprobit, keep(morekids) cells(b(nostar fmt(4)) ///
se(par fmt(4))) stats(ll r2 r2_p N, fmt(%9.3f %9.0g) labels(Log-Likelihood R-squared Psuedo-R2 N)) ///
ti("Table 15.2 Estimated Effect of Having Three or More Children on Women's Labor Force Participation")
Table 15.2 Estimated Effect of Having Three or More Children on Women's Labor Force Participation
-----------------------------------------------------------------------------
LPM_OLS Probit LPM_IV Biprobit_IV Biprobit
b/se b/se b/se b/se b/se
-----------------------------------------------------------------------------
main
morekids -0.1091 -0.2987 -0.2008 -0.7026 -0.9664
(0.0055) (0.0151) (0.0965) (0.2040) (0.2431)
-----------------------------------------------------------------------------
Log-Likeli~d -2.12e+04 -2.02e+04 -4.11e+04 -4.12e+04
R-squared .0817459 .0736536
Psuedo-R2 .0624612
N 31857 31857 31857 31857 31857
-----------------------------------------------------------------------------
. estout LPM_OLS ProbitAPE LPM_IV BiprobitAPE Biprobit_APE, keep(morekids) ///
cells(b(nostar fmt(4)) se(par fmt(4)))
-----------------------------------------------------------------------------
LPM_OLS ProbitAPE LPM_IV BiprobitAPE Biprobit_APE
b/se b/se b/se b/se b/se
-----------------------------------------------------------------------------
morekids -0.1091 -0.1083 -0.2008 -0.1164 -0.1508
(0.0055) (0.0054) (0.0965) (0.0287) (0.0294)
-----------------------------------------------------------------------------
. eststo clear
. // Example 15.5 (Panel Data Models for Women's Labor Force Participation)
. use lfp, clear
. xtset id period
panel variable: id (strongly balanced)
time variable: period, 1 to 5
delta: 1 unit
. eststo FE_Linear: xtreg lfp kids lhinc edu age agesq black i.period, fe cluster(id)
note: educ omitted because of collinearity
note: age omitted because of collinearity
note: agesq omitted because of collinearity
note: black omitted because of collinearity
Fixed-effects (within) regression Number of obs = 28,315
Group variable: id Number of groups = 5,663
R-sq: Obs per group:
within = 0.0031 min = 5
between = 0.0103 avg = 5.0
overall = 0.0091 max = 5
F(6,5662) = 5.61
corr(u_i, Xb) = -0.0073 Prob > F = 0.0000
(Std. Err. adjusted for 5,663 clusters in id)
------------------------------------------------------------------------------
| Robust
lfp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
kids | -.0388976 .0091682 -4.24 0.000 -.0568708 -.0209244
lhinc | -.0089439 .0045947 -1.95 0.052 -.0179513 .0000635
educ | 0 (omitted)
age | 0 (omitted)
agesq | 0 (omitted)
black | 0 (omitted)
|
period |
2 | -.0042799 .003401 -1.26 0.208 -.0109472 .0023875
3 | -.0108953 .0041859 -2.60 0.009 -.0191012 -.0026894
4 | -.0123002 .0044918 -2.74 0.006 -.0211058 -.0034945
5 | -.0176797 .0048541 -3.64 0.000 -.0271957 -.0081637
|
_cons | .8090216 .0375234 21.56 0.000 .7354614 .8825818
-------------+----------------------------------------------------------------
sigma_u | .42247488
sigma_e | .21363541
rho | .79636335 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. eststo Probit_Pooled: probit lfp kids lhinc edu age agesq black i.period, cluster(id) nolog
Probit regression Number of obs = 28,315
Wald chi2(10) = 537.36
Prob > chi2 = 0.0000
Log pseudolikelihood = -16556.671 Pseudo R2 = 0.0651
(Std. Err. adjusted for 5,663 clusters in id)
------------------------------------------------------------------------------
| Robust
lfp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
kids | -.1989144 .0153153 -12.99 0.000 -.2289319 -.1688969
lhinc | -.2110738 .0242901 -8.69 0.000 -.2586816 -.1634661
educ | .0796863 .0065453 12.17 0.000 .0668577 .0925149
age | .1449159 .0122179 11.86 0.000 .1209693 .1688624
agesq | -.0019912 .0001522 -13.08 0.000 -.0022895 -.0016928
black | .2209396 .0659041 3.35 0.001 .09177 .3501093
|
period |
2 | -.0124245 .0104551 -1.19 0.235 -.0329162 .0080672
3 | -.0325178 .0127431 -2.55 0.011 -.0574938 -.0075418
4 | -.046097 .0136286 -3.38 0.001 -.0728087 -.0193853
5 | -.0577767 .014632 -3.95 0.000 -.0864548 -.0290985
|
_cons | -1.064449 .261872 -4.06 0.000 -1.577709 -.5511895
------------------------------------------------------------------------------
. eststo Probit_APE: margins, dydx(kids lhinc) post
Average marginal effects Number of obs = 28,315
Model VCE : Robust
Expression : Pr(lfp), predict()
dy/dx w.r.t. : kids lhinc
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
kids | -.0660184 .0049222 -13.41 0.000 -.0756657 -.0563711
lhinc | -.070054 .0079821 -8.78 0.000 -.0856987 -.0544093
------------------------------------------------------------------------------
. eststo FE_logit: xtlogit lfp kids lhin i.period, fe nolog
note: multiple positive outcomes within groups encountered.
note: 4,608 groups (23,040 obs) dropped because of all positive or
all negative outcomes.
Conditional fixed-effects logistic regression Number of obs = 5,275
Group variable: id Number of groups = 1,055
Obs per group:
min = 5
avg = 5.0
max = 5
LR chi2(6) = 57.27
Log likelihood = -2003.4184 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lfp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
kids | -.6438386 .1247828 -5.16 0.000 -.8884084 -.3992688
lhinc | -.1842911 .0826019 -2.23 0.026 -.3461878 -.0223943
|
period |
2 | -.0928039 .0889937 -1.04 0.297 -.2672283 .0816205
3 | -.2247989 .0887976 -2.53 0.011 -.398839 -.0507587
4 | -.2479323 .0888953 -2.79 0.005 -.422164 -.0737006
5 | -.3563745 .0888354 -4.01 0.000 -.5304886 -.1822604
------------------------------------------------------------------------------
. by id: egen kidsbar = mean(kids)
. by id: egen lhincbar = mean(lhinc)
. eststo RE_Probit: probit lfp kids lhinc kidsbar lhincbar educ black age agesq i.period, cluster(id) nolog
Probit regression Number of obs = 28,315
Wald chi2(12) = 538.09
Prob > chi2 = 0.0000
Log pseudolikelihood = -16516.436 Pseudo R2 = 0.0673
(Std. Err. adjusted for 5,663 clusters in id)
------------------------------------------------------------------------------
| Robust
lfp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
kids | -.1173749 .0269743 -4.35 0.000 -.1702435 -.0645064
lhinc | -.0288098 .014344 -2.01 0.045 -.0569234 -.0006961
kidsbar | -.0856913 .0311857 -2.75 0.006 -.146814 -.0245685
lhincbar | -.2501781 .0352907 -7.09 0.000 -.3193466 -.1810097
educ | .0841338 .0067302 12.50 0.000 .0709428 .0973248
black | .2030668 .0663945 3.06 0.002 .0729359 .3331976
age | .1516424 .0124831 12.15 0.000 .127176 .1761089
agesq | -.0020672 .0001553 -13.31 0.000 -.0023717 -.0017628
|
period |
2 | -.0135701 .0103752 -1.31 0.191 -.0339051 .0067648
3 | -.0331991 .0127197 -2.61 0.009 -.0581293 -.008269
4 | -.0390317 .0136244 -2.86 0.004 -.0657351 -.0123284
5 | -.0552425 .0146067 -3.78 0.000 -.0838711 -.0266139
|
_cons | -.7260562 .2836985 -2.56 0.010 -1.282095 -.1700173
------------------------------------------------------------------------------
. eststo RE_APE: margins, dydx(kids lhinc) post
Average marginal effects Number of obs = 28,315
Model VCE : Robust
Expression : Pr(lfp), predict()
dy/dx w.r.t. : kids lhinc
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
kids | -.038852 .0089243 -4.35 0.000 -.0563433 -.0213608
lhinc | -.0095363 .0047482 -2.01 0.045 -.0188426 -.00023
------------------------------------------------------------------------------
. eststo CRE_Probit: xtprobit lfp kids lhinc kidsbar lhincbar educ black age agesq i.period, re nolog
Random-effects probit regression Number of obs = 28,315
Group variable: id Number of groups = 5,663
Random effects u_i ~ Gaussian Obs per group:
min = 5
avg = 5.0
max = 5
Integration method: mvaghermite Integration pts. = 12
Wald chi2(12) = 623.40
Log likelihood = -8609.9002 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lfp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
kids | -.3970102 .0701298 -5.66 0.000 -.534462 -.2595584
lhinc | -.1003399 .0469979 -2.13 0.033 -.1924541 -.0082258
kidsbar | -.4085664 .0898875 -4.55 0.000 -.5847428 -.2323901
lhincbar | -.8941069 .1199703 -7.45 0.000 -1.129244 -.6589695
educ | .3189079 .024327 13.11 0.000 .2712279 .366588
black | .6388784 .1903525 3.36 0.001 .2657945 1.011962
age | .7282057 .0445623 16.34 0.000 .6408651 .8155462
agesq | -.0098358 .0005747 -17.11 0.000 -.0109623 -.0087094
|
period |
2 | -.0451653 .0499429 -0.90 0.366 -.1430516 .052721
3 | -.1247056 .0501522 -2.49 0.013 -.2230022 -.026409
4 | -.1356834 .0500679 -2.71 0.007 -.2338147 -.0375522
5 | -.200357 .049539 -4.04 0.000 -.2974515 -.1032624
|
_cons | -5.359375 1.000514 -5.36 0.000 -7.320346 -3.398404
-------------+----------------------------------------------------------------
/lnsig2u | 2.947234 .0435842 2.861811 3.032657
-------------+----------------------------------------------------------------
sigma_u | 4.364995 .0951224 4.182484 4.55547
rho | .9501326 .002065 .945926 .9540279
------------------------------------------------------------------------------
LR test of rho=0: chibar2(01) = 1.6e+04 Prob >= chibar2 = 0.000
. eststo CRE_APE: margins, dydx(kids lhinc) post
Average marginal effects Number of obs = 28,315
Model VCE : OIM
Expression : Pr(lfp=1), predict(pr)
dy/dx w.r.t. : kids lhinc
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
kids | -.0301539 .0053261 -5.66 0.000 -.0405928 -.0197149
lhinc | -.0076211 .0035696 -2.13 0.033 -.0146174 -.0006247
------------------------------------------------------------------------------
. estout FE_Linear Probit_Pooled Probit_APE RE_Probit RE_APE CRE_Probit CRE_APE FE_logit, ///
keep(kids lhinc kidsbar lhincbar) cells(b(nostar fmt(4)) se(par fmt(4))) ///
stats(ll r2 r2_p N, fmt(%9.0g) labels(Log-Likelihood R-squared Psuedo-R2 N))
--------------------------------------------------------------------------------------------------------------------
FE_Linear Probit_Poo~d Probit_APE RE_Probit RE_APE CRE_Probit CRE_APE FE_logit
b/se b/se b/se b/se b/se b/se b/se b/se
--------------------------------------------------------------------------------------------------------------------
main
kids -0.0389 -0.1989 -0.0660 -0.1174 -0.0389 -0.3970 -0.0302 -0.6438
(0.0092) (0.0153) (0.0049) (0.0270) (0.0089) (0.0701) (0.0053) (0.1248)
lhinc -0.0089 -0.2111 -0.0701 -0.0288 -0.0095 -0.1003 -0.0076 -0.1843
(0.0046) (0.0243) (0.0080) (0.0143) (0.0047) (0.0470) (0.0036) (0.0826)
kidsbar -0.0857 -0.4086
(0.0312) (0.0899)
lhincbar -0.2502 -0.8941
(0.0353) (0.1200)
--------------------------------------------------------------------------------------------------------------------
Log-Likeli~d 6689.422 -16556.67 -16516.44 -8609.9 -2003.418
R-squared .0031198
Psuedo-R2 .0650713 .0673433 .0140919
N 28315 28315 28315 28315 28315 28315 28315 5275
--------------------------------------------------------------------------------------------------------------------
. eststo clear
. // Example 15.6 (Dynamic Women's LFP Equation)
. xtset id period
panel variable: id (strongly balanced)
time variable: period, 1 to 5
delta: 1 unit
. forv i=2/5 {
by id: gen kids`i' = kids[`i']
}
. forv i=2/5 {
by id: gen lhinc`i' = lhinc[`i']
}
. g lfp_1 = l.lfp
(5,663 missing values generated)
. by id: g lfp1st = lfp[1]
. eststo RE_Probit: xtprobit lfp lfp_1 lfp1st kids kids2-kids5 lhinc lhinc2-lhinc5 ///
black age agesq educ per5 per4 per3, nolog
Random-effects probit regression Number of obs = 22,652
Group variable: id Number of groups = 5,663
Random effects u_i ~ Gaussian Obs per group:
min = 4
avg = 4.0
max = 4
Integration method: mvaghermite Integration pts. = 12
Wald chi2(19) = 4108.39
Log likelihood = -5028.9994 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lfp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lfp_1 | 1.543212 .0666285 23.16 0.000 1.412623 1.673801
lfp1st | 2.523804 .1553997 16.24 0.000 2.219226 2.828382
kids | -.1451527 .0787035 -1.84 0.065 -.2994088 .0091033
kids2 | .3232176 .0965951 3.35 0.001 .1338947 .5125406
kids3 | .1071765 .1232038 0.87 0.384 -.1342985 .3486516
kids4 | .0173548 .1273505 0.14 0.892 -.2322475 .2669572
kids5 | -.3904321 .1058279 -3.69 0.000 -.597851 -.1830131
lhinc | -.0747984 .0508154 -1.47 0.141 -.1743947 .024798
lhinc2 | -.0231497 .0589568 -0.39 0.695 -.1387029 .0924036
lhinc3 | -.0829647 .0624976 -1.33 0.184 -.2054578 .0395284
lhinc4 | -.0864221 .0608129 -1.42 0.155 -.2056133 .032769
lhinc5 | .0622538 .0590987 1.05 0.292 -.0535775 .1780851
black | .1319675 .0980651 1.35 0.178 -.0602365 .3241715
age | .1278587 .0193926 6.59 0.000 .0898499 .1658675
agesq | -.0016877 .00024 -7.03 0.000 -.0021581 -.0012173
educ | .0497964 .0100056 4.98 0.000 .0301859 .069407
per5 | -.0785389 .0464676 -1.69 0.091 -.1696137 .012536
per4 | -.0295055 .0463489 -0.64 0.524 -.1203477 .0613366
per3 | -.055971 .0458111 -1.22 0.222 -.145759 .0338171
_cons | -2.941813 .4359963 -6.75 0.000 -3.79635 -2.087276
-------------+----------------------------------------------------------------
/lnsig2u | .0934029 .1221436 -.1459941 .3327999
-------------+----------------------------------------------------------------
sigma_u | 1.047809 .0639916 .9296036 1.181045
rho | .5233338 .0304694 .4635662 .5824405
------------------------------------------------------------------------------
LR test of rho=0: chibar2(01) = 160.68 Prob >= chibar2 = 0.000
. eststo RE_APE: margins, dydx(lfp_1 lfp1st kids lhinc) post
Average marginal effects Number of obs = 22,652
Model VCE : OIM
Expression : Pr(lfp=1), predict(pr)
dy/dx w.r.t. : lfp_1 lfp1st kids lhinc
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lfp_1 | .1556348 .0097058 16.04 0.000 .1366119 .1746578
lfp1st | .2545288 .0100773 25.26 0.000 .2347776 .2742799
kids | -.0146388 .0079031 -1.85 0.064 -.0301286 .0008509
lhinc | -.0075435 .005124 -1.47 0.141 -.0175864 .0024993
------------------------------------------------------------------------------
. eststo Probit_Pooled: probit lfp lfp_1 kids lhinc kidsbar lhincbar educ black age agesq , nolog
Probit regression Number of obs = 22,652
LR chi2(9) = 17745.39
Prob > chi2 = 0.0000
Log likelihood = -5331.9397 Pseudo R2 = 0.6246
------------------------------------------------------------------------------
lfp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lfp_1 | 2.873296 .026994 106.44 0.000 2.820389 2.926204
kids | -.0408857 .0613472 -0.67 0.505 -.1611241 .0793526
lhinc | -.05965 .0398225 -1.50 0.134 -.1377005 .0184006
kidsbar | -.0209041 .0624636 -0.33 0.738 -.1433306 .1015224
lhincbar | -.0763568 .0467387 -1.63 0.102 -.1679629 .0152494
educ | .030652 .0053293 5.75 0.000 .0202066 .0410973
black | .0741813 .0537819 1.38 0.168 -.0312293 .1795919
age | .0866671 .0101111 8.57 0.000 .0668496 .1064845
agesq | -.0011241 .0001248 -9.01 0.000 -.0013687 -.0008796
_cons | -2.080879 .2301204 -9.04 0.000 -2.531907 -1.629852
------------------------------------------------------------------------------
. eststo Probit_APE: margins, dydx(lfp_1 kids lhinc) post
Average marginal effects Number of obs = 22,652
Model VCE : OIM
Expression : Pr(lfp), predict()
dy/dx w.r.t. : lfp_1 kids lhinc
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lfp_1 | .3575142 .0038879 91.96 0.000 .349894 .3651344
kids | -.0050873 .0076335 -0.67 0.505 -.0200486 .0098741
lhinc | -.007422 .0049559 -1.50 0.134 -.0171354 .0022913
------------------------------------------------------------------------------
. eststo clear
. log close
name: SN
log: myReplications\iiexample15.smcl
log type: smcl
closed on: 9 May 2020, 17:56:03
------------------------------------------------------------------------------------------