I'm running a Heckman model and I wanted to compare the results of the Heckman model with the models ran separately with probit and OLS.
The results show that the results of the probit model is the same with the first-stage results of the Heckman model. However, the OLS results differ with the sedcond-stage results of the Heckman model, which is perplexing.
My codes for the Heckman model is thus:
Code:
global key_control "L1.ln_firmage_w L1.ln_at_w L1.tobinq_w L1.slack_w L1.constraint_w L1.entropy_w L1.ln_tenure_y_w L1.isfounder_w" heckman intratio2_w c.L1.usratio2_w##c.L1.usratio2_w L1.intratio2_w L1.annualreturn5_w L1.regul2 $key_control i.fyear, select(intl = L1.intratio2_w L1.siznumfxhedge_w $key_control i.fyear) twostep
Code:
heckman intratio2_w c.L1.usratio2_w##c.L1.usratio2_w L1.intratio2_w L1.annualreturn5_w L1.regul2 $key_
> control i.fyear, select(intl = L1.intratio2_w L1.siznumfxhedge_w $key_control i.fyear) twostep
note: 2015.fyear omitted because of collinearity
Heckman selection model -- two-step estimates Number of obs = 1,398
(regression model with sample selection) Selected = 366
Nonselected = 1,032
Wald chi2(29) = 280.91
Prob > chi2 = 0.0000
---------------------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
intratio2_w |
usratio2_w |
L1. | .2720963 .1278018 2.13 0.033 .0216094 .5225832
|
cL.usratio2_w#cL.usratio2_w | -.288744 .1455788 -1.98 0.047 -.5740733 -.0034147
|
intratio2_w |
L1. | .5211206 .0653576 7.97 0.000 .393022 .6492192
|
annualreturn5_w |
L1. | 973.2645 1098.729 0.89 0.376 -1180.205 3126.734
|
regul2 |
L1. | -.017766 .3312482 -0.05 0.957 -.6670005 .6314685
|
ln_firmage_w |
L1. | -.0135679 .0209061 -0.65 0.516 -.0545431 .0274074
|
ln_at_w |
L1. | -.0141518 .0068556 -2.06 0.039 -.0275885 -.0007151
|
tobinq_w |
L1. | .0318719 .0118094 2.70 0.007 .008726 .0550179
|
slack_w |
L1. | .1102677 .0534081 2.06 0.039 .0055896 .2149457
|
constraint_w |
L1. | .0030768 .0016573 1.86 0.063 -.0001714 .0063251
|
entropy_w |
L1. | -.0045865 .0376501 -0.12 0.903 -.0783793 .0692064
|
ln_tenure_y_w |
L1. | -.0059873 .0137784 -0.43 0.664 -.0329926 .0210179
|
isfounder_w |
L1. | .0100584 .0269353 0.37 0.709 -.0427339 .0628507
|
fyear |
1999 | -.4294316 .3530869 -1.22 0.224 -1.121469 .262606
2000 | -.6200813 .6436681 -0.96 0.335 -1.881648 .641485
2001 | -.2670098 .2043539 -1.31 0.191 -.667536 .1335164
2002 | -.1345528 .1770313 -0.76 0.447 -.4815277 .2124222
2003 | -.0704241 .0874952 -0.80 0.421 -.2419116 .1010634
2004 | -.1022615 .055527 -1.84 0.066 -.2110925 .0065696
2005 | -.1420184 .1794518 -0.79 0.429 -.4937375 .2097007
2006 | -.1305091 .1355871 -0.96 0.336 -.3962549 .1352367
2007 | -.0117517 .0917541 -0.13 0.898 -.1915866 .1680831
2008 | .0544525 .0590393 0.92 0.356 -.0612624 .1701674
2009 | -.2999764 .3494616 -0.86 0.391 -.9849084 .3849557
2010 | -.1411477 .1266843 -1.11 0.265 -.3894443 .1071488
2011 | .0914906 .0591742 1.55 0.122 -.0244887 .2074698
2012 | .003273 .0605795 0.05 0.957 -.1154607 .1220067
2013 | -.1230197 .1748139 -0.70 0.482 -.4656486 .2196093
2014 | .0185745 .067795 0.27 0.784 -.1143012 .1514502
2015 | 0 (omitted)
|
_cons | -.1252836 .4639153 -0.27 0.787 -1.034541 .7839736
----------------------------+----------------------------------------------------------------
intl |
intratio2_w |
L1. | 4.834204 .3503738 13.80 0.000 4.147484 5.520924
|
siznumfxhedge_w |
L1. | .2002537 .0511131 3.92 0.000 .1000739 .3004336
|
ln_firmage_w |
L1. | .4141059 .0889329 4.66 0.000 .2398006 .5884112
|
ln_at_w |
L1. | .102695 .0317659 3.23 0.001 .0404351 .164955
|
tobinq_w |
L1. | .0066423 .0559791 0.12 0.906 -.1030748 .1163593
|
slack_w |
L1. | .1194309 .2371617 0.50 0.615 -.3453975 .5842593
|
constraint_w |
L1. | -.0130778 .0087029 -1.50 0.133 -.0301351 .0039795
|
entropy_w |
L1. | 2.104377 .3152062 6.68 0.000 1.486584 2.72217
|
ln_tenure_y_w |
L1. | -.2524318 .0708367 -3.56 0.000 -.3912692 -.1135944
|
isfounder_w |
L1. | .151132 .135638 1.11 0.265 -.1147136 .4169775
|
fyear |
1999 | .023452 .385552 0.06 0.951 -.7322161 .7791201
2000 | .0603861 .3656494 0.17 0.869 -.6562735 .7770457
2001 | .4129523 .3549258 1.16 0.245 -.2826895 1.108594
2002 | .5593425 .344546 1.62 0.104 -.1159553 1.23464
2003 | -.2778826 .3745286 -0.74 0.458 -1.011945 .4561799
2004 | .0300237 .3712949 0.08 0.936 -.6977008 .7577483
2005 | .1178042 .3588525 0.33 0.743 -.5855339 .8211422
2006 | -.0076683 .364267 -0.02 0.983 -.7216186 .7062819
2007 | -.3606981 .3688887 -0.98 0.328 -1.083707 .3623105
2008 | -.0865687 .3575869 -0.24 0.809 -.7874262 .6142887
2009 | -.1584412 .3629916 -0.44 0.662 -.8698916 .5530093
2010 | -.0909428 .3651831 -0.25 0.803 -.8066886 .6248029
2011 | -.4961573 .3778998 -1.31 0.189 -1.236827 .2445126
2012 | -.0677228 .3594602 -0.19 0.851 -.7722519 .6368063
2013 | -.5144314 .3728328 -1.38 0.168 -1.24517 .2163074
2014 | -.5559093 .3892982 -1.43 0.153 -1.31892 .2071012
2015 | -.6956374 .4077328 -1.71 0.088 -1.494779 .1035043
2016 | -5.076546 . . . . .
|
_cons | -2.824338 .4026681 -7.01 0.000 -3.613553 -2.035123
----------------------------+----------------------------------------------------------------
/mills |
lambda | .0133232 .0364566 0.37 0.715 -.0581304 .0847768
----------------------------+----------------------------------------------------------------
rho | 0.06670
sigma | .19974236
---------------------------------------------------------------------------------------------Code:
probit intl L1.intratio2_w L1.siznumfxhedge_w $key_control i.fyear if sample==1
Code:
probit intl L1.intratio2_w L1.siznumfxhedge_w $key_control i.fyear if sample==1
note: 2016.fyear != 0 predicts failure perfectly
2016.fyear dropped and 2 obs not used
Iteration 0: log likelihood = -803.15003
Iteration 1: log likelihood = -282.95336
Iteration 2: log likelihood = -275.26049
Iteration 3: log likelihood = -275.10246
Iteration 4: log likelihood = -275.10216
Iteration 5: log likelihood = -275.10216
Probit regression Number of obs = 1,396
LR chi2(27) = 1056.10
Prob > chi2 = 0.0000
Log likelihood = -275.10216 Pseudo R2 = 0.6575
---------------------------------------------------------------------------------
intl | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
intratio2_w |
L1. | 4.834204 .3503738 13.80 0.000 4.147484 5.520924
|
siznumfxhedge_w |
L1. | .2002537 .0511131 3.92 0.000 .1000739 .3004336
|
ln_firmage_w |
L1. | .4141059 .0889329 4.66 0.000 .2398006 .5884112
|
ln_at_w |
L1. | .102695 .0317659 3.23 0.001 .0404351 .164955
|
tobinq_w |
L1. | .0066423 .0559791 0.12 0.906 -.1030748 .1163593
|
slack_w |
L1. | .1194309 .2371617 0.50 0.615 -.3453975 .5842593
|
constraint_w |
L1. | -.0130778 .0087029 -1.50 0.133 -.0301351 .0039795
|
entropy_w |
L1. | 2.104377 .3152062 6.68 0.000 1.486584 2.72217
|
ln_tenure_y_w |
L1. | -.2524318 .0708367 -3.56 0.000 -.3912692 -.1135944
|
isfounder_w |
L1. | .151132 .135638 1.11 0.265 -.1147136 .4169775
|
fyear |
1999 | .023452 .385552 0.06 0.951 -.7322161 .7791201
2000 | .0603861 .3656494 0.17 0.869 -.6562735 .7770457
2001 | .4129523 .3549258 1.16 0.245 -.2826895 1.108594
2002 | .5593425 .344546 1.62 0.104 -.1159553 1.23464
2003 | -.2778826 .3745286 -0.74 0.458 -1.011945 .4561799
2004 | .0300237 .3712949 0.08 0.936 -.6977008 .7577483
2005 | .1178042 .3588525 0.33 0.743 -.5855339 .8211422
2006 | -.0076683 .364267 -0.02 0.983 -.7216186 .7062819
2007 | -.3606981 .3688887 -0.98 0.328 -1.083707 .3623105
2008 | -.0865687 .3575869 -0.24 0.809 -.7874262 .6142887
2009 | -.1584412 .3629916 -0.44 0.662 -.8698916 .5530093
2010 | -.0909428 .3651831 -0.25 0.803 -.8066886 .6248029
2011 | -.4961573 .3778998 -1.31 0.189 -1.236827 .2445126
2012 | -.0677228 .3594602 -0.19 0.851 -.7722519 .6368063
2013 | -.5144314 .3728328 -1.38 0.168 -1.24517 .2163074
2014 | -.5559093 .3892982 -1.43 0.153 -1.31892 .2071012
2015 | -.6956374 .4077328 -1.71 0.088 -1.494779 .1035043
2016 | 0 (empty)
|
_cons | -2.824338 .4026681 -7.01 0.000 -3.613553 -2.035123
---------------------------------------------------------------------------------
Note: 0 failures and 1 success completely determined.Code:
predict probitxb, xb ge pdf = normalden(probitxb) ge cdf = normal(probitxb) ge imr = pdf/cdf reg intratio2_w c.L1.usratio2_w##c.L1.usratio2_w L1.intratio2_w L1.annualreturn5_w L1.regul2 $key_control imr i.fyear if intl==1
Code:
reg intratio2_w c.L1.usratio2_w##c.L1.usratio2_w L1.intratio2_w L1.annualreturn5_w L1.regul2 $key_cont
> rol imr i.fyear if intl==1
note: 2015.fyear omitted because of collinearity
Source | SS df MS Number of obs = 366
-------------+---------------------------------- F(30, 335) = 9.17
Model | 11.9724505 30 .399081684 Prob > F = 0.0000
Residual | 14.5836282 335 .043533219 R-squared = 0.4508
-------------+---------------------------------- Adj R-squared = 0.4017
Total | 26.5560787 365 .07275638 Root MSE = .20865
---------------------------------------------------------------------------------------------
intratio2_w | Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
usratio2_w |
L1. | .2720963 .1335699 2.04 0.042 .0093548 .5348378
|
cL.usratio2_w#cL.usratio2_w | -.288744 .1521393 -1.90 0.059 -.5880128 .0105247
|
intratio2_w |
L1. | .5211206 .0682879 7.63 0.000 .3867934 .6554477
|
annualreturn5_w |
L1. | 973.2645 1148.177 0.85 0.397 -1285.281 3231.81
|
regul2 |
L1. | -.017766 .3461551 -0.05 0.959 -.6986775 .6631455
|
ln_firmage_w |
L1. | -.0135679 .0218491 -0.62 0.535 -.0565466 .0294108
|
ln_at_w |
L1. | -.0141518 .0071649 -1.98 0.049 -.0282457 -.000058
|
tobinq_w |
L1. | .0318719 .0123427 2.58 0.010 .007593 .0561509
|
slack_w |
L1. | .1102677 .0558239 1.98 0.049 .0004582 .2200771
|
constraint_w |
L1. | .0030768 .001732 1.78 0.077 -.0003302 .0064838
|
entropy_w |
L1. | -.0045865 .0393373 -0.12 0.907 -.0819658 .0727929
|
ln_tenure_y_w |
L1. | -.0059873 .0143982 -0.42 0.678 -.0343095 .0223349
|
isfounder_w |
L1. | .0100584 .0281486 0.36 0.721 -.0453119 .0654287
|
imr | .0133232 .0381105 0.35 0.727 -.0616428 .0882893
|
fyear |
1999 | -.4294316 .3689788 -1.16 0.245 -1.155239 .2963757
2000 | -.6200813 .6726388 -0.92 0.357 -1.943209 .7030466
2001 | -.2670098 .213552 -1.25 0.212 -.6870817 .153062
2002 | -.1345528 .184999 -0.73 0.468 -.4984588 .2293533
2003 | -.0704241 .0914325 -0.77 0.442 -.2502784 .1094302
2004 | -.1022615 .0580225 -1.76 0.079 -.2163958 .0118729
2005 | -.1420184 .187529 -0.76 0.449 -.5109012 .2268644
2006 | -.1305091 .1416905 -0.92 0.358 -.4092243 .1482061
2007 | -.0117517 .0958853 -0.12 0.903 -.2003649 .1768614
2008 | .0544525 .0616971 0.88 0.378 -.0669101 .1758152
2009 | -.2999764 .3651913 -0.82 0.412 -1.018333 .4183806
2010 | -.1411477 .1323872 -1.07 0.287 -.4015626 .1192671
2011 | .0914906 .061839 1.48 0.140 -.0301512 .2131323
2012 | .003273 .0633075 0.05 0.959 -.1212573 .1278033
2013 | -.1230197 .1826829 -0.67 0.501 -.4823698 .2363305
2014 | .0185745 .0708436 0.26 0.793 -.1207798 .1579287
2015 | 0 (omitted)
|
_cons | -.1252836 .4847992 -0.26 0.796 -1.078918 .8283506
---------------------------------------------------------------------------------------------Any advice, suggestions will be appreciated.
Thank you in advance.
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