Dear Statalist

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
The results are below

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
---------------------------------------------------------------------------------------------
I run the probit model as:

Code:
probit intl L1.intratio2_w L1.siznumfxhedge_w $key_control i.fyear if sample==1
The results of the probit model is:

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.
After generating the inverse Mills ratio, my codes for OLS is:

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
The results of the OLS:

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
---------------------------------------------------------------------------------------------
I'm having a difficult time figuring out why there is a difference between the OLS and the Heckman model results.

Any advice, suggestions will be appreciated.

Thank you in advance.