How to interpret Heckprob regression Results

[Jay Rege]

Can anyone tell me how to Interpret These heckprobit results?
Do I have to calculate the mrginal effects by using margins, dydx(*)?
How do I have to include the reslust of the first step into the Interpretation of the second step results?

eststo Heckprob_example: heckprobit Abbruch $Region GDP_per_capita_t_1 $Governance, select(Annahme = $Region)

Fitting probit model:

Iteration 0:   log likelihood =  -329.3776 
Iteration 1:   log likelihood = -321.53615 
Iteration 2:   log likelihood = -321.49713 
Iteration 3:   log likelihood = -321.49713 

Fitting selection model:

Iteration 0:   log likelihood = -1887.8222 
Iteration 1:   log likelihood = -1883.4027 
Iteration 2:   log likelihood = -1883.4008 
Iteration 3:   log likelihood = -1883.4008 

Comparison:    log likelihood = -2204.8979

Fitting starting values:

Iteration 0:   log likelihood = -571.15328 
Iteration 1:   log likelihood = -323.53089 
Iteration 2:   log likelihood = -321.35477 
Iteration 3:   log likelihood = -321.34808 
Iteration 4:   log likelihood = -321.34808 

Fitting full model:

initial values not feasible
note:  default initial values infeasible; starting from B=0

Iteration 0:   log likelihood = -2940.3303  (not concave)
Iteration 1:   log likelihood = -2309.2603 
Iteration 2:   log likelihood = -2210.0154 
Iteration 3:   log likelihood = -2209.3384 
Iteration 4:   log likelihood = -2205.0127  (not concave)
Iteration 5:   log likelihood = -2205.0112 
Iteration 6:   log likelihood = -2204.9662 
Iteration 7:   log likelihood =  -2204.965 
Iteration 8:   log likelihood = -2204.9508  (not concave)
Iteration 9:   log likelihood = -2204.9508 
Iteration 10:  log likelihood = -2204.9462 
Iteration 11:  log likelihood = -2204.9381 
Iteration 12:  log likelihood = -2204.9278 
Iteration 13:  log likelihood = -2204.9234 
Iteration 14:  log likelihood = -2204.9181 
Iteration 15:  log likelihood = -2204.9151 
Iteration 16:  log likelihood = -2204.9096 
Iteration 17:  log likelihood = -2204.9083 
Iteration 18:  log likelihood = -2204.9059 
Iteration 19:  log likelihood = -2204.9029 
Iteration 20:  log likelihood = -2204.9016 
Iteration 21:  log likelihood = -2204.9005 
Iteration 22:  log likelihood = -2204.8984 
Iteration 23:  log likelihood = -2204.8981 
Iteration 24:  log likelihood = -2204.8976 
Iteration 25:  log likelihood = -2204.8975 
Iteration 26:  log likelihood = -2204.8974 

Probit model with sample selection              Number of obs      =      3418
                                                Censored obs       =      2594
                                                Uncensored obs     =       824

                                                Wald chi2(10)      =     10.56
Log likelihood = -2204.897                      Prob > chi2        =    0.3927

----------------------------------------------------------------------------------------------
                             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------------+----------------------------------------------------------------
Abbruch                      |
 Latin_America_and_Caribbean |  -.1686985   .7544157    -0.22   0.823    -1.647326    1.309929
  MiddleEast_and_NorthAfrica |   .1864811   .7801773     0.24   0.811    -1.342638    1.715601
                  South_Asia |   .4386175     1.6765     0.26   0.794    -2.847262    3.724497
          Sub_Saharan_Africa |   .0032131   .5846907     0.01   0.996     -1.14276    1.149186
       East_Asia_and_Pacific |  -.2585976   .6775324    -0.38   0.703    -1.586537    1.069341
          Landlocked_country |    -.02292    .199221    -0.12   0.908    -.4133859    .3675459
          GDP_per_capita_t_1 |   .0000105   .0000272     0.38   0.700    -.0000429    .0000638
             Rule_of_Law_t_1 |  -1.696115   2.850002    -0.60   0.552    -7.282015    3.889786
     Political_Stability_t_1 |     .35194   .7662191     0.46   0.646    -1.149822    1.853702
Voice_and_Accountability_t_1 |  -.2529391   .6971437    -0.36   0.717    -1.619316    1.113437
                       _cons |   .0138442   8.613514     0.00   0.999    -16.86833    16.89602
-----------------------------+----------------------------------------------------------------
Annahme                      |
 Latin_America_and_Caribbean |   .1972679   .0870882     2.27   0.024     .0265781    .3679577
  MiddleEast_and_NorthAfrica |   .0825739   .1123576     0.73   0.462    -.1376429    .3027908
                  South_Asia |   .1937339   .0958037     2.02   0.043     .0059621    .3815057
          Sub_Saharan_Africa |   .1076104    .081812     1.32   0.188    -.0527382    .2679589
       East_Asia_and_Pacific |   .2063335   .0828987     2.49   0.013      .043855    .3688119
          Landlocked_country |   .0278059   .0695652     0.40   0.689    -.1085393    .1641511
                       _cons |  -.8502757    .070056   -12.14   0.000    -.9875829   -.7129684
-----------------------------+----------------------------------------------------------------
                     /athrho |  -.3238219   6.297795    -0.05   0.959    -12.66727    12.01963
-----------------------------+----------------------------------------------------------------
                         rho |  -.3129586    5.68097                            -1           1
----------------------------------------------------------------------------------------------
LR test of indep. eqns. (rho = 0):   chi2(1) =     0.00   Prob > chi2 = 0.9737

[Alfonso Sánchez-Peñalver]

Well, the first thing I observe is that none of the coefficients seem to be significantly different from zero in your Abbruch equation (the one that you are actually interested in estimating). They all seem to be categorical variables except for GDP... Am I right? So first there doesn't seem to have much explanatory value (which is confirmed by the Wald test of significance of the overall model).

The second thing I observe is that the LR test for independent equations shows that you cannot reject the null hypothesis that they are in fact independent, so they could be estimated as two separate probits: The selection probit for all observations in the sample, and the marginal probit for only those that are not censored (824).

Looking further I see that only approximately 24% (824 out fo 3418) of the sample are uncensored observations. So basically you want a quarter of the sample to explain what themselves and the other 75% of the sample is doing. I'm not sure if anything in the theory of sample selection models that mentions anything about what share of the sample should be helping to explain overall behavior, but it would definitely make me start looking as to whether it's appropriate to use this type of model with that data structure.

I'm currently giving thought as to whether a mixed model is a better estimation model for sample selection than heckman selection model for any type of censored data. I don't want to deviate your attention here, but I believe that it could be useful for your case. You could estimate the model using meprobit or melogit with a random intercept for the group variable Annahame, so something like meprobit Abbruch $Region GDP_per_capita_t_1 $Governance || Annahame:, intpoints(12) and see how the significance of the coefficients behave, and whether the LR test there is significant. Again this is something I am considering and I would like to find some literature out there, but I can't seem to be able to find anything, so maybe it's not appropriate.

Finally for whether you have to do margins, dydx(*), if you want the partial effects of all the variables, yes that is the way. As to whether you have to integrate the results of the first into the second and all that, it depends on what you want to do, which you don't tell us. I suggest you run help heckrpobit postestimation and scroll down to where you find information on predict to see the options you have to include in the predict option of margins.