Heckman two step model

[Nicola Rossi]

Dear Stata Users,

I am attempting to apply the two step Heckman model, with a Tobit regression as first stage instead of a probit model.

I am proceeding in this way:

a) Tobit model


b) estimation of inverse Mill's ratio (IMR)

command:
predict phat, xb gen mills = exp(-.5*phat²)/(sqrt(2*_pi)*normprob(phat))




c) estimation of a OLS model, including the IMR as additional indep. variable.

My problem is that the OLS model (c) omits the IMR because of multicollinearity.

 reg SHROA_5w_100 RepTrak Td_TE_100 logTA Int_TA_100 Bsize IndBoard_100 Y1 Y2 Y3 Y4 Y5 Sector1 Sector2 Sector3 Sector4 Sector5
> Country1-Country18 GDPperCapita millsTobit
note: Y5 omitted because of collinearity
note: Sector2 omitted because of collinearity
note: Country1 omitted because of collinearity
note: Country17 omitted because of collinearity
note: millsTobit omitted because of collinearity

      Source |       SS           df       MS      Number of obs   =       372
-------------+----------------------------------   F(31, 340)      =      2.20
       Model |  .148992991        31  .004806226   Prob > F        =    0.0004
    Residual |  .741759968       340  .002181647   R-squared       =    0.1673
-------------+----------------------------------   Adj R-squared   =    0.0913
       Total |  .890752959       371  .002400951   Root MSE        =    .04671

------------------------------------------------------------------------------
SHROA_5w_100 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     RepTrak |   .0034099    .001144     2.98   0.003     .0011597    .0056602
   Td_TE_100 |   .0002304   .0006909     0.33   0.739    -.0011286    .0015894
       logTA |  -.0004981   .0026906    -0.19   0.853    -.0057905    .0047943
  Int_TA_100 |  -.0877178   .0709171    -1.24   0.217    -.2272094    .0517738
       Bsize |   .0018275   .0011427     1.60   0.111    -.0004203    .0040752
IndBoard_100 |  -.0083301   .0130468    -0.64   0.524    -.0339926    .0173324
          Y1 |   .0159247   .0116517     1.37   0.173    -.0069937    .0388432
          Y2 |   .0227221   .0110277     2.06   0.040      .001031    .0444133
          Y3 |   .0134447   .0107067     1.26   0.210    -.0076151    .0345045
          Y4 |   .0148655   .0097597     1.52   0.129    -.0043316    .0340625
          Y5 |          0  (omitted)
     Sector1 |  -.0102441   .0089178    -1.15   0.251    -.0277851    .0072969
     Sector2 |          0  (omitted)
     Sector3 |  -.0251224   .0119066    -2.11   0.036    -.0485423   -.0017025
     Sector4 |  -.0134131   .0096315    -1.39   0.165    -.0323578    .0055317
     Sector5 |  -.0138872   .0095445    -1.46   0.147    -.0326609    .0048864
    Country1 |          0  (omitted)
    Country2 |  -.0610968   .0561138    -1.09   0.277    -.1714708    .0492771
    Country3 |   .0409602   .0433195     0.95   0.345    -.0442478    .1261682
    Country4 |  -.0117026   .0440055    -0.27   0.790    -.0982599    .0748547
    Country5 |    .004747    .043461     0.11   0.913    -.0807393    .0902334
    Country6 |   -.045664    .048471    -0.94   0.347    -.1410048    .0496767
    Country7 |  -.0395118   .0453174    -0.87   0.384    -.1286495    .0496259
    Country8 |  -.0332612   .0453622    -0.73   0.464    -.1224872    .0559648
    Country9 |   -.023308   .0556034    -0.42   0.675     -.132678    .0860621
   Country10 |  -.1146152   .0853866    -1.34   0.180    -.2825678    .0533373
   Country11 |  -.0867431   .0551996    -1.57   0.117    -.1953188    .0218326
   Country12 |  -.0452769   .0468803    -0.97   0.335    -.1374888     .046935
   Country13 |  -.0280531   .0576583    -0.49   0.627     -.141465    .0853588
   Country14 |   .0182435   .0413212     0.44   0.659    -.0630338    .0995208
   Country15 |  -.0219888   .0383947    -0.57   0.567    -.0975098    .0535321
   Country16 |  -.0157429    .047691    -0.33   0.742    -.1095494    .0780636
   Country17 |          0  (omitted)
   Country18 |   .0167567   .0355765     0.47   0.638     -.053221    .0867345
GDPperCapita |  -1.95e-06   1.09e-06    -1.79   0.075    -4.10e-06    1.96e-07
  millsTobit |          0  (omitted)
       _cons |  -.0921997   .1135825    -0.81   0.418    -.3156125    .1312131
------------------------------------------------------------------------------

I have also attempted to run a model with IMR as unique indep. v., but i get the same result:

reg SHROA_5w_100 millsTobit
note: millsTobit omitted because of collinearity

Source | SS df MS Number of obs = 454
-------------+---------------------------------- F(0, 453) = 0.00
Model | 0 0 . Prob > F = .
Residual | 1.04345408 453 .002303431 R-squared = 0.0000
-------------+---------------------------------- Adj R-squared = 0.0000
Total | 1.04345408 453 .002303431 Root MSE = .04799

------------------------------------------------------------------------------
SHROA_5w_100 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
millsTobit | 0 (omitted)
_cons | .0481006 .0022525 21.35 0.000 .043674 .0525272
------------------------------------------------------------------------------

.



Any suggestions would be really appreciated.


Thank you in advance

[FernandoRios]

Hi Nicola
Two points on your post. First, next time you provide some output be sure to use the "code wrappers"
If you write anything between the [ CODE ] and [ /CODE ] (omit the spaces), the output there will come well formatted and readable.
Second, if you have stata 15, there is the command eregress, which has the "tobitselect" option
Third, if you still want to do it manually, you can create the Mills ratio using the score option

tobit y x, ll(0) 
predict mill_tobit, score

If you do the latter, you will need to correct the standard errors.
HTH
Fernando