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 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