# st: validity of estimates when fiml heckman converges to rho=1

 From Justin Falk To statalist@hsphsun2.harvard.edu Subject st: validity of estimates when fiml heckman converges to rho=1 Date Wed, 4 Mar 2009 07:10:13 -0800 (PST)

```I estimated a sample selection model using the command heckman (with fiml, not the two-step approach). The program converged to a solution at which rho equals 1. I find the uniform estimates for the t-stats on the instruments in the selection equation suspicious. (I have pasted the output below.) Do you understand how those standard error for the instruments are calculate under such a boundary solution?

Cheers, Justin

heckman \$y \$treatment \$w if \$condition, select(\$s1=\$treatment \$z1 \$w)
> cluster(name)Iteration 0:   log pseudolikelihood = -2.1784177  (not concave)
Iteration 1:   log pseudolikelihood = -2.1784172  (not concave)
Iteration 2:   log pseudolikelihood = -2.1784167  (not concave)
Iteration 3:   log pseudolikelihood = -2.1784161  (not concave)
Iteration 4:   log pseudolikelihood = -2.1784151  (not concave)
Iteration 5:   log pseudolikelihood = -2.1784142  (not concave)
Iteration 6:   log pseudolikelihood = -2.1784122  (not concave)
Iteration 7:   log pseudolikelihood = -2.0504685  (not concave)
Iteration 8:   log pseudolikelihood = -1.8571609  (not concave)
Iteration 9:   log pseudolikelihood =   -1.53331  (not concave)
Iteration 10:  log pseudolikelihood = -1.2231065
Iteration 11:  log pseudolikelihood = -.44859226
Iteration 12:  log pseudolikelihood = -.28555273  (not concave)
Iteration 13:  log pseudolikelihood = -.19045476  (not concave)
Iteration 14:  log pseudolikelihood = -.03164312  (not concave)
Iteration 15:  log pseudolikelihood =    .745585  (not concave)
Iteration 16:  log pseudolikelihood =  2.1089315
Iteration 17:  log pseudolikelihood =  2.8867084
Iteration 18:  log pseudolikelihood =  3.5050768
Iteration 19:  log pseudolikelihood =  3.7131656
Iteration 20:  log pseudolikelihood =  3.7984129
Iteration 21:  log pseudolikelihood =  4.0843501
Iteration 22:  log pseudolikelihood =  4.2175989
Iteration 23:  log pseudolikelihood =  4.2857362
Iteration 24:  log pseudolikelihood =  4.3115319
Iteration 25:  log pseudolikelihood =  4.3253351
Iteration 26:  log pseudolikelihood =  4.3330355
Iteration 27:  log pseudolikelihood =  4.3362203
Iteration 28:  log pseudolikelihood =  4.3380159
Iteration 29:  log pseudolikelihood =  4.3392351
Iteration 30:  log pseudolikelihood =  4.3398897
Iteration 31:  log pseudolikelihood =  4.3404044
Iteration 32:  log pseudolikelihood =  4.3409418
Iteration 33:  log pseudolikelihood =  4.3411832
Iteration 34:  log pseudolikelihood =  4.3413712
Iteration 35:  log pseudolikelihood =  4.3415178
Iteration 36:  log pseudolikelihood =   4.341616
Iteration 37:  log pseudolikelihood =  4.3416821
Iteration 38:  log pseudolikelihood =  4.3417317
Iteration 39:  log pseudolikelihood =  4.3417627
Iteration 40:  log pseudolikelihood =  4.3417861
Iteration 41:  log pseudolikelihood =  4.3417888
Iteration 42:  log pseudolikelihood =  4.3418021
Iteration 43:  log pseudolikelihood =  4.3418142  (not concave)
Iteration 44:  log pseudolikelihood =  4.3418231
Iteration 45:  log pseudolikelihood =  4.3418283
Iteration 46:  log pseudolikelihood =  4.3418317
Iteration 47:  log pseudolikelihood =   4.341835
Iteration 48:  log pseudolikelihood =  4.3418369  (not concave)
Iteration 49:  log pseudolikelihood =  4.3418389
Iteration 50:  log pseudolikelihood =  4.3418396
Iteration 51:  log pseudolikelihood =  4.3418398  (not concave)
Iteration 52:  log pseudolikelihood =  4.3418414
Iteration 53:  log pseudolikelihood =  4.3418432  (backed up)
Iteration 54:  log pseudolikelihood =  4.3418433
Heckman selection model                         Number of obs      =       103
(regression model with sample selection)        Censored obs       =        27
Uncensored obs     =        76                                                Wald chi2(0)       =         .
Log pseudolikelihood =  4.341843                Prob > chi2        =         .                                  (Std. Err. adjusted for 56 clusters in name)
------------------------------------------------------------------------------
|               Robust
|      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
disclosed |  -.2157538     .03195    -6.75   0.000    -.2783746   -.1531331
_cons |   .6482833   .0229978    28.19   0.000     .6032085    .6933581
-------------+----------------------------------------------------------------
nominated    |
disclosed |  -.8478425   .1875101    -4.52   0.000    -1.215356   -.4803295
dpension |   .0075225   .0005421    13.88   0.000       .00646    .0085849
dpensioncdis |  -.0052622   .0003792   -13.88   0.000    -.0060054    -.004519
senelection |  -.0549624   .0039606   -13.88   0.000    -.0627251   -.0471997
senelectio~s |  -.5100564   .0367549   -13.88   0.000    -.5820946   -.4380181
lasttake |   .0004281   .0000309    13.88   0.000     .0003677    .0004886
_cons |   1.098665   .1229111     8.94   0.000     .8577637    1.339566
-------------+----------------------------------------------------------------
/athrho |   18.34718   .0978797   187.45   0.000     18.15534    18.53902
/lnsigma |  -1.764034   .0720605   -24.48   0.000     -1.90527   -1.622798
-------------+----------------------------------------------------------------
rho |          1   6.52e-17                             1           1
sigma |   .1713523   .0123477                      .1487825    .1973458
lambda |   .1713523   .0123477                      .1471512    .1955534
------------------------------------------------------------------------------
Wald test of indep. eqns. (rho = 0): chi2(1) = 35136.11   Prob > chi2 = 0.0000
------------------------------------------------------------------------------

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