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# st: predictions from heckman very different from observed

 From Nikolaos Kanellopoulos To "statalist@hsphsun2.harvard.edu" Subject st: predictions from heckman very different from observed Date Thu, 13 Dec 2012 13:59:22 +0000 (GMT)

```Dear all,

I estimate a wage equation using the ML version of the Heckman command. The dependent variable is the log of hourly wage and I use the procedure described in MUS by Cameron and Trivedi to get the predicted wages in levels. The problem I have is that the predicted wages are very low compared to the observed wages. In particular, y=6.009, E(y)=2.247 or 2.683 for the estimation sample and E(y|y!=.)=6.817.

Moreover, when I run the model separately for men and women the average predicted wages (conditional and unconditional) are larger for women even though their observed average is lower.

Any thoughts why this is happening (see results in the end of email)?

Nikos

. heckman lnhwg \$xvarsac if period == 2, select(\$zvarsac)

Iteration 0:   log likelihood = -56059.406
Iteration 1:   log likelihood = -56050.387
Iteration 2:   log likelihood = -56050.371
Iteration 3:   log likelihood = -56050.371

Heckman selection model                         Number of obs      =    101835
(regression model with sample selection)        Censored obs       =     73243
Uncensored obs     =     28592

Wald chi2(130)     =  27364.89
Log likelihood = -56050.37                      Prob > chi2        =    0.0000

------------------------------------------------------------------------------
lnhwg |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnhwg        |
v1 |
1  |   .1405343   .0367721     3.82   0.000     .0684622    .2126064
2  |   .0469457    .030325     1.55   0.122    -.0124902    .1063816
4  |  -.0263412   .0263633    -1.00   0.318    -.0780123      .02533
5  |  -.1122694   .0403072    -2.79   0.005      -.19127   -.0332688
6  |  -.0555981    .023813    -2.33   0.020    -.1022706   -.0089255
7  |   .1557497    .054379     2.86   0.004     .0491687    .2623306
8  |   -.104675    .085015    -1.23   0.218    -.2713013    .0619514
9  |  -.0340463   .0379109    -0.90   0.369    -.1083502    .0402577
10  |  -.0279233   .0678232    -0.41   0.681    -.1608543    .1050077
11  |  -.0950452   .0333643    -2.85   0.004    -.1604381   -.0296523
12  |  -.1581143   .0908025    -1.74   0.082     -.336084    .0198554
13  |   .0089266   .0378355     0.24   0.813    -.0652296    .0830829
14  |   .2447555   .0743117     3.29   0.001     .0991072    .3904038
15  |     .22781   .0641243     3.55   0.000     .1021286    .3534914
16  |  -.0605822   .0945024    -0.64   0.521    -.2458035    .1246392
17  |  -.0628561   .0816088    -0.77   0.441    -.2228064    .0970943
18  |  -.0554997   .0774083    -0.72   0.473    -.2072173    .0962178
19  |   .2746892   .0477287     5.76   0.000     .1811427    .3682357
20  |   .1212234   .0733686     1.65   0.098    -.0225764    .2650233
21  |   .1279838    .077686     1.65   0.099    -.0242779    .2802456
22  |   .0120982   .0600432     0.20   0.840    -.1055842    .1297806
23  |   .0337195   .0324568     1.04   0.299    -.0298947    .0973337
24  |   .0013841   .0710655     0.02   0.984    -.1379016    .1406699
25  |   .0571335   .0355606     1.61   0.108    -.0125641    .1268311
26  |  -.1264217    .085914    -1.47   0.141    -.2948101    .0419666
27  |   .2729594   .0498995     5.47   0.000     .1751582    .3707606
28  |    .184259    .036492     5.05   0.000     .1127359     .255782
29  |   .2919003   .0698225     4.18   0.000     .1550507      .42875
|
v2 |   .0003214   .0016029     0.20   0.841    -.0028203     .003463
|
v1#c.v2 |
1  |   -.011764   .0025896    -4.54   0.000    -.0168395   -.0066885
2  |  -.0017117   .0025491    -0.67   0.502    -.0067079    .0032845
4  |   .0052595   .0030257     1.74   0.082    -.0006708    .0111898
5  |   .0133875   .0039881     3.36   0.001      .005571     .021204
6  |   .0072001   .0024879     2.89   0.004      .002324    .0120763
7  |   .0032429   .0058415     0.56   0.579    -.0082063    .0146921
8  |    .017078   .0106603     1.60   0.109    -.0038158    .0379718
9  |   .0119582   .0046321     2.58   0.010     .0028794     .021037
10  |   -.004808   .0091992    -0.52   0.601     -.022838     .013222
11  |   .0152968   .0042345     3.61   0.000     .0069972    .0235963
12  |   .0316381   .0117346     2.70   0.007     .0086387    .0546376
13  |   .0056551   .0045055     1.26   0.209    -.0031754    .0144857
14  |  -.0002032   .0076244    -0.03   0.979    -.0151468    .0147403
15  |   .0043123   .0068547     0.63   0.529    -.0091227    .0177472
16  |   .0281485   .0118901     2.37   0.018     .0048444    .0514526
17  |   .0354043   .0109495     3.23   0.001     .0139435     .056865
18  |   .0230234    .008273     2.78   0.005     .0068086    .0392382
19  |  -.0023888   .0056613    -0.42   0.673    -.0134846    .0087071
20  |   .0015243   .0073634     0.21   0.836    -.0129076    .0159563
21  |   .0071125   .0077366     0.92   0.358     -.008051     .022276
22  |   .0209899   .0070073     3.00   0.003     .0072558     .034724
23  |   .0145845   .0036037     4.05   0.000     .0075213    .0216477
24  |   .0104166   .0084007     1.24   0.215    -.0060484    .0268816
25  |    .013635    .003731     3.65   0.000     .0063224    .0209475
26  |   .0313759   .0088994     3.53   0.000     .0139333    .0488185
27  |  -.0058294   .0080356    -0.73   0.468    -.0215787      .00992
28  |   .0165462   .0048772     3.39   0.001     .0069871    .0261054
29  |   .0154256   .0083668     1.84   0.065     -.000973    .0318243
|
c.v2#c.v2 |   .0001343   .0000341     3.94   0.000     .0000674    .0002011
|
v1#c.v2#c.v2 |
1  |    .000106    .000045     2.36   0.018     .0000178    .0001942
2  |  -.0000362   .0000506    -0.72   0.475    -.0001353    .0000629
4  |  -.0000994   .0000758    -1.31   0.190     -.000248    .0000492
5  |  -.0002394   .0000864    -2.77   0.006    -.0004088     -.00007
6  |  -.0000914   .0000582    -1.57   0.116    -.0002054    .0000226
7  |  -.0000908   .0001382    -0.66   0.511    -.0003616    .0001801
8  |  -.0002443    .000265    -0.92   0.357    -.0007638    .0002752
9  |  -.0001587   .0001212    -1.31   0.190    -.0003963    .0000788
10  |   .0005014     .00026     1.93   0.054    -8.10e-06     .001011
11  |   -.000253   .0001176    -2.15   0.031    -.0004834   -.0000225
12  |  -.0008003   .0003418    -2.34   0.019    -.0014703   -.0001304
13  |  -.0000475   .0001224    -0.39   0.698    -.0002875    .0001924
14  |   .0000644   .0001737     0.37   0.711    -.0002761    .0004049
15  |   -.000046   .0001641    -0.28   0.779    -.0003677    .0002756
16  |  -.0006028   .0003105    -1.94   0.052    -.0012114    5.86e-06
17  |  -.0007131   .0003332    -2.14   0.032    -.0013662   -.0000601
18  |  -.0005149   .0001934    -2.66   0.008     -.000894   -.0001358
19  |    .000177   .0001402     1.26   0.207    -.0000978    .0004519
20  |   .0001849   .0001712     1.08   0.280    -.0001507    .0005205
21  |  -.0000862    .000176    -0.49   0.624    -.0004312    .0002588
22  |  -.0003842   .0001727    -2.22   0.026    -.0007226   -.0000458
23  |  -.0001949   .0000882    -2.21   0.027    -.0003678    -.000022
24  |  -.0000582   .0002127    -0.27   0.785    -.0004751    .0003588
25  |  -.0001385   .0000893    -1.55   0.121    -.0003136    .0000366
26  |  -.0005447   .0002211    -2.46   0.014    -.0009781   -.0001112
27  |   .0002167   .0002917     0.74   0.457    -.0003549    .0007884
28  |   -.000404   .0001414    -2.86   0.004    -.0006812   -.0001268
29  |  -.0003773   .0002177    -1.73   0.083     -.000804    .0000493
|
v3 |   .0705147   .0040717    17.32   0.000     .0625344    .0784951
|
v4 |
2  |  -.2370253   .0127142   -18.64   0.000    -.2619448   -.2121059
3  |  -.1941376   .0076409   -25.41   0.000    -.2091134   -.1791618
|
v5 |
1  |  -.0170644    .009481    -1.80   0.072    -.0356469     .001518
2  |  -.0187411   .0096394    -1.94   0.052    -.0376339    .0001517
3  |   .0903678   .0123608     7.31   0.000      .066141    .1145945
4  |   .0372835   .0095881     3.89   0.000     .0184912    .0560758
5  |   .0097628   .0094905     1.03   0.304    -.0088383    .0283638
6  |  -.0306734    .013235    -2.32   0.020    -.0566135   -.0047333
7  |   .0232329   .0096604     2.40   0.016     .0042988    .0421669
8  |   .0254702   .0090799     2.81   0.005     .0076739    .0432664
10  |   .0346836   .0097353     3.56   0.000     .0156027    .0537645
11  |   .0059777   .0138117     0.43   0.665    -.0210928    .0330482
12  |   .0125233   .0122307     1.02   0.306    -.0114484    .0364951
13  |     .02741   .0085307     3.21   0.001     .0106901    .0441299
|
v6 |
2  |  -.0327036   .0114667    -2.85   0.004    -.0551778   -.0102294
3  |  -.0294628    .007212    -4.09   0.000    -.0435979   -.0153276
4  |   -.021645   .0080887    -2.68   0.007    -.0374985   -.0057914
5  |  -.0222819   .0088946    -2.51   0.012     -.039715   -.0048488
|
v7 |
1  |  -.0405702   .0122746    -3.31   0.001     -.064628   -.0165125
2  |   .0763601   .0332315     2.30   0.022     .0112276    .1414926
3  |   .2379452   .0211354    11.26   0.000     .1965206    .2793699
4  |   .0900824   .0062546    14.40   0.000     .0778237    .1023411
5  |   .0839119   .0121623     6.90   0.000     .0600743    .1077495
6  |   .1276211   .0077394    16.49   0.000     .1124522      .14279
8  |   .0497563   .0063019     7.90   0.000     .0374048    .0621077
9  |   .1377267    .012004    11.47   0.000     .1141993     .161254
10  |   .1740053   .0099378    17.51   0.000     .1545275    .1934831
11  |   .0226617   .0083882     2.70   0.007     .0062211    .0391022
12  |   .0430055   .0084472     5.09   0.000     .0264492    .0595617
13  |   .2911112   .0098379    29.59   0.000     .2718292    .3103931
14  |  -.0127426   .0088565    -1.44   0.150     -.030101    .0046158
15  |   .0125831   .0110811     1.14   0.256    -.0091355    .0343017
16  |  -.2060467   .0131847   -15.63   0.000    -.2318882   -.1802053
17  |   .1055014    .076806     1.37   0.170    -.0450355    .2560383
|
v8 |   .0791783   .0036615    21.62   0.000     .0720018    .0863548
1.v9 |   .0937934   .0149065     6.29   0.000     .0645772    .1230095
|
v9#c.v2 |
1  |   .0050052   .0012696     3.94   0.000     .0025168    .0074936
|
v9#c.v2#c.v2 |
1  |  -.0000569   .0000254    -2.24   0.025    -.0001066   -7.15e-06
|
v11 |
7  |   .1325569   .0052178    25.40   0.000     .1223301    .1427836
8  |   .0927179   .0049073    18.89   0.000     .0830997     .102336
|
v12 |
1  |   .0332957    .004646     7.17   0.000     .0241897    .0424017
3  |   .0066404   .0055675     1.19   0.233    -.0042717    .0175526
4  |  -.0059572   .0055663    -1.07   0.285     -.016867    .0049527
|
_cons |    1.49079   .0246423    60.50   0.000     1.442492    1.539088
-------------+----------------------------------------------------------------
select       |
v13 |
1  |   -.312142   .0113899   -27.41   0.000    -.3344659   -.2898182
3  |   .2288368   .0166555    13.74   0.000     .1961926    .2614809
4  |   .4508384   .0190044    23.72   0.000     .4135904    .4880863
5  |   .3995711   .0141445    28.25   0.000     .3718484    .4272938
6  |   .5572528   .0354082    15.74   0.000      .487854    .6266516
|
v14 |   .1866015   .0028108    66.39   0.000     .1810925    .1921105
|
c.v14#c.v14 |  -.0022167   .0000341   -65.07   0.000    -.0022835     -.00215
|
v3 |  -.0694488   .0127675    -5.44   0.000    -.0944727   -.0444249
|
v15 |
1  |    .105427   .0192862     5.47   0.000     .0676267    .1432272
2  |  -.0676413   .0124549    -5.43   0.000    -.0920524   -.0432302
3  |  -.0487929   .0212949    -2.29   0.022    -.0905302   -.0070557
|
v4 |
2  |   .4029376   .0344477    11.70   0.000     .3354213    .4704538
3  |   .4743026   .0171719    27.62   0.000     .4406463    .5079589
|
v5 |
1  |     .00197   .0242813     0.08   0.935    -.0456204    .0495604
2  |  -.0009342   .0247638    -0.04   0.970    -.0494703    .0476018
3  |  -.0194526   .0328239    -0.59   0.553    -.0837863    .0448811
4  |  -.0339977   .0240475    -1.41   0.157    -.0811299    .0131346
5  |  -.0195216   .0243038    -0.80   0.422    -.0671563     .028113
6  |   .1034091    .035394     2.92   0.003     .0340381      .17278
7  |  -.0935439   .0238777    -3.92   0.000    -.1403434   -.0467445
8  |   .0961417   .0238852     4.03   0.000     .0493276    .1429557
10  |  -.0923982   .0255345    -3.62   0.000    -.1424448   -.0423516
11  |  -.1549991   .0346014    -4.48   0.000    -.2228165   -.0871817
12  |   .0099103   .0316818     0.31   0.754    -.0521848    .0720054
13  |   .0601067   .0222389     2.70   0.007     .0165192    .1036942
|
v6 |
2  |  -.0870117   .0298341    -2.92   0.004    -.1454854   -.0285381
3  |  -.1913193    .018651   -10.26   0.000    -.2278745   -.1547641
4  |  -.2409326   .0205058   -11.75   0.000    -.2811232    -.200742
5  |   -.307227    .021781   -14.11   0.000     -.349917    -.264537
|
v16 |  -.4267022   .2584641    -1.65   0.099    -.9332824    .0798781
|
v11 |
7  |   .2301844   .0328466     7.01   0.000     .1658063    .2945625
8  |    .123804   .0215129     5.75   0.000     .0816394    .1659685
|
v12 |
1  |    .028929   .0122591     2.36   0.018     .0049016    .0529564
3  |   .0336482   .0149595     2.25   0.024      .004328    .0629683
4  |   -.022284   .0168357    -1.32   0.186    -.0552814    .0107134
|
v17 |  -.0546934   .0058848    -9.29   0.000    -.0662273   -.0431595
v18 |  -.1423259   .0097779   -14.56   0.000    -.1614903   -.1231615
v19 |   .0805902   .0104115     7.74   0.000     .0601841    .1009964
_cons |  -3.951667   .0820076   -48.19   0.000    -4.112399   -3.790935
-------------+----------------------------------------------------------------
/athrho |  -.6295655   .0382775   -16.45   0.000    -.7045881    -.554543
/lnsigma |  -1.179191   .0137634   -85.68   0.000    -1.206167   -1.152215
-------------+----------------------------------------------------------------
rho |   -.557753   .0263698                      -.607272   -.5039173
sigma |   .3075274   .0042326                      .2993425    .3159361
lambda |  -.1715243   .0103828                     -.1918742   -.1511744
------------------------------------------------------------------------------
LR test of indep. eqns. (rho = 0):   chi2(1) =   113.59   Prob > chi2 = 0.0000
------------------------------------------------------------------------------

. predict probpos, psel
. predict x1b1, xbsel
. predict x2b2, xb
(106970 missing values generated)
. scalar  sig2sq = e(sigma)^2
. scalar  sig12sq = e(rho)*e(sigma)^2
. generate yhatheck = exp(x2b2 + 0.5*(sig2sq))*(1 - normal(-x1b1-sig12sq))
(106970 missing values generated)
. generate yhatposheck = yhatheck/probpos
(106970 missing values generated)
. summarize hwg yhatheck if period == 2

Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
hwg |     28644    6.009612        2.87   2.000454   56.08289
yhatheck |     57370    2.247878    1.490795   .0209093   11.06441

. summarize hwg yhatheck if e(sample) & lnhwg!=.

Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
hwg |     28592    6.013462     2.87082   2.000454   56.08289
yhatheck |     28592    2.683502    1.582859   .0792262   11.06441

. summarize hwg yhatposheck if e(sample) & hwg!=.

Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
hwg |     28592    6.013462     2.87082   2.000454   56.08289
yhatposheck |     28592    6.817118    2.152765   2.821729    19.7986

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```