CMP Commands

[Yasmine Shemeis]

I need to estimate a simultaneous model of health and wages. The health variable is an ordered discrete variable so I used to CMP IV ordered probit command as follows,
cmp(lwagehr = X Y Z) (health= lwagehr X Y A), indicators ($cmp_cont $cmp_oprobit)

Is it possible to also estimate wages using this command? using cmp (health = X Y A) (lwagehr= health X Y Z), indicators ($cmp_oprobit $cmp_cont)

I have tried cmp (lwagehr= health X Y Z) (health= lwagehr X Y A), indicators ($cmp_cont $cmp_oprobit) but it takes a very long time to converge and eventually provides me with a lot of missing results for the different variables.

My main problem is to estimate the model simultaneously but in the same time take into consideration that the health variable is an ordered discrete variable, any suggestions or comments about what I have already done?

Thank you

[David Roodman]

Hi Yasmine. In principle, both the first two commands will work, although there is never a guarantee of convergence. The third will not work however. As explained in the help file, cmp can only do true simultaneous models if you use the # suffix to create references to (latent) linear dependent variables, enough so that the non-suffixed cross-equation references to dependent variables form a recursive/sequentially staged structure. So this might work:

cmp (lwagehr= health# X Y Z) (health= lwagehr# X Y A), indicators ($cmp_cont $cmp_oprobit)

This changes the model so that now lwagehr is not a function of the observed discrete variable health, but of the hypothesized continuous, latent variable within it.

In fact, you might be able to trick cmp into fitting your third model, as follows:

cmp (lwagehr= health X Y Z) (health= lwagehr# X Y A), indicators ($cmp_cont $cmp_oprobit)

Now, leaving out the lwagehr# reference, the two-equation system has a sequential structure...even though referring to lwagehr is mathematically identical to referring to lwagehr#, since lwagehr is uncensored.

--David

[Yasmine Shemeis]

Thank you for your reply, David.

I do have some additional questions concerning the results though.
1- How is the first stage estimation conducted especially, when the first-stage is an estimation of a reduced-form health equation (discrete ordered variable)? Is it possible to get the first stage results for the estimations?
2 - Also, In such a model, is it possible to get the R2 and Root MSE values?

[David Roodman]

1. cmp displays results for all stages.
2. You can compute them manually by first using the predict command to get the linear predictions.

[Yasmine Shemeis]

I have one last question please, when I use such a model:

cmp(lwagehr = X Y Z) (health= lwagehr X Y A), indicators ($cmp_cont $cmp_oprobit)

The results stata reports are first:
"Fitting individual models as starting point for full model fit."

Where I can see the results resembles the ones of running these models separately while estimating single equations with no simultaneity. (so I guess this is not first stage)

This is followed by:
"Fitting full model."
"Mixed-process regression " (the below is just an example of how results come up for me)

| Robust
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwagehr |
age | .0040804 .0015972 2.55 0.011 .0009499 .0072109
mar4 | .1114278 .0216441 5.15 0.000 .0690061 .1538495
mar5 | .0019149 .0740648 0.03 0.979 -.1432495 .1470793
mar6 | .0516699 .0613652 0.84 0.400 -.0686037 .1719436
|
occ |
1 | 0 (empty)
2 | .2665149 .032997 8.08 0.000 .201842 .3311878
3 | .3812626 .0299532 12.73 0.000 .3225554 .4399698
4 | .2207112 .0330792 6.67 0.000 .1558771 .2855453
5 | .0389838 .0338688 1.15 0.250 -.0273978 .1053653
6 | .2460079 .0431883 5.70 0.000 .1613604 .3306554
7 | .2684058 .0333091 8.06 0.000 .2031213 .3336904
8 | .2907843 .035836 8.11 0.000 .220547 .3610217
9 | .6581111 .0501904 13.11 0.000 .5597397 .7564825
|
_cons | .5933987 .0605845 9.79 0.000 .4746553 .7121421
-------------+----------------------------------------------------------------
health |
lwagehr | .238317 .05549 4.29 0.000 .1295586 .3470753
age | .0018509 .0095447 0.19 0.846 -.0168564 .0205583
age2 | -.0004413 .0001187 -3.72 0.000 -.000674 -.0002086
mar4 | -.0169498 .0392193 -0.43 0.666 -.0938183 .0599186
mar5 | -.0569041 .127652 -0.45 0.656 -.3070974 .1932892
mar6 | -.2346993 .1222292 -1.92 0.055 -.4742641 .0048655
|
reg |
1 | 0 (empty)
2 | -.035027 .0343102 -1.02 0.307 -.1022738 .0322198
3 | .1792624 .0395421 4.53 0.000 .1017614 .2567634
4 | .0170639 .0447173 0.38 0.703 -.0705805 .1047083
5 | .2783507 .0505771 5.50 0.000 .1792215 .37748
6 | -.1044731 .0452896 -2.31 0.021 -.1932392 -.0157071
|
mtedu |
1 | 0 (empty)
2 | .111378 .0414416 2.69 0.007 .030154 .192602
|
mtemp |
1 | 0 (empty)
2 | -.0849202 .0462111 -1.84 0.066 -.1754924 .0056519
|
sav |
1 | 0 (empty)
2 | .1385567 .0501687 2.76 0.006 .0402278 .2368856
|
deadsib |
1 | 0 (empty)
2 | -.0968402 .0259145 -3.74 0.000 -.1476316 -.0460487
-------------+----------------------------------------------------------------
/cut_2_1 | -2.502469 .1760263 -14.22 0.000 -2.847474 -2.157463
/cut_2_2 | -1.3712 .1724372 -7.95 0.000 -1.709171 -1.033229
/cut_2_3 | .3298503 .17058 1.93 0.053 -.0044803 .6641809
/lnsig_1 | -.4514667 .0124326 -36.31 0.000 -.4758342 -.4270993
/atanhrho_12 | -.1389769 .0383613 -3.62 0.000 -.2141637 -.0637901
-------------+----------------------------------------------------------------
sig_1 | .6366936 .0079158 .6213665 .6523988
rho_12 | -.138089 .0376298 -.2109483 -.0637037
------------------------------------------------------------------------------


There is no "first" option, so is it possible to clarify how i can get first stage results? I mainly need to verify how the model is fitted in the mixed process. I have specified that the health variable is estimated by a oprobit, but what happens when it is used in the estimation of wages (continuous)

Thanks.

[David Roodman]

It appears that in your model, the first stage is for lwagehr. The first half of the final results displayed above are for the lwagehr equation.