Bug/overcorrection with post-Stata 14.1 margins command after ivprobit?

[Joe Brown]

Hello,
I posted a few days ago with a question about a strange result I get with Stata 16 and ivprobit, using the margins, dydx() predict(pr) syntax to obtain predicted probabilities. Specifically, I find that my endogenous X1 variable, which had a negative coefficient in the ivprobit results, has a positive marginal effect. I saw in an older post (linked below) that Stata 14.1 instituted a fix, based on Skeels & Taylor (2015), which "includes the instrumented variable equation in the computation."

My question is, is the "fix" producing a bug, or at least an overcorrection in certain cases, since it is apparently possible to have a marginal effect with the opposite sign from that of the estimated ivprobit coefficient? (If it is not a bug or an overcorrection, how does one report this strange result in a paper?)

To illustrate, I am including/attaching the results of my ivprobit regression, using the margins command from Stata 16, and the results of the older margins command (using version control, Stata 14) for comparison. See how the ivprobit coefficient is negative, but the estimated probability change is positive. The sign of the probability change reverts to negative when I use the Stata 14 version of margins and predict.


. ivprobit PROTBI (endogenous_X1=IV) X2 X3 X4 X5 X6 X7 X8 , vce(cluster orgId)

Probit model with endogenous regressors Number of obs = 1,492
Wald chi2(8) = 119.90
Log pseudolikelihood = -1403.5646 Prob > chi2 = 0.0000

(Std. Err. adjusted for 106 clusters in orgId)
------------------------------------------------------------------------------------------------
| Robust
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------------------------------------+----------------------------------------------------------------
endogenous_X1 | -1.765481 .5107963 -3.46 0.001 -2.766624 -.7643387
X2 | .2941948 .506894 0.58 0.562 -.6992993 1.287689
X3 | .0003688 .0003185 1.16 0.247 -.0002554 .0009931
X4 | .2330729 .1933046 1.21 0.228 -.1457971 .6119429
X5 | .4271303 .198719 2.15 0.032 .0376481 .8166124
X6 | .5621895 .2282728 2.46 0.014 .1147831 1.009596
X7 | .2013893 .2776837 0.73 0.468 -.3428608 .7456393
X8 | .4314645 .1971322 2.19 0.029 .0450925 .8178365
_cons | -.15545 1.28781 -0.12 0.904 -2.679511 2.368611
----------------------------------------------+----------------------------------------------------------------
corr(e.endogenous_X1,e.PROTBI)| .8989229 .1475742 -.040347 .9947866
sd(e.endogenous_X1)| .4513452 .0497914 .3635852 .5602883
------------------------------------------------------------------------------------------------
Instrumented: endogenous_X1
Instruments: X2 X3 X4 X5 X6 X7 X8 IV
------------------------------------------------------------------------------------------------
Wald test of exogeneity (corr = 0): chi2(1) = 3.64 Prob > chi2 = 0.0565


. margins, dydx(endogenous_X1) predict(pr)

Average marginal effects Number of obs = 1,492
Model VCE : Robust

Expression : Probability of positive outcome, predict(pr)
dy/dx w.r.t. : endogenous_X1

-------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
----------------------+----------------------------------------------------------------
endogenous_X1 | .0908771 .1397807 0.65 0.516 -.1830882 .3648423
-------------------------------------------------------------------------------


. version 14: margins, dydx(endogenous_X1) predict(pr)

Average marginal effects Number of obs = 1,492
Model VCE : Robust

Expression : Prob of positive outcome when rho=0, predict(pr)
dy/dx w.r.t. : endogenous_X1

-------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
----------------------+----------------------------------------------------------------
endogenous_X1 | -.5541947 .2400751 -2.31 0.021 -1.024733 -.0836563
-------------------------------------------------------------------------------


References:
Old post: https://www.statalist.org/forums/for...ivprobit-a-bug
Skeels, C.L. and L.W. Taylor (2015) Prediction in linear index models with endogenous regressors, The Stata Journal (15), 627-644

[Karsten Müller]

Apologies to revive this old thread, but this problem has apparently not been addressed on Statalist.

What is the correct syntax to obtain marginal effects for the endogenous (instrumented) variable using ivprobit starting with Stata 14.1?

As Joe rightly showed above, it is not to use "margins, dydx(endogenous_X1) predict(pr)", which (nonsensically) controls for the instrument ("IV") when calculating marginal effects.

Any pointer would be much appreciated.

[Alper Demirdogen]

Hello Dear All,

Instead of opening a new thread, I would like to post here. I have been experiencing the same problem. Is there any update or idea why we may experience this problem?

Thank you
Alper

[Joe Brown]

Alper and Karsten,
Sorry I'm just seeing your posts now. I was not able to find an answer as to why the sign of the margin is different from the sign of the ivprobit coefficient. I believe that is a bug in the way Stata calculates margins in versions 14.1 and above. I was able to solve the problem by using Stata's version control and specifying version 14.0

The syntax is: version 14.0: margins, dydx(varlist) predict(pr)

Using the version 14.0 margins command, all of the margins' signs are consistent with the ivprobit coefficients' signs. I hope this is useful to you.

Joe

[Jeff Wooldridge]

Joe: Have you done the calculation “by hand” so see whether it’s correct in Stata 14? I’ll give it a go when I have a chance.

[Enrique Pinzon (StataCorp)]

Dear Joe,

If you want, we will look at your data and code to verify what is happening. If possible, send your code and data to [email protected]. On the mean time, let me explain what the differences are between the two computations.

Following the methods and formulas from the manual, the probabilities implied by the model are given by:

$$ P\left(y_1 = 1| y_2, z\right) = \Phi \left[\frac{z_i\delta +\rho \left(y_{2i}- x_i\pi\right)/\sigma}{\left(1-\rho^2\right)^{1/2}} \right]$$

Before Stata 14 this probability was calculated using only \(z_i\delta\). After Stata 14 all the terms in parenthesis are used in the computation. From the expression above, you can see that the computed probabilities and effects may differ. This happens regardless of the sign of the coefficients.

[Joe Brown]

Enrique: Thank you for your reply. I am happy to send my data and .do file and will do so today.

Jeff: Thank you for your reply as well. To be honest, I haven't done these calculations by hand before. Is there an online resource where I can find the formulas/commands? (COVID has locked me out of my office.) Please let me know if you would like me to share my data and .do file. I'm happy to send them.

[Enrique Pinzon (StataCorp)]

Hello Joe,

https://www.stata.com/manuals/rivprobit.pdf

In this entry and the postestimation entry (you can get to postestimation using the link in the 'Also see' section), you can see what we are doing. The calculations are based on the normal c.d.f. The effects calculated by -margins- are numerical derivatives of the c.d.f. The closed form derivative you obtain using the formula should be 'almost' the same.

[Joe Brown]

Enrique and Jeff,
I have done a "hand" calculation of the AMEs for my ivprobit model, using the formula for the current margins command and the Version 14 margins command. (The resources I consulted are here and here.) My output is contained in the attached log file. The file starts by showing the original ivprobit output, the AMEs for X1, and the predicted probabilities of Y at specific values of X1.

I was able to replicate the results of both versions of margins. So unless I have misinterpreted what you meant by hand calculation, the issue must be with the formulas themselves. Is the current formula used to calculate margins more correct than the formula used in Version 14? If so, how can a negative (and significant) probit coefficient give positive marginal effects, both as AMEs and as predicted probabilities that increase at higher values of X1?

I have sent my data set and .do file to tech-support, as you requested, Enrique.

Thank you both,
Joe

[Enrique Pinzon (StataCorp)]

Dear Joe,

Thanks for sending the data and code to us. The reason why the sign of the coefficient and the sign of the predicted effects might be different is that the endogenous variables appears in two terms in the expression below:

$$ P\left(y_1 = 1| y_2, z, x\right) = \Phi \left[\frac{z_i\delta +\rho \left(y_{2i}- x_i\pi\right)/\sigma}{\left(1-\rho^2\right)^{1/2}} \right]$$

It appears in \(z_i\delta\) and it appears in \(\rho \left(y_{2i}- x_i\pi\right)/\sigma\). If the endogenous variable only appeared in \(z_i\delta\) your intuition would be correct.
If you were to condition on \(y_2, z, x,\) and on \(\nu \ \equiv (y_{2i}- x_i) \) then the sign would not change. If you wanted to condition on \(\nu\) you could use margins with the
-expression()- option.

[Jeff Wooldridge]

Joe, Enrique: That formula on which the partial effects are computed is incorrect. This is tantamount, in the linear case, to compute the effect of y2 as E(y1|y2,x). If we could do that, there'd be no reason to actually have instruments. We could just estimate

The derivative should only be with respect to the occurrence of y2 in z. The part (y2 - x*pi) is the so-called control function, and it should be held fixed. I'm not sure why this is used in the full MLE, anyway, as the proper APEs are obtained by dropping the CF term in the expression above. I show this in my 2010 MIT Press book. If you do leave the CF in, then it gets averaged out. You don't take the derivative of y2 in the CF.

When I have a bit more time, I'll find an example and post.

Jeff

[Joe Brown]

Thank you, Jeff. This is very helpful!
I look forward to seeing your example when you have time to post.

Best wishes,
Joe

[Jeff Wooldridge]

I confirmed that Stata is not computing the APEs correctly. I don't know whether the calculations were correct prior to Stata 14, but I used them in my course slides and got similar answers to my two-step "by hand" calculations. In any case, the current calculations are not correct. Prediction is not the same as computing causal effects -- an obvious point, I know, but one that seemed to slip past the Stata people. I'm not sure that Skeels and Taylor (2015) were suggesting changing the marginal effect calculations but it seemed to have that effect.

In any case, it is easy to do the "by hand" calculation using the two-step method. (Stata doesn't allow the marginal effect calculation in the two-step method, something that I also hope is corrected in the next version.)

Here is the example that I use for one of my classes. It confirms that the two-step estimates that ivprobit reports and that I compute are identical. The APE calculation is then simple. What is not so simple is getting a standard error. I would put the two-steps (first stage by OLS, second by probit) in a little bootstrap program and resample 1,000 times or so. This will give a good standard error.

. ivprobit inlf educ c.exper c.exper#c.exper age kidslt6 kidsge6 ///
>         (nwifeinc = huseduc), first

Fitting exogenous probit model

Iteration 0:   log likelihood =  -514.8732  
Iteration 1:   log likelihood = -401.13728  
Iteration 2:   log likelihood = -400.30361  
Iteration 3:   log likelihood = -400.30301  
Iteration 4:   log likelihood = -400.30301  

Fitting full model

Iteration 0:   log likelihood = -3230.6635  
Iteration 1:   log likelihood = -3230.6421  
Iteration 2:   log likelihood = -3230.6421  

Probit model with endogenous regressors         Number of obs     =        753
                                                Wald chi2(7)      =     200.50
Log likelihood = -3230.6421                     Prob > chi2       =     0.0000

-----------------------------------------------------------------------------------------
                        |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
inlf                    |
               nwifeinc |  -.0355243   .0161904    -2.19   0.028    -.0672569   -.0037916
                   educ |   .1640289   .0312249     5.25   0.000     .1028293    .2252285
                  exper |    .112085   .0211991     5.29   0.000     .0705356    .1536344
                        |
        c.exper#c.exper |  -.0018751   .0005915    -3.17   0.002    -.0030345   -.0007158
                        |
                    age |  -.0433193   .0113314    -3.82   0.000    -.0655284   -.0211101
                kidslt6 |  -.8137458   .1299442    -6.26   0.000    -1.068432   -.5590599
                kidsge6 |   .0460536   .0431386     1.07   0.286    -.0384966    .1306037
                  _cons |   .0164965   .5300821     0.03   0.975    -1.022445    1.055438
------------------------+----------------------------------------------------------------
nwifeinc                |
                   educ |   .6746951   .2125447     3.17   0.002     .2581151    1.091275
                  exper |  -.3129877   .1375186    -2.28   0.023    -.5825191   -.0434563
                        |
        c.exper#c.exper |  -.0004776   .0044955    -0.11   0.915    -.0092885    .0083334
                        |
                    age |   .3401521   .0593903     5.73   0.000     .2237492     .456555
                kidslt6 |   .8262719   .8140196     1.02   0.310    -.7691772    2.421721
                kidsge6 |   .4355289   .3202738     1.36   0.174    -.1921962    1.063254
                huseduc |   1.178155   .1600877     7.36   0.000      .864389    1.491921
                  _cons |  -14.72048   3.767154    -3.91   0.000    -22.10397   -7.336999
------------------------+----------------------------------------------------------------
             /athrho2_1 |   .2737896   .1929615     1.42   0.156    -.1044081    .6519873
              /lnsigma2 |   2.339812   .0257684    90.80   0.000     2.289307    2.390317
------------------------+----------------------------------------------------------------
 corr(e.nwifeinc,e.inlf)|   .2671475   .1791903                     -.1040303    .5730063
          sd(e.nwifeinc)|   10.37928   .2674576                      9.868095    10.91695
-----------------------------------------------------------------------------------------
Instrumented:  nwifeinc
Instruments:   educ exper c.exper#c.exper age kidslt6 kidsge6 huseduc
-----------------------------------------------------------------------------------------
Wald test of exogeneity (corr = 0): chi2(1) = 2.01        Prob > chi2 = 0.1559

. 
. * Following is incorrect starting with Stata 14:
.         
. margins, predict(pr) dydx(*)

Average marginal effects                        Number of obs     =        753
Model VCE    : OIM

Expression   : Probability of positive outcome, predict(pr)
dy/dx w.r.t. : nwifeinc educ exper age kidslt6 kidsge6 huseduc

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    nwifeinc |   -.003046   .0050727    -0.60   0.548    -.0129882    .0068962
        educ |   .0456518   .0095799     4.77   0.000     .0268755    .0644281
       exper |   .0256561   .0034917     7.35   0.000     .0188124    .0324997
         age |  -.0162091   .0032176    -5.04   0.000    -.0225156   -.0099027
     kidslt6 |  -.2599143    .035065    -7.41   0.000    -.3286404   -.1911881
     kidsge6 |   .0108458   .0131829     0.82   0.411    -.0149922    .0366838
     huseduc |  -.0094389   .0012977    -7.27   0.000    -.0119824   -.0068955
------------------------------------------------------------------------------

. 
. * Could fill in the by hand calculation based on parameters. See
. * Wooldridge (2010, p. 586).
. 
. ivprobit inlf educ c.exper c.exper#c.exper age kidslt6 kidsge6 ///
>         (nwifeinc = huseduc), twostep
Checking reduced-form model...

Two-step probit with endogenous regressors        Number of obs   =        753
                                                  Wald chi2(7)    =     173.79
                                                  Prob > chi2     =     0.0000

---------------------------------------------------------------------------------
                |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
       nwifeinc |  -.0368641   .0186314    -1.98   0.048    -.0733809   -.0003472
           educ |   .1702153   .0384014     4.43   0.000     .0949499    .2454806
          exper |   .1163123   .0197084     5.90   0.000     .0776846      .15494
                |
c.exper#c.exper |  -.0019459   .0006129    -3.17   0.001    -.0031471   -.0007446
                |
            age |   -.044953    .010327    -4.35   0.000    -.0651936   -.0247125
        kidslt6 |  -.8444363   .1218529    -6.93   0.000    -1.083264    -.605609
        kidsge6 |   .0477905    .045177     1.06   0.290    -.0407549    .1363359
          _cons |   .0171187   .5498911     0.03   0.975    -1.060648    1.094885
---------------------------------------------------------------------------------
Instrumented:  nwifeinc
Instruments:   educ exper c.exper#c.exper age kidslt6 kidsge6 huseduc
---------------------------------------------------------------------------------
Wald test of exogeneity: chi2(1) = 1.99                   Prob > chi2 = 0.1584

.         
. * Unfortunately, the two-step option does not compute the APE.
. 
. * Do two-step by hand. Standard errors need to be corrected.
. * Putting both steps in a bootstrap routine is easy.
. * See Wooldridge (2010, top of page 589).
. 
. reg nwifeinc huseduc educ c.exper c.exper#c.exper age kidslt6 kidsge6

      Source |       SS           df       MS      Number of obs   =       753
-------------+----------------------------------   F(7, 745)       =     27.13
       Model |  20676.7705         7  2953.82436   Prob > F        =    0.0000
    Residual |  81120.3451       745  108.886369   R-squared       =    0.2031
-------------+----------------------------------   Adj R-squared   =    0.1956
       Total |  101797.116       752  135.368505   Root MSE        =    10.435

---------------------------------------------------------------------------------
       nwifeinc |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        huseduc |   1.178155   .1609449     7.32   0.000     .8621956    1.494115
           educ |   .6746951   .2136829     3.16   0.002     .2552029    1.094187
          exper |  -.3129877   .1382549    -2.26   0.024    -.5844034   -.0415721
                |
c.exper#c.exper |  -.0004776   .0045196    -0.11   0.916    -.0093501     .008395
                |
            age |   .3401521   .0597084     5.70   0.000     .2229354    .4573687
        kidslt6 |   .8262719   .8183785     1.01   0.313    -.7803305    2.432874
        kidsge6 |   .4355289   .3219888     1.35   0.177    -.1965845    1.067642
          _cons |  -14.72048   3.787326    -3.89   0.000    -22.15559   -7.285383
---------------------------------------------------------------------------------

. predict v2hat, resid

. probit inlf nwifeinc educ c.exper c.exper#c.exper age kidslt6 kidsge6 v2hat

Iteration 0:   log likelihood =  -514.8732  
Iteration 1:   log likelihood = -401.13728  
Iteration 2:   log likelihood = -400.30361  
Iteration 3:   log likelihood = -400.30301  
Iteration 4:   log likelihood = -400.30301  

Probit regression                               Number of obs     =        753
                                                LR chi2(8)        =     229.14
                                                Prob > chi2       =     0.0000
Log likelihood = -400.30301                     Pseudo R2         =     0.2225

---------------------------------------------------------------------------------
           inlf |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
       nwifeinc |  -.0368641   .0182706    -2.02   0.044    -.0726738   -.0010543
           educ |   .1702153   .0376718     4.52   0.000     .0963798    .2440507
          exper |   .1163123   .0193312     6.02   0.000     .0784239    .1542007
                |
c.exper#c.exper |  -.0019459   .0006009    -3.24   0.001    -.0031235   -.0007682
                |
            age |   -.044953   .0101367    -4.43   0.000    -.0648206   -.0250855
        kidslt6 |  -.8444363   .1198154    -7.05   0.000     -1.07927   -.6096025
        kidsge6 |   .0477905   .0443204     1.08   0.281    -.0390758    .1346568
          v2hat |   .0267093   .0189352     1.41   0.158    -.0104031    .0638217
          _cons |   .0171187   .5392914     0.03   0.975    -1.039873     1.07411
---------------------------------------------------------------------------------

. margins, dydx(nwifeinc)

Average marginal effects                        Number of obs     =        753
Model VCE    : OIM

Expression   : Pr(inlf), predict()
dy/dx w.r.t. : nwifeinc

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    nwifeinc |  -.0110576   .0054418    -2.03   0.042    -.0217234   -.0003918
------------------------------------------------------------------------------

[Enrique Pinzon (StataCorp)]

Dear Jeff and Joe,


Just for clarity, the predicted probability formula is correct. What Jeff
refers to is the computation of effects based on that formula.

Calculating average partial effects based on this probability formula gives a
statistic that does not have an average structural function interpretation,
because we are perturbing both observables and unobservables. What Jeff wants,
and is more useful to ask questions about counterfactuals, is to integrate over
the unobservables and then compute average partial effects.

You can get the predictions Jeff and Joe want using -eprobit-. We are working
on adding these predictions to -ivprobit-, it is in a beta version that is in
your code currently but not documented. -eprobit- gives you equivalent point
estimates to ivprobit but allows you more postestimation options. -margins-
after -eprobit- computes an average structural function and allows you other
options to handle the unobservable components. It also allows for multiple
endogenous equations with different instruments. Here is a simulated data
example of how to get the effects for the average structural function.

. clear

. set seed 123

. set obs 5000
number of observations (_N) was 0, now 5,000

. gen id  = _n

. mat cov = (1,-0.5\-0.5,4)

. drawnorm e1 e2, cov(cov)

. gen x1  = runiform()

. gen x2  = runiform()

. gen z1  = runiform()

. gen z2  = runiform()

. gen zb  = 1 + z1 + z2

. gen y2  = zb + e2

. gen xb  = -1.5 + x1 + x2 + 0.75*y2

. gen y1  = (xb + e1) > 0

. eprobit y1 x1 x2, endog(y2 = x1 x2 z1 z2)

Iteration 0:   log likelihood = -12274.567  
Iteration 1:   log likelihood = -12274.567  

Extended probit regression                      Number of obs     =      5,000
                                                Wald chi2(3)      =     592.69
Log likelihood = -12274.567                     Prob > chi2       =     0.0000

---------------------------------------------------------------------------------
                |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
y1              |
             x1 |   1.044111   .0887834    11.76   0.000     .8700984    1.218123
             x2 |   1.040255   .0890415    11.68   0.000     .8657372    1.214774
             y2 |   .7476604   .0497003    15.04   0.000     .6502497    .8450712
          _cons |  -1.525274   .1211866   -12.59   0.000    -1.762796   -1.287753
----------------+----------------------------------------------------------------
y2              |
             x1 |  -.0647558    .097615    -0.66   0.507    -.2560777    .1265662
             x2 |  -.1312252   .0986173    -1.33   0.183    -.3245114    .0620611
             z1 |   .8950109   .0980193     9.13   0.000     .7028967    1.087125
             z2 |    .857016   .0985302     8.70   0.000     .6639004    1.050132
          _cons |   1.213411   .1019993    11.90   0.000     1.013496    1.413326
----------------+----------------------------------------------------------------
       var(e.y2)|    3.98964   .0797928                      3.836274    4.149137
----------------+----------------------------------------------------------------
 corr(e.y2,e.y1)|  -.2022677   .1319464    -1.53   0.125    -.4420192    .0644564
---------------------------------------------------------------------------------

. margins, dydx(y2) predict(pr fix(y2))

Average marginal effects                        Number of obs     =      5,000
Model VCE    : OIM

Expression   : Pr(y1==1), predict(pr fix(y2))
dy/dx w.r.t. : y2

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          y2 |   .1371811   .0057121    24.02   0.000     .1259857    .1483766
------------------------------------------------------------------------------

This quantity has an average structural function interpretation. -margins- is
integrating over the distribution of the unobservable.

In the current version of -ivprobit- you would type:

. ivprobit y1 x1 x2 (y2 = z1 z2)

Fitting exogenous probit model

Iteration 0:   log likelihood = -2946.6422  
Iteration 1:   log likelihood = -1784.0064  
Iteration 2:   log likelihood = -1721.2204  
Iteration 3:   log likelihood = -1720.6217  
Iteration 4:   log likelihood = -1720.6216  

Fitting full model

Iteration 0:   log likelihood = -12274.568  
Iteration 1:   log likelihood = -12274.567  
Iteration 2:   log likelihood = -12274.567  

Probit model with endogenous regressors         Number of obs     =      5,000
                                                Wald chi2(3)      =     592.69
Log likelihood = -12274.567                     Prob > chi2       =     0.0000

---------------------------------------------------------------------------------
                |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
             y2 |   .7476604   .0497003    15.04   0.000     .6502496    .8450712
             x1 |   1.044111   .0887834    11.76   0.000     .8700984    1.218123
             x2 |   1.040255   .0890415    11.68   0.000     .8657372    1.214774
          _cons |  -1.525274   .1211866   -12.59   0.000    -1.762796   -1.287753
----------------+----------------------------------------------------------------
 corr(e.y2,e.y1)|  -.2022676   .1319464                     -.4420192    .0644565
        sd(e.y2)|   1.997408   .0199741                      1.958641    2.036943
---------------------------------------------------------------------------------
Instrumented:  y2
Instruments:   x1 x2 z1 z2
---------------------------------------------------------------------------------
Wald test of exogeneity (corr = 0): chi2(1) = 2.22        Prob > chi2 = 0.1360

. margins, dydx(y2) predict(pr fix(y2))

Average marginal effects                        Number of obs     =      5,000
Model VCE    : OIM

Expression   : Probability of positive outcome, predict(pr fix(y2))
dy/dx w.r.t. : y2

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          y2 |   .1371811   .0057121    24.02   0.000     .1259856    .1483766
------------------------------------------------------------------------------

The syntax for the estimation may change but the option is currently there.
Joe, thanks again for the data and inquiries. We are working in adding more
predictions to -ivprobit-. Thanks to Jeff too.

[Joe Brown]

Jeff and Enrique,
Thank you both for your very detailed responses on this thread. I've found them very helpful and I'm sure other Statalist-ers will too.

Best wishes,
Joe