margins after ivprobit: a bug?

[Lorenzo Rocco]

Dear all,
I suspect there is a bug in the command margins when used after ivprobit.
Or, perhaps, I've just missed something....
Anyway the problem occurs with Stata 14.1 and not with Stata 14...


Look at the following code:

clear
sysuse auto.dta

ivprobit foreign (weight = length) headroom price
predict xb,xb

margins, dydx(weight) predict(pr) atmeans

sum xb
display "Marginal effect : " _b[weight]*normalden(r(mean)) /* here I compute the marginal effect manually and I get a different marginal effect */



* Check on probit

dprobit foreign weight headroom price
predict xb2,xb
sum xb2
display "Marginal effect : " _b[weight]*normalden(r(mean)) /* note that I get the same marginal effects */


probit foreign weight headroom price
margins, dydx(weight) predict(pr) atmeans /* so it's here */


Any guess on what's wrong?
Many thanks in advance

Lorenzo

[Richard Williams]

If you use version control, you get the same results as in earlier Stata:

. version 13.1: margins, dydx(weight) predict(pr) atmeans

Conditional marginal effects                    Number of obs     =         74
Model VCE    : OIM

Expression   : Prob of positive outcome when rho=0, predict(pr)
dy/dx w.r.t. : weight
at           : weight          =    3019.459 (mean)
               headroom        =    2.993243 (mean)
               price           =    6165.257 (mean)
               length          =    187.9324 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      weight |  -.0003723   .0002152    -1.73   0.084    -.0007941    .0000495
------------------------------------------------------------------------------

Now, the question is, what is right and what is wrong? According to -help whatsnew-, the Oct 29, 2015 update did this:

7. predict with option pr after ivprobit has been improved to compute probability estimates that account for endogeneity. The old behavior is preserved under version control.

This means that the results of margins, estat classification, lroc, and lsens after ivprobit also have been improved to account for endogeneity.

So, I am guessing the current results are correct, but I am not sure how one "corrects for endogeneity" so I don't know how to confirm by hand.

[Richard Gates (StataCorp)]

Lorenzo,

In Stata 14.1 there was an improvement made to ivprobit postestimation predict, pr estimating the conditional probabilities of a positive outcome of the dependent variable. As recommended by Skeels and Taylor (2015) the computation now includes the instrumented variable equation in the computation. This is the definition of m_i in the Methods and formulas section of [R] ivprobit.

Listed below is your do code modified to include the computations that reproduce the 14.1 marginal effects.

sysuse auto.dta

ivprobit foreign (weight = length) headroom price
predict xb,xb

margins, dydx(weight) predict(pr) atmeans

version 14: margins, dydx(weight) predict(pr) atmeans

sum xb
display "Marginal effect : " _b[weight]*normalden(r(mean))

scalar rho = tanh([athrho2_1]_b[_cons])
scalar sigma = exp([lnsigma2]_b[_cons])

di rho
di sigma

mat b = e(b)
mat score double xp = b, eq(weight)
scalar rs = scalar(rho)/scalar(sigma)
scalar sr = sqrt(1-scalar(rho)^2)

gen double m = (xb+scalar(rs)*(weight-xp))/scalar(sr)
sum m

display "Marginal effect : " ///
    ((_b[weight]+scalar(rs))/scalar(sr))*normalden(r(mean))

I hope this helps.


References:
Skeels, C.L. and L.W. Taylor (2015) Prediction in linear index models with endogenous regressors, The Stata Journal (15), 627-644

[Lorenzo Rocco]

Thank you Richard & Richard for your quick and detailed answers. They fully answers my question
Best
Lorenzo

[Lutz Schneider]

Dear Richard (Gates), Dear all,

thank you very much for the code which is helpful to disentangle the difference between the margins command after ivprobit in the newer vs. older versions of Stata. In my case, I have a high negative correlation (rho in your code) between the residuals of the first stage and the structural equation. Consequently, the marginal effect "correcting for endogeneity" becomes considerably smaller in comparison to the simple marginal effect of the old Stata version (see code below, my Stata version 14.2).

. ivprobit xenophob (inequal = standard) age male, vce(robust) nolog
Probit model with endogenous regressors         Number of obs     =        939
                                                Wald chi2(3)      =      10.95
Log pseudolikelihood = -1412.8872               Prob > chi2       =     0.0120
--------------------------------------------------------------------------------------------
                           |               Robust
                           |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
                   inequal |    .774823   .3302386     2.35   0.019     .1275672    1.422079
                       age |   .0029153   .0024547     1.19   0.235    -.0018959    .0077264
                      male |   .1665353   .0805488     2.07   0.039     .0086625    .3244081
                     _cons |  -1.356366   .4690679    -2.89   0.004    -2.275722   -.4370099
---------------------------+----------------------------------------------------------------
 corr(e.inequal,e.xenophob)|  -.3913516   .1905433                     -.6933585    .0275976
              sd(e.inequal)|   .5517135    .017141                      .5191203    .5863532
--------------------------------------------------------------------------------------------

. margins, dydx(inequal) predict(pr)
------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     inequal |   .0278264   .1401031     0.20   0.843    -.2467705    .3024233
------------------------------------------------------------------------------

. version 14: margins, dydx(inequal) predict(pr)
------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     inequal |   .2795939   .1008357     2.77   0.006     .0819596    .4772282
------------------------------------------------------------------------------

My first question concerns the reason (intuition) of the correction: Is it that unobserved factors drive the endogenous regressor (inequal) as well as the dependent variable of the structural equation (xenophob) that are canceled out by the IV strategy? Does the correction try to take into account the effect of these unobserved factors? However, I guess, that a causal interpretation of marginal effects in a strict sense should ignore those unobserved factors. Am I right here?

A second question: Why the correction for endogeneity is implemented in the case of ivprobit but not in the ivreg command?

Many thanks in advance
Lutz