margins after ivprobit in Stata 14

[Francisco Eslava Saenz]

Dear all,

I am currently estimating an instrumented probit model and trying to obtain the correct marginal effects -on probability- afterwards (i.e ivprobit followed by margins). Nevertheless, I am confused with the changes introduced with Stata 14 to the margins command when following the ivprobit estimation. In particular, I do not completely understand why does Stata report a marginal effect for the instrument (given that it is not a covariate) and how it should be interpreted. To illustrate my problem, I am posting the commands and results obtained using Stata's manual example under Stata 13 and 14:


version
version 13.1

webuse laborsup

ivprobit fem_work fem_educ kids (other_inc = male_educ)

Fitting exogenous probit model

Iteration 0: log likelihood = -344.63508
Iteration 1: log likelihood = -255.36855
Iteration 2: log likelihood = -255.31444
Iteration 3: log likelihood = -255.31444

Fitting full model

Iteration 0: log likelihood = -2371.4753
Iteration 1: log likelihood = -2369.3178
Iteration 2: log likelihood = -2368.2198
Iteration 3: log likelihood = -2368.2062
Iteration 4: log likelihood = -2368.2062

Probit model with endogenous regressors Number of obs = 500
Wald chi2(3) = 163.88
Log likelihood = -2368.2062 Prob > chi2 = 0.0000

------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
other_inc | -.0542756 .0060854 -8.92 0.000 -.0662027 -.0423485
fem_educ | .211111 .0268648 7.86 0.000 .1584569 .2637651
kids | -.1820929 .0478267 -3.81 0.000 -.2758316 -.0883543
_cons | .3672083 .4480724 0.82 0.412 -.5109975 1.245414
-------------+----------------------------------------------------------------
/athrho | .3907858 .1509443 2.59 0.010 .0949403 .6866313
/lnsigma | 2.813383 .0316228 88.97 0.000 2.751404 2.875363
-------------+----------------------------------------------------------------
rho | .3720374 .1300519 .0946561 .5958135
sigma | 16.66621 .5270318 15.66461 17.73186
------------------------------------------------------------------------------
Instrumented: other_inc
Instruments: fem_educ kids male_educ
------------------------------------------------------------------------------
Wald test of exogeneity (/athrho = 0): chi2(1) = 6.70 Prob > chi2 = 0.0096


margins, dydx(*) predict(pr)

Average marginal effects Number of obs = 500
Model VCE : OIM

Expression : Probability of positive outcome, predict(pr)
dy/dx w.r.t. : other_inc fem_educ kids male_educ

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
other_inc | -.014015 .0009836 -14.25 0.000 -.0159428 -.0120872
fem_educ | .0545129 .0066007 8.26 0.000 .0415758 .06745
kids | -.0470199 .0123397 -3.81 0.000 -.0712052 -.0228346
male_educ | 0 (omitted)
------------------------------------------------------------------------------


************************************************** ***************************
************************************************** ***************************
************************************************** ***************************

. version
version 14.2

. ivprobit fem_work fem_educ kids (other_inc = male_educ)

Fitting exogenous probit model

Iteration 0: log likelihood = -344.63508
Iteration 1: log likelihood = -252.10819
Iteration 2: log likelihood = -252.04529
Iteration 3: log likelihood = -252.04529

Fitting full model

Iteration 0: log likelihood = -2368.2142
Iteration 1: log likelihood = -2368.2062
Iteration 2: log likelihood = -2368.2062

Probit model with endogenous regressors Number of obs = 500
Wald chi2(3) = 163.88
Log likelihood = -2368.2062 Prob > chi2 = 0.0000

-----------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------+----------------------------------------------------------------
other_inc | -.0542756 .0060854 -8.92 0.000 -.0662028 -.042348
fem_educ | .211111 .0268648 7.86 0.000 .1584569 .2637651
kids | -.1820929 .0478267 -3.81 0.000 -.2758315 -.0883542
_cons | .3672086 .4480724 0.82 0.412 -.5109971 1.245414
------------------+----------------------------------------------------------------
corr(e.other_inc,|
e.fem_work)| .3720375 .1300518 .0946562 .5958136
sd(e.other_inc)| 16.66621 .5270318 15.66461 17.73186
-----------------------------------------------------------------------------------
Instrumented: other_inc
Instruments: fem_educ kids male_educ
-----------------------------------------------------------------------------------
Wald test of exogeneity (corr = 0): chi2(1) = 6.70 Prob > chi2 = 0.0096

. margins, dydx(*) predict(pr)

Average marginal effects Number of obs = 500
Model VCE : OIM

Expression : Probability of positive outcome, predict(pr)
dy/dx w.r.t. : other_inc fem_educ kids male_educ

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
other_inc | -.0097802 .0014994 -6.52 0.000 -.012719 -.0068414
fem_educ | .0623273 .007099 8.78 0.000 .0484135 .076241
kids | -.0614265 .0139446 -4.41 0.000 -.0887574 -.0340956
male_educ | -.0194406 .0022103 -8.80 0.000 -.0237728 -.0151084
------------------------------------------------------------------------------

************************************************** **************************
************************************************** **************************
************************************************** **************************

As noted above, the marginal effect for each dependent variable in the second-stage regression is different under each version (as expected), but when using Stata 14.2 an additional marginal effect is presented. The one corresponding to male_educ (the instrument). Note that this variable is "dropped" when using Stata 13.1 (actually, Stata doesnt take it into account given that it is not a second stage covariate).

I am familiar with related posts (such as the one linked below) and have already read Skeels and Taylor (2015). Nevertheless, although I understand the underlying change to the estimation procedure, still can't figure out the interpretation of these new results.

Any guess on how should this "new" effect should be interpreted?
Many thanks in advance,

Francisco

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

[Arthur Heim]

Hi,
I face the exact same situation and with my data, the results are very different (from .5*** to 0 basically). Moreover, while the former command (Stata 13) provided marginal effect (in probability) that were close to what you get using a 2SLS model, the new results are now 0.
I don't see the rational in computing marginal effet of the instrument on the outcome.

Did anyone figure what is going on and what estimation is the correct one ?

Thank you very much in advance.