ivprobit: coefficient is negative but margin is positive?

[Joe Brown]

Hello,

I’m writing with a problem related to Stata’s ivprobit command and post estimation. Specifically, I’m wondering if it’s possible for a variable’s marginal effect on the predicted probability of a positive outcome to be positive, when the original probit coefficient was negative. It doesn’t make sense to me intuitively, but perhaps I am missing something.

Here is the output Stata is producing when I enter the commands (starting with the correlation of the endogenous X1 variable and the exogenous IV). If anyone can help me understand the peculiar results I’ll appreciate it very much.

Thank you!

corr endogenous_X1 IV

(obs=1,720)
| endogenous_X1 IV
-------------+------------------
endogenous_X11 | 1.0000
IV | -0.1427 1.0000


ivprobit Y (endogenous_X1=IV) X2 X3

Probit model with endogenous regressors Number of obs = 1,600
Wald chi2(3) = 246.81
Log likelihood = -1441.9858 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------------+----------------------------------------------------------------
endogenous_X1 | -1.366359 .3718464 -3.67 0.000 -2.095165 -.6375535
X2 | .2505178 .125386 2.00 0.046 .0047658 .4962699
X3 | .0004856 .0000747 6.50 0.000 .0003391 .000632
_cons | -.6382642 .335679 -1.90 0.057 -1.296183 .0196546
-----------------------+----------------------------------------------------------------
corr(e.endogenous_X1,e.Y)| .8369293 .0989804 .5103483 .9525369
sd(e.endogenous_X1)| .4395636 .0077705 .4245946 .4550603
-------------------------------------------------------------------------------------------
Instrumented: endogenous_X1
Instruments: X2 X3 IV
-------------------------------------------------------------------------------------------
Wald test of exogeneity (corr = 0): chi2(1) = 13.43 Prob > chi2 = 0.0002


margins, dydx(*) predict(pr)

Average marginal effects Number of obs = 1,600

Model VCE : OIM

Expression : Probability of positive outcome, predict(pr)

dy/dx w.r.t. : endogenous_X1 X2 X3 IV

-------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
--------------+--------------------------------------------------------------
endogenous_X1 | .1654096 .0574563 2.88 0.004 .0527973 .278022
X2 | .0767575 .021691 3.54 0.000 .0342439 .1192711
X3 | .0000598 .0000246 2.43 0.015 .0000116 .000108
IV | .055347 .0151233 3.66 0.000 .0257059 .0849881
-------------------------------------------------------------------------------

[Jordan Sydenham]

This "peculiar" result is likely because you have estimated the probit model using an instrumental variable (IV), but when you calculate marginal effects you include both endogenous_X1 and IV. In essence this means that you have first estimated one model and then have estimated a separate model (with both endogenous_X1 and IV.) only reporting the marginal effects of this latter model.

[Jeff Wooldridge]

Agree with Jordan. When properly computed, they must have the same sign.

[Joe Brown]

Thank you, Jordan and Jeff, for your responses.
My results are identical when using the following syntax to obtain margins only for the X variables (not the IV):

margins, dydx(endogenous_X1 X2 X3) predict(pr)

I have reproduced the results below and the sign of endogenous_X1 is still positive. Can you please tell me if I am still missing something?

(Thank you again for your time.)

Joe


Average marginal effects Number of obs = 1,600
Model VCE : OIM

Expression : Probability of positive outcome, predict(pr)
dy/dx w.r.t. : endogenous_X1 X2 X3

-------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
----------------------+----------------------------------------------------------------
endogenous_X1 | .1654096 .0574563 2.88 0.004 .0527973 .278022
X2 | .0767575 .021691 3.54 0.000 .0342439 .1192711
X3 | .0000598 .0000246 2.43 0.015 .0000116 .000108
-------------------------------------------------------------------------------

[Emily Carmichael]

Hi Joe, I'm having the exact same problem. Is this something you were able to resolve? Let me know how if so!

[Joe Brown]

Hi Emily,
Sorry I'm just seeing this now! I haven't found an answer to my question (although maybe there has been a new thread since this post). My solution was to use version control to force Stata to use the old version 14.0 margins command. This solved the problem with the sign of margin flipping. I do believe this is a bug in Stata itself, and I hope they will fix it in the next update to the software.

Best,
Joe