# Re: st: Probit and Marginal Effects

 From May Boggess To statalist@hsphsun2.harvard.edu Subject Re: st: Probit and Marginal Effects Date 03 Mar 2004 08:09:48 -0600

```On Tueday, Kristi wrote:
>
> I have run into an unusual scenario, and was wondering if someone has an
> explanation.  Say that I run a probit estimate on
> the following:
>
> Gender = a + b1SIZE +b2AGE +b3DUMMY
>
> why would the dummy variable be significant in the probit estimate, but not
> in the marginal effects estimate?
>

It depends on the prediction function you specify in the command -mfx-:

clear
sysuse auto
gen dum=rep>3
probit for disp dum
mfx compute, predict(p)
mfx compute, predict(xb)

The default prediction option after -probit- is p, so if you didn't
specify the -predict- option on -mfx-, that is what it was using for
the prediction function. This is the same as my first -mfx- in my
example.

If you specify a different prediction function, you will get different
marginal effects (that is because marginal effects are the derivatives
of the prediction function). If you specify -xb- as the prediction
function, you should get the coefficient and standard errors of the
model back again (because the derivative of xb with respect to x is b).

So, my example shows that with one prediction function you can have a
signficant marginal effect and with another an insignficant marginal
effect.

For a more mathematical/numerical reason....
the standard error of the marginal effect is obtained by the delta
method, which means that the standard error for the marginal effect of
one independent variable involves the whole variance-covariance matrix
from the estimation together with the appropriate entries from the
Jacobian. In other words, there is a lot of stuff that goes into the
calculation beyond just the standard error of the coefficient of that
variable, and these other things can cause it to be greater than 0.05,
even when the coefficient standard error is less than 0.05.

--May
mboggess@stata.com

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```