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st: margins for endogenous regressor following recursive biprobit


From   David Quinn <dxquinnx@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: margins for endogenous regressor following recursive biprobit
Date   Mon, 19 Nov 2012 14:19:46 -0500

Hello,

I am estimating a recursive biprobit model with endogenous regressor,
Y2, as such:

Y1 = X1 + X2 + Y2
Y2 = X1 + X3 + X4

I want to calculate the marginal effect of Y2 on Y1.  I know that when
an X variable appears in both equations of a recursive biprobit--such
as X1 in my example--the overall effect of that variable on the
outcome Y1 is the sum of its direct and indirect effects on Y1, the
indirect effect consisting of its direct effect on Y2.  And I also
know that the effect of any variable that is unique to one of the
equations in a biprobit--such as X2 (or X3 or X4) in my example--is
simply the direct effect of that variable on whichever of the two
outcomes that it is supposed to be predicting, the endogenous
regressor (Y2) or the non-endogenous outcome of concern (Y1).

But I am wondering if there is a special formula required to calculate
the marginal effect of the endogenous regressor (Y2) on the outcome of
concern (Y1), since the model is recursive?  Does one have to account
for the intercept of the Y2 equation in a particular manner, or
something of the sort, when making this calculation since Y2 is
endogenous?  If so or if not, does Stata's -margins- command
automatically account for this, or is there some special command or
set of commands that I must instruct Stata to execute in order to make
the proper calculation?

Thank you in advance for any insight on the topic,
--David
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