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Re: st: marginal effects in biprobit and average treatment effect in switching probit


From   Monica Oviedo <monica.oviedo@uab.cat>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: marginal effects in biprobit and average treatment effect in switching probit
Date   Thu, 14 Jun 2012 03:45:09 -0700 (PDT)

Dear Statalist: 

 I'm estimating the effect of an endogenous dichotomous variable y2 on a
dichotomous variable y1 using a recursive biprobit model: 

biprobit (y1=x y2) (y2=x z) 

Where z is the exclusion restriction. I'm interested in the marginal effect
of y2 on y1, which I think is: 

E[y1/y2=1] - E[y1/y2=0]

I did what Austin Nichols suggested in this thread (namely, the conditional
prob of Y1=1 given y2=1 less the conditional probability of Y1=1 given y2=0,
letting y2=1 and y2=0 in turn for each observation, and then averaging over
observations). In addition, I followed the procedures sugested by him in
this file: 
http://www.stata.com/meeting/chicago11/materials/chi11_nichols.pdf

This is: 

margins, dydx(y2) predict(pmarg1) force

I think the latter is correct for estimating what I need. However, I get
very different results from both procedures (in the first case a marginal
effect of 0.08 vs a marginal effect of 0.45 using the second way). 

What is the difference between both procedures? Is it supposed that they
estimate the same effect?

A final question is if biprobit is well suited for estimate the following: 

biprobit (y1=x y2 x*y2) (y2=x z) 

This is, if  there is any problem when an interaction term between the
endogenous variable y2 and a continous x is added. 

Regards, 

Monica Oviedo






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