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

[Austin Nichols <austinnichols@gmail.com>]

Monica Oviedo <monica.oviedo@uab.cat>:
The relevant code appears on slide 14 of 46 and is prefaced by the text:
*
How do we calculate the marginal effect of treatment after biprobit? Three
"obvious" approaches: use -margins-, use -predict- to get probabilities, or use
binormal() with predicted linear indices. The last is more correct, but all
should give essentially the same answer.
*
Evidently, the -margins- approach is the least correct.
If results differ, you should prefer the other approaches, but
read the references on interpretation of various ATE estimates.

Also, read the Statalist FAQ on not replying to an old thread to
initiate a new query.

I doubt -biprobit- will work well for the model with an endogenous interaction.
You have a single instrument z for two endogenous variables y2 and x*y2.

Instead of
biprobit (y1=x y2 xy2) (y2=x z)
try
ivreg2 y1 x (y2 xy2=z xz)
(ivreg2 is on SSC) and read the references on weak instruments
diagnostics in the -ivreg2- help file.

On Thu, Jun 14, 2012 at 6:45 AM, Monica Oviedo <monica.oviedo@uab.cat> wrote:
> 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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