RE: st: binary endogenous interaction

["Gregory, Christian" <cgregory@ers.usda.gov>]

Hi Melissa,

Thanks for your suggestion. The issue is that there is no selection: we
observe y2 whether or not y1=1. Y1 is endogenous to y2 in the sense that
they are chosen simultaneously and likely chosen dependent on
unobservables. Bivariate logit/probit have been used when the
interaction term isn't present and isn't the quantity of interest. In
this application, I've used those models as first passes and they
produce interesting results; however, I'm not sure about how to account
for the endogeneity of the interaction. 

I have also estimated a simultaneous 3 equation ML model with a discrete
distribution of household unobservables, again with interesting results.
This approach, while interesting, does not seem standard--or, at least,
I haven't seen it anywhere else.

Thanks,
Christian

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Garrido,
Melissa
Sent: Thursday, April 21, 2011 10:56 AM
To: 'statalist@hsphsun2.harvard.edu'
Subject: Re: st: binary endogenous interaction

Hi Christian,
Have you considered a selection model such as -heckprob-  ?
y1 would be your selection equation dependent variable, and y2 would be
outcome equation dependent variable.
You could then explore the different margin options in [R] heckprob
postestimation to get the effect in which you are interested.

Hope this helps,
Melissa



>st: binary endogenous interaction
>
>From	  "Gregory, Christian" <cgregory@ers.usda.gov>
>To	  <statalist@hsphsun2.harvard.edu>
>Subject	  st: binary endogenous interaction
>Date	  Wed, 20 Apr 2011 10:35:26 -0400
> Hello Statalist,
>
>I have the following model.
>
>y1 = xb + e
>y2 = y1*b1 + c1*b2 + y1*c1*b12 + xb + e
>
>y1 and y2 are both binary. y1 is endogenous to y2. c1 is continuous and
>exogenous. The marginal effect of interest is the effect of y1*c1 in
the
>second equation. I do have instruments for y1. I'm wondering if (1)
>anyone knows of other applications in which the interaction of an
>endogenous dummy and exogenous continuous variable is the outcome of
>interest and (2) whether anyone has any intuition about a way to model
>this. (ML models with 2 or 3 equations work and give interesting
>results, but seem non-standard.)

>Thanks for your help.

>Christian

-------------------------------------------------------------------- 
Melissa Garrido, PhD 

Research Health Science Specialist 
GRECC/REAP, James J Peters VA Medical Center 
130 West Kingsbridge Road 
Bronx, NY 10468 
718-584-9000 x 3804 
melissa.garrido@va.gov 

Assistant Professor 
Brookdale Department of Geriatrics & Palliative Medicine 
Box 1070 
Mount Sinai School of Medicine 
One Gustave L. Levy Place 
New York, NY 10029 
melissa.garrido@mssm.edu 


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