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RE: st: testing endogeneity in a two-equation model with censored and binary dependent variables.


From   "Mark Schaffer" <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   RE: st: testing endogeneity in a two-equation model with censored and binary dependent variables.
Date   Wed, 9 Jul 2003 16:49:45 +0100

Ricardo,

Date sent:      	Wed, 09 Jul 2003 11:30:11 -0400
From:           	Ricardo Henriquez <rhenriquez@sii.cl>
Subject:        	RE: st: testing endogeneity in a two-equation model with censored and
	binary dependent variables.
To:             	statalist@hsphsun2.harvard.edu
Send reply to:  	statalist@hsphsun2.harvard.edu

> Prof. Schaffer:
> 
> 1. Thanks for your suggestions.
> 
> 2 With respect to your comment: "This last statement confuses me. The
> standard DWH test of endogeneity is used when estimating a single equation
> using instrumental variables. The endogeneity relates to one or more
> regressors in this single equation. These regressors can be binary -it
> doesn't matter for either the IV estimation or the DWH test."
> 
> Ronna Cong, from Stata Corporation, wrote an excelent response to the
> questions: "How to test endogeneity?",  "How do I perform a
> Durbin-Wu-Hausman test?" (see the FAQs under endogeneity).
> In her response she uses as an example a simultaneous two-equation model and
> utilises regression analysis (regress), indicating, indirectly, that the two
> dependent variables are continuous. However, you cannot use the procedure
> suggested by Ronna Cong when one of the the dependent variables (in my case
> the endogenous)is binary. In other words, it seems to me that does matter
> what type of variables your are considering. Am I wrong?......

Yes and no, or not necessarily. :)

If you want to do a test of endogeneity in the context of estimating 
the *entire system* of equations, then you are right.  In other 
words, one option is to an endogeneity test in the context of 
estimating your 2-equation system.  Since you would be explicitly 
estimating not only your Y1 equation but also your Y2 equation, and 
Y2 is a binary variable, you would need to get the functional form 
for Y2 right.

On the other hand, you can do a test of endogeneity in the context of 
a *single-equation estimation*.  In your case, you could explicitly 
estimate only the Y1 equation using, say, -ivtobit-.  Since you're 
not estimating the Y2 equation, you don't have to worry about whether 
or not you get the functional form for Y2 right.

--Mark

> 
> Regards,
> 
> 
> Ricardo Henríquez
> Chile
> 
> 
> 
> -----Mensaje original-----
> De: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu]En nombre de Mark Schaffer
> Enviado el: Miércoles, 09 de Julio de 2003 9:29
> Para: statalist@hsphsun2.harvard.edu
> Asunto: Re: st: testing endogeneity in a two-equation model with
> censored and binary dependent variables.
> 
> 
> Ricardo,
> 
> > Dear Statalist readers,
> >
> > I am estimating the following two-equation model using a two-stage
> procedure
> > suggested by Maddala (1983):
> >
> > Y1 = a1X1 + B1Y2 + e1
> >
> > Y2*= a2X2 + e2
> >
> > where Y2=1 if Y2*>0
> > 	Y2=0 otherwise
> >
> > Y1 is censored at zero and Y2 is binary (the realised value of the latent
> > variable
> > Y2*). Since Y2 is assumed to be endogenous, I would like to test the
> > endogeneity of Y2. I checked the Durbin-Wu-Hausman test but it is not
> > appropriate when one of the dependent variable is binary.
> 
> This last statement confuses me.  The standard DWH test of
> endogeneity is used when estimating a single equation using
> instrumental variables.  The endogeneity relates to one or more
> regressors in this single equation.  These regressors can be binary -
> it doesn't matter for either the IV estimation or the DWH test.
> 
> If I understand correctly, you can't use the DWH test for a different
> reason - Y1 is censored and you can't us straightforward IV to
> estimate the Y1 equation.
> 
> Would the following work?
> 
> 1. Estimate the Y1 equation using Joe Harkness' -ivtobit-, i.e.,
> treat Y2 as endogenous.  This is your efficient but possibly
> inconsistent estimator.
> 
> 2. Estimate the Y1 equation using -tobit-, i.e., treat Y2 as
> exogenous.  This is your inefficient but consistent estimator.
> 
> 3. Use -hausman- to perform a Hausman test.  It should be distributed
> as chi-squared with 1 degree of freedom (because you are testing 1
> variable for endogeneity).  The output of -hausman- may suggest that
> there are 2 degrees of freedom (because -hausman- tries to be clever
> in working out the df and occasionally doesn't get it right), but
> df=1.
> 
> Comments, anybody?
> 
> --Mark
> 
> > Thus, does anyone
> > know if there is an alternative way to test for endogeniety in such a
> > models.
> >
> > Any help will be much appreciated.
> >
> >
> > Ricardo Henríquez
> > Chile
> >
> > *
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> 
> 
> Prof. Mark E. Schaffer
> Director
> Centre for Economic Reform and Transformation
> Department of Economics
> School of Management & Languages
> Heriot-Watt University, Edinburgh EH14 4AS  UK
> 44-131-451-3494 direct
> 44-131-451-3008 fax
> 44-131-451-3485 CERT administrator
> http://www.som.hw.ac.uk/cert
> 
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> 
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Prof. Mark E. Schaffer
Director
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS  UK
44-131-451-3494 direct
44-131-451-3008 fax
44-131-451-3485 CERT administrator
http://www.som.hw.ac.uk/cert

*
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*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/



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