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

 From Ricardo Henriquez <[email protected]> To [email protected] Subject RE: st: testing endogeneity in a two-equation model with censored andbinary dependent variables. Date Wed, 09 Jul 2003 11:30:11 -0400

```Prof. Schaffer:

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?......

Regards,

Ricardo Henr�quez
Chile

-----Mensaje original-----
De: [email protected]
[mailto:[email protected]]En nombre de Mark Schaffer
Enviado el: Mi�rcoles, 09 de Julio de 2003 9:29
Para: [email protected]
Asunto: Re: st: testing endogeneity in a two-equation model with
censored and binary dependent variables.

Ricardo,

>
> I am estimating the following two-equation model using a two-stage
procedure
>
> 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.

--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 Henr�quez
> Chile
>
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/

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
http://www.som.hw.ac.uk/cert

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/

*
*   For searches and help try:
*   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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