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

 From "Mark Schaffer" 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 14:29:05 +0100

```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 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