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Re: st: testing endogeneity in a two-equation model with censored and binary dependent variables.
> 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
> 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
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
> Thus, does anyone
> know if there is an alternative way to test for endogeniety in such a
> Any help will be much appreciated.
> Ricardo Henríquez
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Prof. Mark E. Schaffer
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS UK
44-131-451-3485 CERT administrator
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