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st: how to do endogeniety test with two suspect endogenous variables

To   statalist<>
Subject   st: how to do endogeniety test with two suspect endogenous variables
Date   Thu, 21 May 2009 23:25:45 +0800

Dear all,
I encountered a problem with endogeniety.Concretely, I have a equation below:
where z is exogenous definitely.However, I suspect whether x1 and x2 are endogenous.
and there are two instrument variables, z1 for x1 and z2 for x2.

In wooldridge book, there is an introduction about how to test whether one variable is endogenous.i.e,hausman test. First get the residual and then add the residual to the equation.If the p value of residual is significant, the suspect variable is endogenous.

However, how to test with two suspect endogenous variables? What confuses me is how to treat the other suspect endogenous variable when testing one endogenous variable.Treat it exogenous or endogenous? Because the treating mode has something to do with the residual computation for the tested variable. Take the above equation for example, maybe I can compute joint F statistic of the two residuals. If the p value of residuals is not significant, I can conclude both of x1 and x2 are exogenous. However, if the p value is significant, it shows that at least one of the two variables are endogenous. Then next what should I do? I want to judge the endogeniety for 
each of the two. Can I just take the residual of each of x1 and x2 for judgement? (I note the results are not equal to ivendog x1 or ivendog x2 in stata.)

By the way, in stata -ivendog- can give the result of endogenous test after -ivreg2- and -ivreg. 
I type ivreg2 y z (x1 x2=z1 z2 z);then type ivendog;
the result of the joint F statistic is equal to the "residual method" above in which I compute manually.
then type ivendog x1 or ivendog x2;
I get some results of p values for x1 or x2, but I do not know how stata get them, I can not get the statistics manually. 

could anyone tell me how to do endogeniety test with two suspect endogenous variables manually or by stata?

Hope sincerely replies. Thank you in advance.


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