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st: ivendog - testing endogeneity of several regressors


From   Jennifer Beardsley <jenn_beardsley@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: ivendog - testing endogeneity of several regressors
Date   Wed, 15 Apr 2009 09:42:22 -0700 (PDT)

Dear List,

I have a quick question on the appropriate way to test the endogeneity of more than one regressors in an equation using ivendog. Suppose my model is 

Y = a + b1 X1 + b2 X2 + b3 X3 + e

and I suspect either X2 or X3 or both endogenous, and I want to instrument them with Z and W. Let's say that Z and W meet all of the requirements of instrument strength and validity (highly correlated with X2 and X3, not correlated with Y). There are a few ways I could test for endogeneity; below I present 3 of these ways, and would like to understand which is the appropriate way, and why:

ivreg2 Y X1 (X2 X3 = Z W)
ivendog X2 X3

or 

ivreg2 Y X1 (X2 X3 = Z W)
ivendog X2
ivendog X3

or 

ivreg2 Y X1 X2 (X3 = Z W)
ivendog X3
ivreg2 Y X1 X3 (X2 = Z W)
ivendog X2

In a sense, I am asking 1) what it means to test the endogeneity of both potentially endogenous vars together, versus testing one by one, and 2) whether in testing the endogeneity of one, I need to necessarily assume that the other is also endogenous. I would appreciate any insights!

Thanks,
Jennifer


      

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