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st: selection model with endogenous regressor

From   sara borelli <[email protected]>
To   [email protected]
Subject   st: selection model with endogenous regressor
Date   Thu, 21 Aug 2008 16:55:47 +0000 (GMT)

Dear all,
I am trying to estimate a selection model with endogenous regressor.
Following Wooldridge(2002), I include the mills ratio in the reduced form of my endogenous variable. Suppose Y2 is my endogenous variable, then I estimate the following reduced form:

reg Y2 on X, Z, IMR

Where X are the exogenous regressors appearing in the system, Z my identifying instruments, and IMR the inverse mills ratio.
I would like to test whether my instruments are weak or not. Thus I was thinking to apply the rule of thumb that the first stage F-statistics on the identifying instruments (Z) is greater than 10 [Staiger and Stock (1997)]. However, I noticed that including or not the mills ratio in the reduced form crucially affects the result. I would like to know:
First, does anyone know if the standard approach of Staiger and Stock (1997) is appropriate in this context?
Second, the F-test has to be performed on a reduced form including or excluding the IMR? 

Thank you in advance for any help,
Sara Borelli

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