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st: Instrument validity


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Instrument validity
Date   Fri, 21 Nov 2008 19:17:10 -0000

Not sure why this didn't go through the first time, so if at first you don't succeed....

-----Original Message-----
From: Schaffer, Mark E 
Sent: 21 November 2008 14:59
To: 'statalist@hsphsun2.harvard.edu'
Subject: RE: Instrument validity

Filipa,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Filipa Aragão
> Sent: 21 November 2008 12:27
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Instrument validity
> 
> Hello,
> In Stata list
> (http://www.stata.com/statalist/archive/2006-06/msg00461.html) I found
> the folling:  
> "Reverse causality in the first stage is irrelevant to consistency of
> LIML (or 2SLS etc.)."
> Does this mean the excluded instrument be correlated with the error in
> the first regression as long as it is not correlated with the error in
> the main equation (and is, of course, correlated with the endogenous
> variable)?

You mean, "Does this mean the excluded instrument CAN be correlated with the error in the first [stage] regression?"  The answer is yes.  The requirement of orthogonality applies only to the main equation.

This is because IV/2SLS and LIML are single-equation, "limited information" estimators.  The "first-stage" equation is an auxiliary step but isn't part of the model - there are no model parameters there.  If you want your first-stage equation to be interpreted as a model equation, then you are in the land of system estimation, 3SLS, FIML, etc., and you need to take a new set of baggage with you.

HTH.

Cheers,
Mark

Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University
Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
http://ideas.repec.org/e/psc51.html


>  
> I am doing an ivreg2 model and my excluded instrument does not reject
> the null in the orthog() test but if, on a side, I do a 
> Hausman test for
> its exogeneity in the first regression, I reject the null.
> Is the instrument valid anyway?
>  
> Any help would be most appreciated. Thank you.
>  
> 
> 
> 
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