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Re: st: RE: LIML excluding exogenous variables from "first stage"?


From   "Catherine Guirkinger" <catherin@primal.ucdavis.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: LIML excluding exogenous variables from "first stage"?
Date   Mon, 12 Jun 2006 17:35:16 -0700

Dear Mark,
 
Thank you very much for your quick answer. I have two
follow-up questions:
 
 I am estimating the following equation:
 Y= aX1 + bX2 + bT + cX2*T
 where T is an endogenous treatment, I have a set of 
 instrument Z that I use for T, so I can use X2*Z as an 
 instruments for X2*T.
 
 I follow your advice and use all the variables in X1 and X2
 in my "first stage" (although one of them is very much a 
 function of the treatment). Here are my question: 

 1) Is it also OK to use X2 in the first stage when one 
 regress X2*T on X2*Z and X1??
 2) What about using ivreg in that case? By default, ivreg 
 would also use X2*Z (along with Z and X2) in the 
 "instrumentalization" of T. Even if the "first stage" does 
 not have to be well specified, this procedure increases 
 dramatically my number of instruments and I am worried
about 
 having too many (weak) instruments.
 
 Thanks!
 Catherine

---- Original Message Follows -----
From: "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To: <statalist@hsphsun2.harvard.edu>
Subject: st: RE: LIML  excluding exogenous variables from
"first stage"?
Date: Tue, 13 Jun 2006 00:33:27 +0100

> Catherine,
> 
> > -----Original Message-----
> > From: owner-statalist@hsphsun2.harvard.edu 
> > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf
> > Of  Catherine Guirkinger
> > Sent: 12 June 2006 23:49
> > To: statalist@hsphsun2.harvard.edu
> > Subject: st: LIML excluding exogenous variables from
> > "first stage"? 
> > Hi!
> > 
> > I am estimating a linear model that contains endogenous 
> > regressors (due to omitted variable problems). I first 
> > applied a 2SLS procedure using a set of instruments but
> > my  instruments seem to be week (low F in the first
> > stage) and I  would like to estimate the same model with
> > Limited  Information Maximum Likelihood. 
> > My problem is the following: When I estimate the first
> > stage  of the 2SLS, I exclude some exogenous regressors
> > that are in  the main equation (I exclude them because
> > of problems of  reverse causality in the first stage)
> > and I am wondering  whether I can apply a LIML method
> > and NOT use all the  exogenous variables from the main
> > equation as explanatory  variables of the endogenous
> variables. 
> 
> This is a general IV issue that applies to 2SLS, LIML, GMM
> etc.  It also comes up on the list fairly regularly; see,
> e.g.,
> 
>
http://www.stata.com/statalist/archive/2005-11/msg00123.html
> 
> and the FAQ on the Stata website,
> 
> http://www.stata.com/support/faqs/stat/ivreg.html
> 
> Basically, you probably don't want to do it.  Reverse
> causality in the first stage is irrelevant to consistency
> of LIML (or 2SLS etc.).  These are single equation
> estimators, and the first-stage equation (which you are
> probably thinking of as a "second equation") does not have
> to be well-specified in the same way that the main
> equation does.
> 
> 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
> email: m.e.schaffer@hw.ac.uk
> web: http://www.sml.hw.ac.uk/ecomes
> 
> > I know that ivreg2 does not allow to do it, so I was
> > prepare  to compute the estimator "by hand" but when I
> > look at the  matrix algebra of computing the LIML (using
> > the formula  involving eigenvalue of a matrix of the
> > data), I wonder  whether it can be used when some
> > exogenous regressors are  excluded from the "first
> > stage" (the derivation of this  formula is very intense
> > in matrix algebra and quite obscure to me).  Does
> > anybody have an answer? Has anybody seen an application 
> of LIML where not all exogenous variables are used to
> > explain  the endogenous variables?
> > 
> > Thanks for your help!
> > 
> > Catherine
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> > 
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