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" <[email protected]>
To: <[email protected]>
Subject: st: RE: LIML excluding exogenous variables from
"first stage"?
Date: Tue, 13 Jun 2006 00:33:27 +0100
> Catherine,
>
> > -----Original Message-----
> > From: [email protected]
> > [mailto:[email protected]] On Behalf
> > Of Catherine Guirkinger
> > Sent: 12 June 2006 23:49
> > To: [email protected]
> > 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: [email protected]
> 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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> > * http://www.stata.com/support/statalist/faq
> > * http://www.ats.ucla.edu/stat/stata/
> >
> >
>
> *
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*
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