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

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Catherine,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Catherine Guirkinger
> Sent: 13 June 2006 01:35
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: LIML excluding exogenous variables from 
> "first stage"?
> 
> 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??

Since X2 is exogenous in the equation to be estimated, then the answer
is yes, by definition.

>  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.

ivreg and ivreg2 don't differ here; they both estimate standard
single-equation IV.  In both, the excluded instruments would be X2, Z
and X2*Z.  Excluding X2 from the first-stage regression is just like
going from a single-equation estimation framework to a system framework.
You can if you want to, and then you get the standard tradeoff of
efficiency vs. robustness.  As for weak instruments, going from 2->3
doesn't look like a dramatic increase, at least in this context.  The
literature on this focuses on problems caused by scores (or even
hundreds) of instruments.  You're a long way from there!

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


>  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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