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: 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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