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RE: st: 2SLS with nonlinear exogenous variables


From   Mark Schaffer <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu, "Shaw, Jim (NIH/NCI)" <shawjim@mail.nih.gov>
Subject   RE: st: 2SLS with nonlinear exogenous variables
Date   Fri, 18 Jul 2003 12:48:49 +0100 (BST)

Jim,

Quoting "Shaw, Jim (NIH/NCI)" <shawjim@mail.nih.gov>:

> Thanks for the response.  Yes, I mean to estimate the equations
> separately.
> My primary concern relates to discussions I have read (e.g.,
> Davidson and
> MacKinnon 1993, pp. 224--226) about the application of the IV
> procedure to
> nonlinear regression models.  My overall sense is that if the
> endogenous
> right-hand side variables are nonlinear (e.g., binary, squared),
> then 2SLS
> will be both inconsistent and inefficient.  In the example I
> provided in my
> previous e-mail, it was the exogenous variables that were nonlinear.
>  I was
> told that 2SLS will still be inefficient when one or more of the
> exogenous
> variables are nonlinear.

I think this is wrong.  There's no problem in particular when the equation 
is nonlinear in the exogenous variables.  (Aside from the usual ones, e.g., 
multicollinearity.)

>  However, I have been unable to find any
> literature
> that clearly discusses the issue.

Maybe have a look at Wooldridge's (2002) book on econometric analysis of 
cross-section and panel data - I know he has some discussion of issues 
relating to nonlinearity.

Cheers,
Mark

> 
> Thanks for the suggestion regarding ivreg2.  I will definitely look
> into it.
> 
> 
> --
> James Shaw
> Research Associate
> College of Pharmacy
> The University of Arizona
> 
> 
> -----Original Message-----
> From: Mark Schaffer [mailto:M.E.Schaffer@hw.ac.uk]
> Sent: Friday, July 18, 2003 5:13 AM
> To: statalist@hsphsun2.harvard.edu; Shaw, Jim (NIH/NCI)
> Cc: Mark Schaffer
> Subject: Re: st: 2SLS with nonlinear exogenous variables
> 
> 
> Jim,
> 
> Quoting "Shaw, Jim (NIH/NCI)" <shawjim@mail.nih.gov>:
> 
> > Dear Statalist:
> > 
> > Is 2SLS (as implemented by ivreg) still efficient if dummy
> variables
> > or
> > polynomials are included as exogenous variables/instruments? 
> For
> > example,
> > would 2SLS be efficient if applied to the following system of
> > equations:
> > 
> > y1 = y2 + x1 + x1^2 + x2 + e1
> > 
> > y2 = y1 + X1 + x3 + x4 + e2
> > 
> > where y1, y2, and x1-x3 are continuous variables, and x4 is a
> > binary variable.
> 
> I am not absolutely sure I understand what you mean here.  2SLS is a
> single-
> equation method of estimation.  Strictly speaking, if you want to
> apply it 
> to the example above, then your first question is whether 2SLS
> applied to 
> the y1 equation would be efficient in the class of of
> single-equation 
> estimates even if some of the exogenous variables were binary or 
> polynomials.  Your second question is the same question but
> regarding the 
> y2 equation.
> 
> Hopefully someone will correct me if I'm wrong, but my recollection
> is that 
> applied equation-by-equation, 2SLS is efficient in the class of
> single 
> equation estimators (assuming some other conditions hold - more on
> that 
> shortly).  You can get efficiency gains over 2SLS if you estimate
> your 
> system *as a system*, e.g., 3SLS or FIML.
> 
> >  I believe that 2SLS would yield consistent estimates in
> > the above
> > scenario.  However, if not efficient, then what method (Stata
> > command) would
> > one want to use?  I am dealing with repeated measures on
> subjects
> > (i.e., my
> > data are clustered)
> 
> Here is where you lose efficiency with 2SLS.  Clustering means you
> lose the 
> independence of observations assumption needed for efficiency. 
> -xtivreg- 
> is one alternative; another is our (me, Kit Baum, Steve Stillman)
> -ivreg2- 
> with the -cluster- and -gmm- options.  The former is an IV approach
> that 
> models the intra-group correlation as a "fixed effect" or "random
> effect"; 
> the latter is a GMM approach that allows for intra-group correlation
> of an 
> arbitrary form and is also robust to heteroskedasticity.
> 
> Hope this helps.
> 
> --Mark
> 
> >, so I would want to use a command that could
> > address
> > this concern.  Thanks.
> > 
> > --
> > James Shaw
> > Research Associate
> > College of Pharmacy
> > The University of Arizona
> > *
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> > 
> 
> 
> 
> Prof. Mark Schaffer
> Director, CERT
> Department of Economics
> School of Management & Languages
> Heriot-Watt University, Edinburgh EH14 4AS
> tel +44-131-451-3494 / fax +44-131-451-3008
> email: m.e.schaffer@hw.ac.uk
> web: http://www.sml.hw.ac.uk/ecomes
> ________________________________________________________________
> 
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Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3008
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes
________________________________________________________________

DISCLAIMER:

This e-mail and any files transmitted with it are confidential
and intended solely for the use of the individual or entity to
whom it is addressed.  If you are not the intended recipient
you are prohibited from using any of the information contained
in this e-mail.  In such a case, please destroy all copies in
your possession and notify the sender by reply e-mail.  Heriot
Watt University does not accept liability or responsibility
for changes made to this e-mail after it was sent, or for
viruses transmitted through this e-mail.  Opinions, comments,
conclusions and other information in this e-mail that do not
relate to the official business of Heriot Watt University are
not endorsed by it.
________________________________________________________________
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