# RE: st: 2SLS with nonlinear exogenous variables

 From "Shaw, Jim (NIH/NCI)" To "Statalist (E-mail)" Subject RE: st: 2SLS with nonlinear exogenous variables Date Fri, 18 Jul 2003 07:08:00 -0400

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

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
> 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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```