# Re: st: IVreg and curvelinear effects

 From "Mark Schaffer" <[email protected]> To [email protected] Subject Re: st: IVreg and curvelinear effects Date Wed, 19 Jan 2005 11:09:14 -0000

```Christer,

To:             	[email protected]
From:           	[email protected]
Subject:        	st: IVreg and curvelinear effects
Date sent:      	Tue, 18 Jan 2005 19:35:39 +0100

>
> Hi listers,
>
> My substantive curvelinear regression equation is
>
> Y = a + b1(x1) + b2(x1*x1) + control1 + control2
>
> However, I'm pretty certain that x1 is endogenous and determined by
> the instruments z1 and z2. My intuition then tells me that x1*x1 must
> be endogenous too.

As Ricardo pointed out, just because x1 is correlated with the error
term doesn't mean that x1^2 is as well.  That is, E(x1*u) might be
nonzero, yet E(x1^2*u)=0.

> Hence my "manual" solution would be to:
>
> reg x z1 z2
> predict test
> gen testsq=test*test
> reg y test testsq control1 control2

Two problems here.  First, this isn't how you do IV "by hand",
because the first stage regression has to include *all* exogenous
regressors.  This comes up on the list a lot.  See the Stata FAQ on
this, http://www.stata.com/support/faqs/stat/ivreg.html.

Second, I think this is an example of what has been dubbed the
"forbidden regression".  Plugging fitted values in place of
endogenous variables into nonlinear functions to try to mimic 2SLS
won't give you consistent estimates of the coefficients.  See
Wooldridge's 2002 book, p. 235-36.

--Mark

>
> Two qustions:
> 1. Is my intuition/reasoning correct here?
> 2. Can this be done more automatically, so that I get correct standard
> errors (I assume they ar wrong in my manual solution)?
>
> Thanks in advance for any help.
>
> Best regards,
>
> Christer Thrane
>
>
>
>
> qustion: How do I perform the IVreg in this setting
>
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Prof. Mark E. Schaffer
Director
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS  UK
44-131-451-3494 direct
44-131-451-3296 fax