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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


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

> 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 

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.


> 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
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
44-131-451-3485 CERT administrator

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