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st: RE : 2SLS with quadratic RHS endogenous vars


From   "Olivier Paradis-Beland" <obeland@ecn.ulaval.ca>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE : 2SLS with quadratic RHS endogenous vars
Date   Fri, 28 Nov 2003 09:19:42 -0500

I don't think that stata can do it (I may be wrong though) buy your model could be easily estimated with SAS's nonlinear GMM procedure. Don't hesitate if you want more details.
 
Olivier Paradis Béland

	-------- Message d'origine-------- 
	De: Morris, Stephen [mailto:s.morris@imperial.ac.uk] 
	Date: ven. 2003-11-28 08:40 
	À: statalist@hsphsun2.harvard.edu 
	Cc: 
	Objet: st: 2SLS with quadratic RHS endogenous vars
	
	

	Hi,
	
	Does anyone know of a way to run a 2SLS model in Stata where the endogenous RHS variable would ideally appear in a quadratic form?
	
	I am using -ivreg2- to find the effect of an independent variable x on a dependent variable y, where I believe that x and y will be simultaneously determined. I have what I think are a set of non-weak, orthogonal instruments for x, namely z. So, the command I use is:
	
	ivreg2 y q (x = z)
	
	q is a set of exogenous variables also thought to influence y.
	
	I have reason to believe that the true impact of x on y is non-linear, and I would ideally like to estimate a model including x and x squared. Given that x is simultaneously determined with y I am not sure how to proceed.
	
	Option 1:
	
	One approach would be to run –ivreg2- as normal and instrument both x and x squared. That is, to run:
	
	ivreg2 y q (x xsquared = z)
	
	This produces a set of results, but the sign and magnitude of the coefficients on x and x squared are counterintuitive. I think this might be because unless my first stage model is able to predict perfectly x and x squared (which it is not) I will not actually be modelling a quadratic form (i.e. the predicted value of x squared from the first stage regressions does not equal the square of the predicted value of x).
	
	Option 2:
	
	So, the other thing I thought to do was to estimate the first stage equation for x and compute the linear prediction (call this xhat). Then square these predictions (call this xhatsquared) and use these to measure the effects of x squared in my second stage:
	
	reg y q xhat xhatsquared
	
	The results appear to be more sensible, but I am not sure if the approach is valid.
	
	Any thoughts on which option to use, if either, would be greatly appreciated. I am using Stata version 8.2. I have previously searched the FAQ and the Statalist archives, and the question I pose is similar to one posted by Jim Shaw on 18 July, but with respect to non-linear RHS endogenous variables rather than non-linear RHS exogenous variables.
	
	Thanks very much.
	
	Steve
	
	
	
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