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st: 2SLS with quadratic RHS endogenous vars


From   "Morris, Stephen" <s.morris@imperial.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: 2SLS with quadratic RHS endogenous vars
Date   Fri, 28 Nov 2003 13:40:02 -0000

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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