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
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
