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st: Non-linear simultaneous equations


From   "Thomas Cornelissen" <cornelissen@mbox.iqw.uni-hannover.de>
To   "Statalist" <statalist@hsphsun2.harvard.edu>
Subject   st: Non-linear simultaneous equations
Date   Sun, 14 Nov 2004 18:09:16 +0100

Dear statalist,
I am trying to estimate non-linear (in variables and coefficients) simultaneous equations.
I want to estimate the following equations:

y1 = a0 + a1 x1 + a2 y2 + u1
y2 = b0 + b1 x2 - exp( -b2 x3 - b3 y1 ) + u2

where a0, ..., a2 and b0, ... b3 are the coefficients
and x1, ... x3 are exogenous variables
and y1, y2 are endogenous variables.
Cov(u1, u2) = s12 not equal to zero

The equation of interest is the second one. My questions are:

1.) Do 2SLS and 3SLS estimators have the same properties as when the equations where strictly linear?

2.) As to my knowledge there is no non-linear 2SLS or 3SLS estimation command in Stata, I intend to proceed manually:
First stage: Regress y1 on all exogenous variables by OLS.
Second stage: Replace y1 in the second equation by y1_hat from the first step and estimate the second equation by non-linear least squares (nl in stata). ==> 2SLS-estimates
Questions:
a) Are the standard errors from the second stage estimation usable for inference or do I need to transform them ? How ?
b) Is it possible to add a third stage (SUR) to obtain 3SLS estimates ? I can see how to compute the estimated covariance matrix of the error terms, but how would I use it in the non-linear estimation?

Thanks a lot for any help!
Thomas
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