st: re: nonlinear constrained estimation: a clarification

[Kit Baum <baum@bc.edu>]

Francesco said

Y1=X1*b1+X2*b2+X3*b3
Y2=X1*t1+X2*t2+X3*t3

where X1 X2 and X3 are the same in both equations. I have to estimate  
these
two imposing the restriction t1/b1=t2/b2. I have the additional issue  
that
X3 (I have several variables in X3, so I was just using a more  
compact form)
is potentially correlated with the errors. How can I tackle the whole  
thing
imposing the restrictions and without having to specify other  
equations for
the endogenous variables in X3?


If you take the view that the correlation between X3 and one or more  
of the errors is not due to simultaneity, but rather due to some  
other cause (e.g. measurement error would do it) then what you need  
is FIML (full information maximum likelihood), or nonlinear three- 
stage least squares (NL3SLS). Stata does not have a canned routine  
for NL3SLS. You can implement FIML with the -ml- commands. That will  
permit you to deal with the parameter restrictions as well as  
providing an appropriate number of instruments to address the  
endogeneity of the X3 variables.

There is an extensive example of MLE used to fit a linear -sureg-  
system in section 12.7 of Gould et al. 3d ed.
http://ideas.repec.org/b/tsj/spbook/ml3.html
As linear 3SLS is merely -sureg- with 2SLS regressions rather than  
OLS regressions, the guidance they provide to fit -sureg- by FIML  
should be instructive for the problem where you want to substitute  
the 2SLS estimator for the OLS estimator usually employed in SUR.

Kit

Kit Baum, Boston College Economics and DIW Berlin
http://ideas.repec.org/e/pba1.html
An Introduction to Modern Econometrics Using Stata:
http://www.stata-press.com/books/imeus.html


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