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st: re: nonlinear constrained estimation: a clarification


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: re: nonlinear constrained estimation: a clarification
Date   Mon, 28 Apr 2008 13:20:02 -0400

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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