# st: RE: re: nonlinear constrained estimation and "makecns"

 From "Francesco Mariotti" <[email protected]> To <[email protected]> Subject st: RE: re: nonlinear constrained estimation and "makecns" Date Mon, 28 Apr 2008 13:10:23 +0100

```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?

-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Kit Baum
Sent: 28 April 2008 12:36
To: [email protected]
Subject: st: re: nonlinear constrained estimation and "makecns"

fm514 said

I'm sorry, probably I just made things a bit uclear in the attempt of
simplifying my question too much. I just wanted to focus the attention on
those two equations. I am not sure I can use SUR since I am instrumenting X3
in the model.

Given the model

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

If you are 'instrumenting X3' then it is either (a) Y1 or Y2, or (b) you
have not written down the full simultaneous system. For X3 to be endogenous
in a simultaneous system, you must have an equation in which it appears on
the LHS.

Suggest you write down the full system which you are trying to estimate. It
may be that the suggested MLE approach (i.e. FIML) is the only way to
address this problem, if these equations are truly simultaneous and subject
to nonlinear constraints across equations.

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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