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Re: st: use -nlsur- to deal with nonlinear IV estimation?


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: use -nlsur- to deal with nonlinear IV estimation?
Date   Fri, 11 Jul 2008 12:01:11 -0400

Hau Chyi <hauchyi@gmail.com>:
I assume this is related to "The effects of single mothers' welfare
participation and work decisions on children's attainments" at
http://www.stata.com/meeting/snasug08/abstracts.html which cites
existing results (e.g. "children's number of years of schooling is
relatively unresponsive to mothers' work and welfare participation
choices"  --is this a statement about statistical significance or
substantive size of effect?).  What do those preliminary results look
like in an -esttab- table?  What are the instruments Z?

In general, it sounds like you have a regression of Y on X,W,E where
the two variables W and E might be endogenous, so you are using IV.
If you then interact W and E with some X, you have four endogenous
variables W and E and XW and XE, and you can still run IV.  But the
issues involved in running IV are likely much more important to your
interpretation of results than some weak endogeneity and some modest
nonlinearity or interactions; see Stata Journal 7(4) pp. 465-541.
http://www.stata-journal.com/article.html?article=st0030_3
http://www.stata-journal.com/article.html?article=st0136

On Fri, Jul 11, 2008 at 10:58 AM, Hau Chyi <hauchyi@gmail.com> wrote:
> Dear Stata users,
>
> I sent this email to the list but didn't see it showing up (I think
> the problem is beause gmail default setting is formatted). Allow me to
> try again.
>
> Bear me if this question is somewhat long.
>
> I have a model of a child's outcome (Y) which is determined by
> time-invariant exogenous charactersitics (X) and years of childhood
> welfare (W) and mother's work experiences (E):
>
>      Y = f(X) + gamma_1*W + gamma_2*E + gamma_3*f(X)*W +
> gamma_4*f(X)*E + epsilon,
>
> where f(X)=X'b is a linear combination of X. Since X is
> time-invariant, people in the literature typically use it as a measure
> of initial ability. In my model, marginal productivity of a mother's
> decisions depend on child's initial ability. So, for example, dY/dW =
> gamma_1 + gamma_3* f(X).
>
> Given that the mother's deicisions, W and E, may be correlated with
> her child's unobserved characteristics, I find a set of IV (Z) for W
> and E.
>
> The problem is this model is nonlinear in parameters (b, gamma). As a
> result, I can't use standard IV method. Given a (somewhat) detailed
> search, I realize Stata doesn't have a command for nonlinear IV
> estimation. So the first question is, does anyone know if Stata has
> one (I know from Stata archive that EViews has it).
>
> What I figure I can do in Stata is a 3-stage type of method, where I
> use -nlsur- to specify three equations: first one is the child's
> attainments equation; the other two are linear projections of W and E
> on (X and Z).
>
> I want to ask if a nonlinear 3-stage approach like this behave
> differently than typical 3-stage linear approach?
>
> Thanks a lot!
>
> Hau
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