Ang. [Gretl-users] nonlinear IV (fwd)

[Riccardo (Jack) Lucchetti]

On Tue, 22 May 2007, Sven Schreiber wrote:

> Riccardo (Jack) Lucchetti schrieb:
> 
>> 
>>> svetosch at gmx.net @ INTERNET skrev 2007-05-22 13:12:59 :
> 
>>>> I'm interested in applying nonlinear instrumental variables, like in
>>>> section 7.6 of the Davidson/MacKinnon book.
>>>> 
>> 
>> I don't have the book with me atm. I suppose it can be done, but would I
>> be very mistaken in thinking that the gmm command already does what you
>> want?
> 
> No and yes; no you're not mistaken that one could use the gmm command,
> but yes you're mistaken that that's what I want :-) I was hoping to
> exploit the properties of the special case of nonlinear IV, and spare me
> some thinking about the correct formulation of orthogonality conditions.
> For example, in Eviews I believe it's possible to specify a nonlinear
> equation and a list of instruments and you're done. (I know that Eviews
> has a bad reputation with numerical optimization, that's one of the
> reasons why I'm looking for alternatives.)

Could you be more specific on this? I mean, suppose you want to estimate 
something like y_t = f(x_t, \theta) + \epsilon_t via NLIV. What you can do with 
GMM is write the orthogonality condition as y_t - f(x_t, \theta) and go from 
there.

A little example script follows, where I set up a simple example of NLIV 
estimation in a measurement error textbook situation:

#---- begin example script ----------------------------------

nulldata 100

set seed 23897

genr e = normal()*0.1
genr xstar = 3 + uniform()
genr x = xstar + e
genr y = sqrt(xstar) + normal() + e
genr z1 = xstar + normal()
genr z2 = xstar + normal()

scalar theta = 0.25
matrix W = I(2)
list Z = z1 z2

gmm
   series e = y - x^theta
   orthog e ; Z
   weights W
   params theta
end gmm --iterate

#---- end example script ------------------------------------

Is the problem you have at hand too hard to tackle via the above approach?


Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche

r.lucchetti at univpm.it
http://www.econ.univpm.it/lucchetti