Re: Ang. [Gretl-users] nonlinear IV (fwd)
On Tue, 22 May 2007, Sven Schreiber wrote:
Riccardo (Jack) Lucchetti schrieb:
>
>> svetosch(a)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(a)univpm.it
http://www.econ.univpm.it/lucchetti