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st: RE: GMM estimation: restricting parameter estimates


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: GMM estimation: restricting parameter estimates
Date   Wed, 5 Jun 2013 10:49:00 +0000

Markus,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
> statalist@hsphsun2.harvard.edu] On Behalf Of mibert@mail.uni-
> mannheim.de
> Sent: 29 May 2013 17:27
> To: statalist@hsphsun2.harvard.edu
> Subject: st: GMM estimation: restricting parameter estimates
> 
> Dear Statalist Community,
> 
> I have N moment conditions of the form E[m*R(i)]=0 where m=a+b*Rvw.
> Basically, it's a panel where i refers to firm i. Rvw is the return on a value-
> weighted portfolio. R(i) stores the returns for firm i's stock. The STATA code
> looks something like this:
> 
> #delimit ;
> 
> gmm (({a}+{b}*Rvw)*R1)
> (({a}+{b}*Rvw))*R2)
> (({a}+{b}*Rvw))*R3)
> , winitial(identity);
> 
> #delimit cr
> 
> a and b are the parameters which I would like to estimate. Now, what STATA
> does is it sets a=0 and b=0 and all N moment conditions are fullfilled.
> Obviously though, that is not the solution I am looking for.
> 
> Does anybody now how I can restrict the parameter estimates such that
> a!=0 and b!=0 ?

(Apologies to you and list if someone has already answered.)

You could try a variation on a trick that is sometimes used in code to restrict the range of parameter values.  Instead of estimating a and b you could estimate 1/a and 1/b.  Or some other function that prevents Stata (not "STATA" btw) from deciding on exact zeros as solutions.

For an example of how official Stata code does something similar, have a look at the manual entry for -heckman- and in particular the discussion of how rho is estimated.

HTH,
Mark

> 
> Thank you.
> 
> Markus
> 
> 
> 
> 
> 
> 
> 
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