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Re: st: GMM with inequality and equality constraints


From   Stas Kolenikov <skolenik@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: GMM with inequality and equality constraints
Date   Thu, 15 Mar 2012 10:52:32 -0400

The first one looks like the regular GMM equation to me. The second
one is pretty much impossible to implement directly. You can introduce
a Lagrange multiplier in front of it:

E lambda[ gamma y_i + delta z_i ] = 0

You would probably run into identification problems and/or problems
with the standard errors: if the constraint is active, then gamma and
delta are not identified; if it is not, then lambda is identically
zero, and would have to have a missing standard error.

On Thu, Mar 15, 2012 at 10:40 AM, Marder, Andrew <amarder@hbs.edu> wrote:
> Dear statalisters,
>
> The generalized method of moments estimation in Stata is great!  It was wonderful how easy it is to estimate a nonlinear GMM model.  I am trying to replicate part of a paper that estimates a GMM model subject to equality and inequality constraints that look like:
>
> E[ alpha w_i + beta x_i ] = 0
> E[ gamma y_i + delta z_i ] >= 0
>
> How hard would it be to modify Stata's gmm function to accommodate constraints like these?
>
> Thanks, Andrew
>
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-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.

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