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# st: RE: Nonlinear GMM

 From "Brian P. Poi" To Subject st: RE: Nonlinear GMM Date Sat, 13 Nov 2010 11:55:32 -0500

```On Friday, November 12, 2010 2:51 PM McLaughlin, David wrote:

I was able to estimate the following equation in nl(), but replicating these
results using gmm() in Stata 11.1 has proved difficult.

y={b0}*(1-exp({gamma0}*x1)+{b1}*(1-exp({gamma0}*l1_x1)+{b2}*(1-exp({gamm
a0}*l2_x1)+{b3}*
(1-exp({gamma0}*l3_x1)+{alpha}*x2

Can the moment evaluator program version of gmm() estimate this nonlinear
function?

Note that: 1) it is nonlinear in the parameters; 2) there are more
parameters than covariates; 3) and the gamma0 parameter appears with x1 and
its lags (l1_x1, l2_x1 and l3_x1).

My goal is to replicate the results of the nl() estimation prior to using
gmm() to instrument for x1.
--------

You can use -gmm- to replicate the results of -nl-, and the help file for
-gmm- includes an example for the case of a probit model.  Notice that the
orthogonality conditions used in that example are based on the derivatives
of the regression function; you cannot just use the regressors in the model
as instruments.

-gmm- can easily estimate nonlinear models like yours assuming you have
valid instruments.  I think the confusion you are having arises from trying
to equate -gmm- as "-nl- with instruments."  That's not an accurate
comparison.  Davidson and MacKinnon's textbooks on econometrics (both the
1993 one and the newer one from 2005 or so) discuss nonlinear least-squares
and nonlinear instrumental variables in depth.

-- Brian Poi
-- brian@poiholdings.com

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```