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st: RE: -gmm- and incorporate offset/exposure variable?

From   "Brian P. Poi" <>
To   <>
Subject   st: RE: -gmm- and incorporate offset/exposure variable?
Date   Tue, 11 Jan 2011 18:48:25 -0500

-----Original Message-----
[] On Behalf Of David Ward
Sent: Tuesday, January 11, 2011 4:48 PM
Subject: st: -gmm- and incorporate offset/exposure variable?

The article by Brian Poi starting on page 6 of Stata News (Vol. 25(2)) at
contains an example on using -gmm- to estimate a Poisson model with

. webuse docvisits, clear
. gmm (docvis - exp({xb:private chronic female income}+{b0})),
instruments(private chronic female age black hispanic)

Is there an easy way to modify this to include an offset variable; that is,
a variable that is constrained to enter with a coefficient equal to 1.0?

Dave Ward



To include an offset variable, just include it in the moment equation with
an (implied) coefficient of one.  Here's an example that uses an exposure
variable from -help poisson-:

. webuse dollhill3, clear
. gen lnpyears = ln(pyears)
. poisson deaths smoke, offset(lnpyears) vce(robust)
. gmm (deaths - exp({b0} + {b1}*smokes + lnpyears)), instruments(smokes)

Notice there is no parameter on lnpyears in the -gmm- command; the
coefficient is by definition one.  Also, that variable is not included in
the list of instruments.  In this example, -gmm- doesn't even converge when
I do include lnpyears as an instrument, and I'm not sure whether it's a
valid instrument or not--I suppose it depends on your application.  The
standard errors differ by a factor of sqrt{N/(N-1)}, where N is sample size,
because -poisson- with the 'vce(robust)' option makes a small-sample
adjustment but -gmm- does not.

I didn't include an endogenous regressor in this example, but there's
nothing special about including an offset variable that stops you from doing

I hope this helps.

   -- Brian Poi

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