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st: More about -ivpois- on SSC


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: More about -ivpois- on SSC
Date   Mon, 12 Nov 2007 15:32:12 -0500

Several interlocutors have asked about the availability of slides from
the Nov 2 talk by Bill Gould and David Drukker, which I intimated to
the list was the bee's knees, or at least a useful demonstration of
how easy it was to use Mata to program a new estimator.  I hope Bill
and David will post the slides from that talk on stata.com, since I
think it would provide a tremendous incentive for folks to buy Stata
10, but if they don't, I can write up a different version of that
demonstration and make it available.  I don't think I can simply scan
their handout and post it on the web, however.

Another correspondent observed that "one can set up the moment
conditions with an additive error or a multiplicative error (Mullahy,
1997)" and asked which version of the moment conditions were used.
The answer is the latter (more details below).  He also asked about
panel models (which are not available from -ivpois- but I agree would
be a good extension to pursue, though one can include dummy variables
to get a FE estimator) and about cluster-robust SEs.  Given that the
SEs are supplied by -bootstrap-, the cluster() option may be
specified. Here is a silly example:

ssc inst ivpois
sysuse auto, clear
g manuf=word(make,1)
ivpois mpg wei, exog(turn) endog(disp) cl(manuf)

On the moment conditions, the additive form posits that y=exp(xb)+u
and gives moment conditions of the form z(y-exp(xb))=0, whereas the
multiplicative form posits y=exp(xb)u and gives moment conditions of
the form z(y-exp(xb)/exp(xb)))=z(y*exp(-xb)-1))=0 for excluded
instruments z satisfying E(z'u)=0.  Angrist (2001) shows that in a
model with endogenous binary treatment and a binary instrument, the
latter procedure (assuming a multiplicative error) estimates a
proportional local average treatment effect (LATE) parameter in models
with no covariates.  The latter is also more intuitively appealing and
congruent with -poisson- and -glm-, and the assumption can be
rewritten y=exp(xb)u=exp(xb)*exp(v)=exp(xb+v) so ln(y)=xb+v if y!=0 to
provide the natural link to OLS.

Windmeijer (2006) has a very useful discussion and further models that
someone should implement in Mata.  Maybe me.

Angrist, Joshua D., 2001. "Estimation of limited dependent variable
models with dummy endogenous regressors: simple strategies for
empirical practice." Journal of Business and Economic Statistics, 19:
2-16.
Mullahy, John. 1997. "Instrumental-Variable Estimation of Count Data
Models: Applications to Models of Cigarette Smoking Behavior." The
Review of Economics and Statistics, 79(4): 586-593.
Windmeijer, Frank. 2006. "GMM for Panel Count Data Models." Discussion
Paper No. 06/591, Department of Economics, University of Bristol.
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