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Re: st: What multiple regression model for extreme distributions


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: What multiple regression model for extreme distributions
Date   Wed, 3 Feb 2010 14:15:13 -0500

David Greenberg <dg4@nyu.edu>:
That Poisson regression is appropriate only for counts is a common
misconception.  So common that perhaps several more articles need to
written about it, though Wooldridge has pointed out the robustness
properties of the Poisson QMLE, and Mullahy has proselytized for
Poisson regression (see also work by Manning, and
http://www.nber.org/papers/t0246 leaving out the zero problem).

The Poisson assumption is merely E(y|X)=exp(Xb) or:
  ln E(y|X) = Xb
which is distinct from the OLS with lny assumption:
  E(lny|X) = Xb
with some distinct advantages, one of which is that the OLS assumption
makes no sense for an outcome y that can be zero, but the Poisson
assumption does.

No further assumptions about the error distribution need be made for
consistency of the Poisson QMLE.  However, if you specify a Tobit with
lny as the outcome variable, with y sometimes zero, a variety of
unpleasant assumptions must be made, and consistent estimates are
highly implausible.

On the other hand, the original poster claims that negative saving is
never observed, though it is certainly possible in reality, so perhaps
the zeros do represent censored observations rather than true zeros.
I suspect better use of existing data is the answer here, rather than
a different estimator, since many data sources include both red and
black ink on the balance sheet:
http://www.federalreserve.gov/PUBS/oss/oss2/scfindex.html

On Tue, Feb 2, 2010 at 8:09 PM, David Greenberg <dg4@nyu.edu> wrote:
> Poisson and negative binomial regressions, along with their zero-inflated versions, are models for counts, not for levels of a continuous variable. That makes me think their use for this problem is dubious. Something on the other of a Tobit might be more appropriate. David Greenberg, Sociology Department, New York University

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