----- Original Message -----
From: "Wendy Edelberg" <[email protected]>
To: <[email protected]>
Sent: Wednesday, May 21, 2003 10:43 AM
Subject: st: RE: testing exclusion restriction for selection model
> Hi stata users. I got no response from my initial posting -- but perhaps
> if I ask again... There must be a selection bias expert out there!
>
Isn't James Heckman at University of Chicago?
> Can anyone offer a test of my exclusion restrictions for a heckman
> selection
> model (beyond that theoretically they don't belong in the regression
> stage)? If I include them in the regression, aren't I committing the
> error of having Z=X and thus relying on the distributional assumptions
> to identify my model?
I don't believe it is an error, but just a weak assumption.
> It has been suggested that my excluded variables
> (in the probit) should not be correlated with the regressors in the
> linear regression, but this seems too stringent. I have more than one
> excluded variable, so I have been including them in small batches in the
> regression and doing an F-test on their coefficients.
> Any thoughts?
>
There is a very good Stata FAQ "What is the difference between 'endogeneity'
and 'sample selection bias'?" by Daniel Millimet at
http://www.stata.com/support/faqs/stat/bias.html
On the issue of identification, he writes:
"Because the IMR is a non-linear function of the variables included in the
first-stage probit model, call these Z, then the second-stage equation is
identified - because of this non-linearity - even if Z=X. However, the
non-linearity of the IMR arises from the assumption of normality in the
probit model. Since most researchers do not test or justify the use of the
normality assumption, it is highly questionable whether this assumption
should be used as the sole source of identification. Thus, it is advisable,
in my opinion, to have a variable in Z that is not also included in X. This
makes the source of identification clear (and debatable). "
Not that this directly answers your question, but you (or others) may find
it useful to look at Anne Sartori's paper "An Estimator for Some
Binary-Outcome Selection Models without Exclusion Restrictions" and Stata
software at http://www.princeton.edu/~asartori/
Abstract:
"This paper provides a new estimator for selection models with dichotomous
dependent
variables when identical factors affect the selection equation and the
equation of
interest. Such situations arise naturally in game-theoretic models where
selection is
typically nonrandom and identical explanatory variables influence all
decisions under
investigation. When its own identifying assumption is reasonable, the
estimator allows
the researcher to avoid the painful choice among identifying from functional
form alone
(using a Heckman-type estimator), adding a theoretically unjustified
variable to the
selection equation in a mistaken attempt to "boost" identification, or
giving upon estimation
entirely. The paper compares the small-sample properties of the estimator
with
those of the Heckman-type estimator and ordinary probit using Monte Carlo
methods.
A brief analysis of the causes of enduring rivalries and war, following
Lemke and Reed
(2001), demonstrates that the estimator affects the interpretation of real
data."
Hope some of this is helpful,
Scott
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