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st: too small standard errors in Stata bivariate probit


From   David K Evans <dkevans@fas.harvard.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: too small standard errors in Stata bivariate probit
Date   Mon, 11 Oct 2004 13:14:32 -0400 (EDT)

Hi all,

I'm estimating an equation with a binary outcome and a binary endogenous
regressor. Wooldridge (2002) recommends bivariate probit for this.
Although regular IV often works in these cases, my endogenous regressor is
quite uncommon (only occurs in 1.5% of the population), so we may be
seeing a tail phenomenon.

Specifically, I'm estimating the impact of "having an orphan in your
household" on the school enrollment of non-orphans in the household,
instrumenting for having an orphan in the household.

When I run regular IV, I get a coefficient of -0.133 (s.e. 0.372). So,
kids with orphans are 13.3% less likely to be in school.

But when I run bivariate probit, the marginal effect (at the means of the
regressors) is -0.002 (s.e. 0.002).

Because of the tail phenomenon, I'm not surprised that the coefficient is
different. But the STANDARD ERROR ON THE BIVARIATE PROBIT MARGINAL EFFECT
IS 1/90th THE SIZE OF THE IV MARGINAL EFFECT. This increase in efficiency
seems implausible (i.e. "too efficient to be true").

Any ideas on what could be going on here?
Thanks so much,
Dave

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PhD student, Harvard Economics Department
Phone: (O) 617-495-5634, (H) 617 - 493 - 1536
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