And a second thought.... the comparison of coefficients across logit
equations can be tricky for reasons having nothing to do with getting the
right standard errors. Even if the dropped variables are uncorrelated
with the regressor that you are interested in, the value of the
coefficient for that regressor may change since there is no set variance
for the latent variable being mapped onto the observed dichotomy (and
identification is typically achieved by setting the error variance at 1 in
both equations...) So even if you in some sense reject the hypothesis
that a coefficient for a given variable is the same in two different
equations, it is tough to rule out the possibility that the coefficient
values might not be the same under alternative normalizations. Cameron
and Heckman 1998 hammer on this point from a slightly different angle, and
see the recent papers by Hauser and Mare in *Soc Meth 2006*
I have a couple of handouts that illustrate this issue:
