Say I am using a Cragg-type double hurdle model to estimate the
determinants of expenditures on food away from home.  I am interested
in differences between two subgroups - those who are food secure and
those who are food insecure.  I want to make a statement about whether
the effects of one variable (say, receipt of welfare) is different for
each group.  Can I run two
separate regressions for each group, then calculate whether the
difference between the coefficients is significant using a two-sample
t-test with the pooled standard errors, ignoring the rest of the
variables? If not, why not? [Why is very important] Will it produce
the same as running a model with all variables interacted with an
indicator for food secure  I'm reviewing a paper which took this
approach and I'm skeptical about it but not quite sure why.  I would
put both groups in one regression and use interacted terms on all
variables in the regression and use the coefficient on the interacted
term of interest.