> > If possible, how can I get the ceteris paribus effect of X on logint
> > (adjusted for logZ only) in the present context?
> Perhaps I misunderstand the problem, but this is what the coeff on X
> will tell you if you estimate using reg3 or ivreg.
To most social scientists, including a variable into a regression
means trying to explain something about the dependent variable in that
regression with the regressor. The auxiliary regression estimators
(such as instrumental variables regression, either for the mean or for
quantiles), one should not be taking the first stage regressions that
seriously and apply this concept of "explaining" or "controlling for"
or "mediating with", as including all of the exogeneous variables at
that first stage is the only way to mathematically ensure the
consistency of the estimates at the second stage. In other words, if
you were concerned with building a nice interpretable model for your Z
variable, then you would start thinking whether you want to include X
in that regression for the substantive reasons, i.e. whether there
really is any causal relation between the two. For the instrumental
variable regression, this is just how this method works: you must
include all the exogenous variables into the first stage regressions,
as Mark explained.
--
Stas Kolenikov
http://stas.kolenikov.name
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