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st: hurdle nb model marginal effects?


From   Brent Gibbons <brent.gibbons@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: hurdle nb model marginal effects?
Date   Mon, 18 Mar 2013 11:30:26 -0400

Dimitriy, thanks for reminding me about the fact that the hurdle-nb
model can be decomposed into a logit and a zero-truncated nb. To
explain my concerns, let me label the binary outcome of the logit by
B=1 if in fact the response is non-zero (and B=0 otherwise) and let me
label the continuous outcome of the truncated nb as Y.

The combined marginal effect of a continuous X variable on the
conditional expected value of the outcome is = d[E{(B|X)*(Y|X)}/dX.
(Consider "d" as the relevant symbol for the partial derivative. Sorry
I can't do the correct symbol in g-mail.)

The first problem is how do I compute this derivative if all I have
are d[E(B|X)]/dx and d[E(Y|X)]/dx?  Can independence of the
conditional expectations be assumed?

I assume that if this derivative can be computed, I would follow the
procedure used in the Stata "margins" command and just take the sample
average of this derivative. but this leads to the second question: how
should I compute the estimated variance of this sample average of
d[E{(B|X)*(Y|X)}/dX?

The third question arises when the X in question is a dummy variable
rather than continuous. How do I deal with the computation of the
average differential (rather than derivative) in dealing with marginal
effects of dummy variables?

Thanks for any suggestions.
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