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Re: st: xtpoisson, fe marginal effects interpretation

From   maarten buis <>
Subject   Re: st: xtpoisson, fe marginal effects interpretation
Date   Wed, 4 May 2011 09:37:05 +0200

On Tue, May 3, 2011 at 7:52 PM, john sanders wrote:
> which should give the marginal effects under the assumption that the
> multiplicative fixed effect is equal to 1. This strikes me as a bit
> strange, as I am used to a linear model where the fixed effect is
> additive, essentially shifting the intercept, and where we would not
> think that a fixed effect equal to 0 (or log(1)) makes any a priori
> sense.

Actually, given the way Stata parameterized the fixed effects model an
additive fixed effects of 0 or a multiplicative effect of exp(0)=1 makes
perfect sense. There are roughly two ways of parameterizing fixed
either as separate constants for each higher level unit or as a combination
of one overall constant and deviations from that overall constant for each
higher level unit. In the former parameterization an additive fixed effect of
0 does not make sense, but Stata uses the latter parameterization, in
case a fixed effect of 0 means a person/firm/cow/lower level unit from an
average higher level unit.

Even though it makes sense there is still a complication. The current
flavor of the month concerning marginal effects is the average marginal
effect, that is we compute the marginal effect for every individual in your
dataset and report the average of these individual marginal effects.  This
is typically not the same the marginal effect for someone with average
values on the explanatory variables. So computing an average marginal
effect while fixing the fixed effect at its average value is a less than
pretty mixing of logics. However, I am too worried about that: A marginal
effect is a linear approximation of the non-linear regression line. If that
approximation is meaningful, i.e. the non-linear regression line is not too
non-linear, than the marginal effect at the average and the average
marginal effect won't differ enough to lead to substantively different
conclusions. The difference only starts to bite when the regression line
is very non-linear, but then the linear approximation implicit in the
marginal effect is too problematic anyhow. However, it this still makes
you worried than you can always report incidence rate ratios, i.e.
specify the -irr- option in your -xtpoisson- model. These are independent
of all other explanatory variables including the fixed effects, so that
solves the entire problem.

> The further issue is that I have no idea how to intepret the
> estimates. Are these counts or rates? Looking at the documentation (as
> well as Cameron and Trivedi's STATA book) would suggest they are
> counts (i.e. dy/dx = Beta*E(Y|x,controls,fixed effect)), but I always
> thought of Poisson estimates as being equivalent to rates.

A rate is an expected count per some time unit. My interpretation of this
is that the interpretation in terms of expected counts comes from applications
where the time unit is so fixed that it becomes trivial. Say we want to model
the number of kids a woman gets during her entire live, than we would get
a rate expected number of kids per live, but since we have only one live
(assuming there is no reincarnation) we can leave the time unit away and
are thus left with an expected count.

> Lastly, since each of these geographic units are of a different
> population size, I want my coefficient estimates to reflect this. In a
> linear probability world, I would simply use aweight, but this is not
> possible using xtpoisson, fe.

If I remember correctly this is what the exposure/offset are for. I have
never used them, so my memory is not complete on this point, but I do
remember that this changes the interpretation of your coefficients, but in
a way that made sense, i.e. it was a logical consequence of what you want
them to do. So, if you want to go that route I would look it up in some book
on count models to see all the details.

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen

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