KW,
Hausman, Hall and Griliches (1984) is often cited as having developed (what
has become) the conventional negative binomial model for panel data. Allison
and Waterman (2002) recently criticized Hausman et al.'s (1984) conditional
negative binomial fixed effects model as not being a "true" fixed effects
method in that it does not control for all time invariant covariates.
According to Allison and Waterman, HHG did not formulate a true fixed
effects model in the mean of the random (dependent) variable. Their
formulation layers the fixed effect into the heterogeneity portion of the
model and not the conditional mean. This portion is then conditioned out of
the distribution to produce the HHG model that is estimated. Allison and
Waterman (2002) developed an unconditional negative binomial model that uses
dummy variables to represent fixed effects, which effectively controls for
all stable individual effects. However, estimates of b are inconsistent in
negative binomial models when using such a dummy variable approach in short
panels due to the incidental parameters problem (Cameron & Trivedi, 1998:
282). Contrary to linear regression models, the maximum likelihood estimates
for ai and b are not independent for negative binomial models since the
inconsistency of the estimates of ai are transmitted into the MLE of b.
Given that this method is a true fixed effects specification it does not
allow for time-invariant covariates. The panel Poisson FE specification is a
standard fixed effects estimator and does not suffer from the incidental
parameters problem.
Allison, P. and R. P. Waterman. 002 "Fixed-effects negative binomial
regression models." Sociological Methodology, 32: 247-265.
Hausman, J. A. 1978 "Specification tests in econometrics." Econometrica,
46(6): 1251-1271.
I hope this helps.
Corey
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of KBW
> Sent: Friday, April 06, 2007 12:44 PM
> To: [email protected]
> Cc: [email protected]
> Subject: st: negative binomial models with large fixed effect
> group size
>
> Hi Statalist,
> 1) I am having trouble making sense of the best route to
> take regarding
> fixed effects and negative binomial regression. I have
> approximately 5,000
> individuals with an average of 10 observations each that I
> would like to
> obtain fixed effects estimates (within-individuals) for in a negative
> binomial regression. I've read the "xtnbreg, fe" does not perform a
> conventional individual fixed effects estimator, but that I
> can obtain what
> I am looking for by running nbreg with dummy variables for
> each individual
> and then correcting the standard errors afterwards. The
> problem is that it
> is challenging, if not realistically impossible, time-wise,
> to run these
> models with 5,000 dummy variables. Does anyone know of an
> alternative way
> to achieve this goal (in Stata, or even another package)?
>
> 2) In addition, if I were to run nbreg with dummy variables
> for the fixed
> effects, how does one interpret time-invariant independent
> variables in
> models? I realize that in theory time-invariant variables and fixed
> effects don't make sense, but in the few test models I have run (with
> smaller subsets of the dataset and using reg instead of
> nbreg) running
> "reg" with fixed effect dummy variables produces the same
> coefficients as
> "xtreg" for the time-variant variables, but "xtreg" drops the
> time-invariant one (expected) and "reg" does not. What, then, is the
> meaning of the "reg" output for time-invariant variables when
> individual
> dummies have been included in the model?
>
> Thanks very much for your assistance!
> KW
>
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