Re: st: nbreg with fixed effect vs xtnbreg,fe

[Richard Williams <richardwilliams.ndu@gmail.com>]

At 08:52 PM 2/7/2012, Shikha Sinha wrote:
> Hi all,
>
> I emailed my query to tech support at Stata corp and below is the response;
>
>
> Typically for a fixed effects negative binomial model, you would want to use
> the -xtnbreg, fe- command.   -xtnbreg, fe- is fitting a conditional fixed
> effects model.  When you include panel dummies in -nbreg- command, you are
> fitting an unconditional fixed effects model.  For nonlinear models such as
> the negative binomial model, the unconditional fixed effects estimator
> produces inconsistent estimates.  This is caused by the incidental parameters
> problem.  See the following references for theoretical aspects on the
> incidental parameters problem:
>
>                Greene, William H. "Econometric Analysis". Prentice Hall.
>                Seventh Edition, page 413.
>
>                Baltagi, Badi "Econometric Analysis of Panel Data".
>                        4th. Edition. John Wiley and Sons LTD.
>                        Section 11.1 (pages 237-8).

Here is the abstract for the Allison & Waterman paper I mentioned before:

"This paper demonstrates that the conditional negative binomial model 
for panel data, proposed by Hausman, Hall, and Griliches (1984), is 
not a true fixed-effects method. This method which has been 
implemented in both Stata and LIMDEP-does not in fact control for all 
stable covariates. Three alternative methods are explored. A negative 
multinomial model yields the same estimator as the conditional 
Poisson estimator and hence does not provide any additional leverage 
for dealing with overdispersion. On the other hand, a simulation 
study yields good results from applying an unconditional negative 
binomial regression estimator with dummy variables to represent the 
fixed effects.
There is no evidence for any incidental parameters bias in the 
coefficients, and downward bias in the standard error estimates can 
be easily and effectively corrected using the deviance statistic. 
Finally, an approximate conditional method is found to perform at 
about the same level as the unconditional estimator."

And, from the conclusion:

"The negative binomial model of Hausman, Hall, and Griliches (1984) 
and its associated conditional likelihood estimator does not 
accomplish what is usually desired in a fixed-effects method, the 
control of all stable covariates. That is because the model is based 
on a regression decomposition of the overdispersion parameter rather 
than the usual regression decomposition of the mean. Symptomatic of 
the problem is that programs that implement the conditional estimator 
have no difficulty estimating an intercept or coefficients for 
time-invariant covariates."

The empirical examples Allison provides (p. 64 of his book), for 
which he says "None of this makes sense for a true fixed effects 
estimator" seem pretty compelling to me, but I remain open to 
persuasion or correction.

Allison, Paul D. and Richard Waterman (2002) "Fixed effects negative 
binomial regression models." In Ross M. Stolzenberg (ed.), 
Sociological Methodology 2002. Oxford: Basil Blackwell.

Also, Paul Allison, "Fixed effects regression models", Sage, 2009.




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Richard Williams, Notre Dame Dept of Sociology
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