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

From   Richard Williams <>
Subject   Re: st: nbreg with fixed effect vs xtnbreg,fe
Date   Wed, 08 Feb 2012 00:33:27 -0500

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.

Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu

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