Fixed-Effects Negative Binomial Regression Models

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 over-dispersion. 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.