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

[Shikha Sinha <shikha.sinha414@gmail.com>]

Another response from Statacorp;

Dear Shikha,

I just wanted to add to my previous response.  In the typical panel data
setting, you would generally want to use the conditional fixed effects model.
However, because you mention that you have cross sectional data, I cannot say
with certainty which model in best in your particular case.

Let me be a bit more specific about the incidental parameters problem.
Essentially, the argument is that in the typical panel data model, the number
of time periods per panel is assumed to be fixed.  To get asymptotic results,
we assume the sample size goes to infinity, and since T is fixed, that means
the number of panels is increasing.  As we increase the number of panels, we
increase the number of fixed effect parameters.  Hence, the number of
parameters in the model is growing with the sample size, so it is impossible
to get consistent estimates.  Moreover, because the model is nonlinear, the
estimated betas depend on the estimated fixed-effect parameters.  Since the
latter are inconsistent, so to are the betas.


If you are not working with panel data, you would need to decide whether a
similar problem arises in your case with the unconditional fixed effects
estimator.

Kristin
StataCorp

On Wed, Feb 8, 2012 at 10:22 AM, Brian P. Poi <bpoi@stata.com> wrote:
> Richard Williams wrote:
>>
>> At 12:50 AM 2/8/2012, Muhammad Anees wrote:
>>>
>>> Also the abstract in online from Guimarães, P (2008) is
>>>
>>> In this paper I show that the conditional fixed effects negative
>>> binomial model for count panel data does not control for individual
>>> fixed effects unless a very specific set of assumptions are met. I
>>> also propose a score test to verify whether these assumptions are met.
>>>
>>> The full reference for the paper is
>>> Guimarães, P., (2008), The fixed effects negative binomial model
>>> revisited, Economics Letters, 99, pp63­66
>>>
>>> It, thus, indicates to take care when to choose the fixed effects
>>> model while using Negative Binomial Regressions.
>>
>>
>> William Greene also has some working papers on this, e.g.
>>
>> http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1281928
>>
>> I can't say that I fully understand his arguments, but he says things like
>> "The difference between the HHG and true FE models is that HHG builds the
>> effects into the variance of the random variable, not the mean. Thus, we
>> cannot conclude that the HHG estimator is a consistent estimator of a model
>> that contains a heterogeneous mean...it is reasonable to conclude that the
>> HHG estimator is at least potentially problematic...In the HHG fixed effects
>> NB model, the fixed effects enter the model through the dispersion parameter
>> rather than the conditional mean function. This has the implication that
>> time invariant variables can coexist with the effects. This calls the
>> interpretation of the heterogeneity in the model into question."
>>
>> On the other hand he proposes some alternatives but notes that they have
>> problems too. At this point I am thinking the safest route is to make sure
>> you never study a problem that requires negative binomial regression with
>> fixed effects. ;-)
>>
>
> Recently Richard Williams mentioned research by Allison and Waterman (2002)
> indicated that the conditional fixed-effects negative binomial regression
> estimator due to Hall, Hausman, and Griliches (HHG, 1984) as implemented in
> Stata via the -xtnbreg, fe- command is not a true fixed-effects estimator.
>
> Allison and Waterman motivate their argument by considering an unconditional
> fixed-effects estimator in which a set of dummy variables representing the
> panels in the dataset are included in the regression specification.  HHG
> show that the variance of the dependent variable in their model is a
> function of the with the panel-level heterogeneity terms.  Allison and
> Waterman then argue that because the panel dummies and their coefficients do
> not play the same role as the other regressors and their coefficients in the
> HHG model, that model is not a true fixed-effects model.
>
> Whether one considers HHG's conditional estimator a "true" fixed-effects
> estimator really depends on how one defines a fixed-effects estimator.  If
> one thinks of fixed-effects estimators as extensions of pooled estimators
> with the inclusion of a set of dummy variables to allow for panel-specific
> constant terms, then Allison and Waterman's argument stands.  If, on the
> other hand, one thinks of fixed-effects estimators as estimators that allow
> for panel-level heterogeneity without making the strict exogeneity
> assumptions typically required for (more efficient) random-effects
> estimators, then HHG's estimator is a valid fixed-effects estimator.
>
> HHG's conditional fixed-effects estimator avoids the incidental parameters
> problem by conditioning the likelihood function for each panel by the sum of
> the counts for that panel.  That eliminates the panel-level heterogeneity
> terms from the likelihood; see, for example, the Methods and Formulas of
> [XT] xtnbreg.  With the panel-level heterogeneity term eliminated, we can
> use standard asymptotic theory with fixed T and N tending to infinity to
> establish that HHG's estimator is consistent.
>
> Allison and Waterman propose using a set of panel dummies to implement an
> unconditional fixed-effects estimator, and their simulation results suggest
> the estimator works well.  However, Greene (2007) claims that such an
> unconditional fixed-effects negative binomial estimator nevertheless does
> suffer from the incidental parameters problem.
>
>
>   -- Brian Poi             -- Gustavo Sanchez         -- Kristin MacDonald
>      bpoi@stata.com           gsanchez@stata.com
> kmacdonald@stata.com
>
>
> ----
> References
>
> Allison, P. D. and Waterman, R. P. (2002). Fixed-effects negative binomial
>     regression models.  Sociological Methodology, 32, 247--265.
>
> Greene, W. (2007). Fixed and random effects models for count data.  Working
>     paper, Department of Economics, Stern School of Business, New York
> University.
>
> Hausman, J., Hall, B. H., and Griliches, Z. (1984). Econometric models for
>     count data with an application to the patents-R&D relationship.
>     Econometrica, 52, 909--938.
>
>
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