Bootstrapped vs Robust Standard Errors

[Maya Taylor]

Hi,

For my undergraduate dissertation I am conducting a study on panel data where my dependent variable is a count variable.

I believe my dependent variable to be overdispersed, and due to the nature of my study it could be the case that this overdispersion is not just "white noise" - it may be meaningful. This implies that a Negative Binomial model is better for my data than a Poisson model, and after checking AIC/BIC values, the negative binomial model has lower values than the Poisson indicating better fit.

I plan on including fixed effects using the ,fe option and I also want to include Robust standard errors to address heteroskedasticity. However, in Stata there is no option to include Robust standard errors (vce(robust)) for xtnbreg using fe, but there is an option for bootstrapping the errors. Therefore, I would like to know whether using bootstrapped errors addresses heteroskedasticity; is it the same/equivalent to using the vce(robust) option?

Should I do a Poisson regression with robust standard errors, or a Negative Binomial regression with bootstrapped standard errors? Both provide similar results in terms of significance and coefficients, I just want my methodology to be correct.

Any help or advice would be greatly appreciated, thank you

[Andrew Musau]

You should avoid FE NegBin. See #3 in the following link for an explanation: https://www.statalist.org/forums/for...-poisson-model

[Maya Taylor]

Hi Andrew, thank you for your reply. I understand the advice that FE NegBin should be avoided, however I see limited options when I believe my overdispersion could be related to something real, rather than just random/white noise. In this situation is it worth it to use FE NegBin as that addresses real overdispersion, or still continue with a Poisson? Thank you

[Andrew Musau]

Did you read the link in #2? This point is addressed.

c. The Poisson estimator allows any kind of variance-mean relationship. Some units can be overdispersed, some underdispersed. The same unit can exhibit both depending on the covariate values.

[Maya Taylor]

Hi Andrew, thank you for your response. It is my understanding that although the Poisson estimator can handle overdispersion, this is only the case when overdispersion comes from a random process or "white noise", rather than a non random process - i.e. it could be something meaningful driving the overdispersion. In this case a negative binomial estimator is preferred. Please correct me if this is not the case?

[Andrew Musau]

Poisson gives consistent coefficient estimates even under overdispersion, as long as the mean is correctly specified. If your claim is that conditional mean assumption is violated, is FE NegBin appropriate? That is unlikely the case, as outlined by the points covered in the link in #2, especially concerning points 1-3:

1. FE NegBin imposes a very specific overdispersion of the form (1 + c(i)) where the mean effect is c(i). Why this would ever be true is beyond me.
a. There's only one source of heterogeneity.

2. FE NegBin imposes conditional independence.
a. Serial correlation is not allowed.

3. FE NegBin is not known to be robust to failure of any of its assumptions.

In other words, there are very few universes in which one would reject FE Poisson in favor of FE NegBin. How do you arrive at the conclusion that Poisson’s conditional mean assumption is violated?