Fixed-effects Poisson with robust standard errors

[Eran Itskovich]

Dear all,

I'm working on a project in which I run a fixed-effects Poisson regression with dummy variables for panel and time:

poisson dep_var indep_var i.panel i.time

1. I have read that one should use robust standad error when running a fixed-effects linear regression model. Does it also applies to fixed-effects poisson?

2. In a fixed-effects poisson using dummy variables (and not -xtpoisson, fe-), should I also use clustered standard errors (using -vce(cluster panel)-)? if so, can I run both cluster and robust standard errors in the same command?

Thanks!
Eran

[Joao Santos Silva]

I am not sure if I fully understand your questions, but in short you should always cluster your standard errors when estimating Poisson regression with a panel.

[Jeff Wooldridge]

As Joao said, with xtproisson, fe you should always use vce(robust). This is the same as what vce(cluster id) would accomplish (where id is in "xtset id year") but unfortunately Stata doesn't have a cluster option with xtpoisson (which would be very useful for clustering at a higher level).

If you implement Poisson FE by using the pooled command as above, you must be careful in using vce(robust) rather than vce(cluster id). Now these two are not the same, as vce(robust) does not account for serial correlation. In the linear case, we know doing vce(robust) after the dummy variable regression does not produce proper standard errors (unless T is "large"). I haven't tried but I wouldn't be surprised if using vce(cluster id) with poisson i.panel i.time provides proper standard errors for the betas; not for the i.panel coefficients. But then you should just use xtpoisson, fe vce(robust), anyway.

The bottom line is you should use xtpoisson, fe vce(robust) unless you can point to a source that justifies using poisson i.panel i.time, vce(robust). I know of none and I doubt it generally exists. Plus, these would not be robust to serial correlation. You can also use the user written command ppmlhdfe (which I haven't used).