Mediation in panel FE Poisson model

[Daniela Kaiser]

Hello,

I´m working with a panel dataset, where each row corresponds to a county-week. I am modeling a fixed effects Poisson regression, with a categorical independent variable (4 types of treatment - type of school instruction on each week) and a count outcome (count of reports by week):


xtset county week

xtpoisson num_rpts_county i.instruction_county, exposure(population) vce(robust) fe


I would like to incorporate a count mediator but I'm not sure if it's possible to adapt the mediate command (for a count outcome and a count mediator) to a panel dataset and a fixed effects model. I found this sem discussion on mediation in panel data with a continuous outcome but I'm not sure whether/how this can be adapted to a count outcome.

Any insight/advice on this issue would be greatly appreciated!

[Clyde Schechter]

I have not worked with the -mediate- command very much. As far as I know, it will not accommodate fixed-effects models. However, if you have a large number of counties, you can do an unconditional fixed effects poisson analysis by simply adding i.county as a term in your -mediate- model equations. The usual objection to unconditional fixed effects models, the incidental parameters problem, is mitigated with large N of panels.

[Daniela Kaiser]

Thank you so much, Clyde Schechter! Do you know whether/how the mediate command can accommodate panel data?

[Clyde Schechter]

As I said in #2, it does not specifically handle panel data. There is no -xt- version of it. But incorporating i.panel_var into your models will produce unconditional Poisson regressions, which are acceptable provided the number of panels is large.

[Daniela Kaiser]

Thank you Clyde Schechter - just to make sure I understand your advice, you're suggesting I incorporate my panel variable ( i.county) in the mediate model equation and make no mention of the time variable, correct? I have approximately 700 counties.Thanks!

[Clyde Schechter]

I didn't actually comment on the time variable. You should handle it whatever way you would have if you could have done this modeling in -xtpoisson-.

With 700 counties you certainly have enough counties that an unconditional Poisson model is acceptable. The worry now, though, is that with 700 counties, you may exhaust the limits of matrix size in your version of Stata. I don't know exactly how that will work with -mediate-, so you'll just have to try it and see.

[Joao Santos Silva]

Dear Daniela Kaiser ,

Actually, in the Poisson case, the conditional and unconditional fixed effects estimators will give exactly the same result for any T and any N. The problem with the unconditional estimator is that, with small T, the estimates of the fixed effects will be noisy. Therefore, anything that depends on the fixed effects (e.g., predictions and partial effects) will be noisy, and therefore consistency requires T to go to infinity. Now, with weakly data, your T is likely to be large enough for you to trust the estimated fixed effects. I suspect this is what Clyde Schechter is trying to say.

Best wishes,

Joao