I have panel data on several thousand individuals and I am trying to estimate a model to look at the effect of a variable x_i on an outcome y_i. There is definitely a reverse causality relationship occurring between these two variables, as well as time constant unobserved error terms affecting both. There are no plausible instruments in this data either.

I am aware of the Arellano Bond dynamic panel estimator which can help in correcting for reverse causality. However, my outcome variable is a count variable, I was wondering whether this sort of model can be applied in this case as I haven't been able to link up with the correct literature on this.

Any help is greatly appreciated! Thanks