Addressing omitted variable bias in count panel model

Hello dear forum members,

My study aims to address the question about physician ratings: Do they have an impact on the business value (as proxied with new patient referrals)? The sample is a panel of of U.S. oncologists (N=1,694) observed from 2009 to 2013. The outcome is a count, so for the over-dispersed (1.674) model, in the preliminary analysis I employed negative binomial regression with fixed effects (FE) (i.e., -xtnbreg y x1 x2 x3 x4 x5, fe-)

I used FE to (a) "control" for the unobserved variables, and (b) adjust for serial correlation. Yet, one of the co-authors insists (and I do not blame him) on a more robust way to address endogeneity. Particularly, the omitted variable bias, as there could be (unobserved) factors that cause high ratings and performance (e.g., quality related).

One of the considerable approaches (yet not without limitations following Clarke 2005), is to additionally collect data on a relevant variable (i.e., physician quality) and include it in the model as a control. However, even though I found a potential data source, the data are not without limitations -- only 2013 cross-sectional snapshot is available

Having said the above, I am seeking your advise on the suitable econometric techniques to address the endogeneity caused by omitted variables in a panel count model.

Thank you in advance for comments and suggestions.
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