Addressing endogeneity in panel count model

[Anton Ivanov]

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.

[Jorge Eduardo Perez Perez]

From a quick read about panel data count models, it appears that fixed effects in a negative binomial model are not analogous to traditional fixed effects as in the linear panel data model. Did you consider this?

[Anton Ivanov]

From a quick read about panel data count models, it appears that fixed effects in a negative binomial model are not analogous to traditional fixed effects as in the linear panel data model. Did you consider this?

Thank you for reply, Jorge.

I developed the model for preliminary estimation based on papers by Allison and Waterman (2002), Williams (2015), Koop (2008), Sacheti et al. (2015), and some others. So, I do not see a flaw in my reasoning for using FE.

So, I understand that the above is not without its limitations, and thus explore other suitable techniques.

[Joao Santos Silva]

Dear Anton,

Apart from echoing Jorge's concerns about using FE in negbin regression, I would like to point out that you can address the endogeneity problem using instrumental variables; have a look at -ivpoisson-.

Joao

[Anton Ivanov]

Dear Anton,

Apart from echoing Jorge's concerns about using FE in negbin regression, I would like to point out that you can address the endogeneity problem using instrumental variables; have a look at -ivpoisson-.

Joao

Joao, I appreciate your suggestion on the -ivpoisson-. Surely, will explore.

Also, I realize Jorge's and your concerns on FE are indeed true and must be addressed.

Thank you for the comments!

[Jeff Wooldridge]

I just gave a talk at the International Panel Data Meetings in Budapest. Attached are the slides. Ideally you can account for unobserved heterogeneity and, in addition, find time-varying instruments. And you should use the FE Poisson estimator. In my view, it's not even debatable because FE Poisson is fully robust. My suggestion, which starts on slide 25, is to add the fixed effects residuals obtained in the first stage to the FE Poisson estimation in the second stage. If you have time-varying IVs you at least get a test, and even a valid correction under certain assumptions. This is stuff I've been working on but have not yet written a complete paper. JW

[Anton Ivanov]

Additional exploration of the topic reveals a number of methods suitable to control for endogeneity (e.g., RDD, DID, ME, LIV, Copula). Yet, they require transformation of the count outcome (as in my case) into a continuous variable (e.g., ln, sqrt, or inverse sine).

Does such transformation (and consequently methods mentioned) sound appropriate for count non-negative outocmes?

[Joao Santos Silva]

Dear Anton,

The transformations you mention will not make your variable continuous and can create other big problems. In general, it is not advisable to transform the variable of interest.

All the best,

Joao

[Anton Ivanov]

Dear Anton,

The transformations you mention will not make your variable continuous and can create other big problems. In general, it is not advisable to transform the variable of interest.

All the best,

Joao

Thank you for reply, Joao.

I agree with you completely. So, I guess I just need to find relevant literature support for this notion and counter argue my co-author's suggestion to transform it.

[Joao Santos Silva]

Dear Anton,

There is a large literature on the dangers of transforming the dependent variable; see for example this paper and this one.

All the best,

Joao