Poisson fixed effect + instrument varaible

[Chen Jing]

Hi all,

I am interested in using Poisson fixed effect regression (count as DV, control for time and unit fixed effects) with the instrument variable approach (address endogenous explanatory variables). However, I could not find any package containing both functions. I noticed the ivpoisson function can implement IV but without fixed effects; xtpoisson with fixed effects but without IV. I think I can do a 2SLS and then apply the Poisson FE. But I still want to check whether there is a package containing both features.

In R, there seems an underdeveloped function in "fixest" for the purpose: https://github.com/lrberge/fixest/issues/176

Is the lack of both features simultaneously due to computation limitations or am I missing some statistics simulation flaw?

Thanks to anyone for any help.

Best,
Chen

[Joao Santos Silva]

Dear Chen Jing,

The IV estimator for Poisson-type regression suffers from the incidental parameter problem and that is why you do not see commands implementing that estimator.

Best wishes,

Joao

[Chen Jing]

Thank you Joao Santos Silva for your reply. I checked and learned the issue of incidental parameter problem (FE with nonlinear).

I am curious how it impacts if I am using 2SLS to get the fitted_v first and then apply it to the method like xtpoisson?

[haiyan lin]

Dear Chen Jing,

The IV estimator for Poisson-type regression suffers from the incidental parameter problem and that is why you do not see commands implementing that estimator.

Best wishes,

Joao

Dear Professor Silva,

Would it be possible to run PPML with endogeous variable and fixed effects in bilateral trades? According to this website: https://personal.lse.ac.uk/tenreyro/lgw.html, Martin Weidner and Tom Zylkin have shown that PPML is also largely immune to the incidental parameter problem when the model contains three sets of fixed effects. Joao Santos Silva

Many thanks!
Haiyan

[Joao Santos Silva]

Dear haiyan lin,

The result by Martin and Tom is only valid when the regressors are exogenous or pre-determined. So, with endogenous regressors, there will be incidental parameter bias.

Best wishes,

Joao

[haiyan lin]

Dear haiyan lin,

The result by Martin and Tom is only valid when the regressors are exogenous or pre-determined. So, with endogenous regressors, there will be incidental parameter bias.

Best wishes,

Joao

Thank you very much, Professor Joao Santos Silva !

I wonder if there is a way to estimate a model with nonnegative outcome variables, nonnegative endogenous variables, and fixed effects. I am working with bilateral trade data, the outcome variable is nonnegative. The main explanatory variable is non-negative as well, with endogeneity. I need to control for three levels of fixed effects: importer-exporter, importer-year, and exporter-year. I have searched around and could not find an ideal estimation method. Any advice is appreciated!

Regards,
Haiyan

[Joao Santos Silva]

Dear haiyan lin,

As you noted in your other post, one solution is to use a control function approach, but make sure you are clear about the implied assumptions.

Best wishes,

Joao

[haiyan lin]

Dear haiyan lin,

As you noted in your other post, one solution is to use a control function approach, but make sure you are clear about the implied assumptions.

Best wishes,

Joao

Great! That's really good news! Thank you very much for your expertise! Joao Santos Silva

I want to make sure whether this way works: estimating the first stage with PPMLFE and then inserting the residuals in the second stage with PPMLFE? That is, use the control function method with PPMLFE in the two stages.

I am not familiar with nonlinear regressions. I wonder whether the assumptions of a continuous endogenous explanatory variable (here a nonnegative trade variable) and exogenous instruments are enough to make the above procedure valid? I think I also need to adjust the standard error with bootstrapping. If possible, could you please let me know any caveats that I need to pay attention to? Or any papers recommended?

Much appreciated for your help!

Best,
Haiyan

[Joao Santos Silva]

I am afraid I am not en expert on the control function approach; I am sure others will help.

[haiyan lin]

Okay~Thanks anyway for your time and consideration!

Best,
Haiyan