Xtlogit with random effects and robust standard errors: Prob > chi2 >0.05 How can I solve the issue?

[Franka Gutzmer]

Dear all,

I have a binary DV (existence of a specific job position at the board of directors yes/no) and three IV of which one is also of a binary nature and time-invariant (belonging to certain industries yes/no). Thus, I use xtlogit with random effects (confirmed by Hausman test). I have round about 970 observations (139 entities over 8 year, unbalanced panel data).

In order to care for potential heteroscedasticity and autocorrelation I should include robust standard errors. In addition, I want to integrate country and year fixed effects.
My regression equations look as following in Stata:
(1) xtlogit DV IV1 IV2(binary) CVs i.country i.year, re vce(robust)
(2) xtlogit DV IV3 IV2(binary) CVs i.country i.year, re vce(robust)

I seperated IV1 and IV3 as they are medium correlated and included IV2 (the binary time invariant IV in both equations).

Now I face the following issue:
Both regression outcomes look fine in stata when I include the country and year fixed effects but not the robust standard errors. IV significant and prob>chi2 = 0.0000
Once I add vce(robust) to the equation all previously significant variables become insignificant and more concerning: Prob>chi2 is bigger than 0.05 (for the first regression even 1.0000).
As far as I know, prob>chi2 tells me if my model is better fitting than the 0-Model and with values above 0.05 I cannot reject the 0-model.

Here my questions:
1a: Does anyone know why this is happening (how I could explain that result) or...
1b: ...what I can do with my variables (transform...) in order to receive a prob>chi2 below 0.05?
2: Is the inclusion of vce(robust) really necessary or is there a way I could justify the exclusion?
3: Is my general approach (xtlogit re) correct or does a different approach seem more fitting in your eyes?

Help is really much appreciated.

Thank you in advance and best regards,
Franka

[Carlo Lazzaro]

Franka:
please share Stata outcome tables, too. Thanks.

[Franka Gutzmer]

Hi Carlo,

Thank you for your quick reply!
Please find the outcomes of regression 1 for the versions with and without robust standard errors attached.

Let me know if more details are needed.

Thanks!

[Carlo Lazzaro]

Franka:

1) it may well be that you have an autocorrelation issue that drops the statistical significance when you go non-default standard errors;
2) it may also be that you have redundant predictors.
I would start it all over again, adding one predictor at a time and see when problems creep up with cluster-robust standard errors (with 139 panels is the way to go).

[Franka Gutzmer]

Thanks Carlo,

I will give it a try.

But the xtlogit re model choice seems correct for you, right? Or do you have other model suggestions for me?

[Carlo Lazzaro]

Franka:
it seems reasonable with the proviso that I do not know your dataset, not to say your research goal(s).

[Franka Gutzmer]

Thanks Carlo!

The research goal is to identify predictors of the board role "cso".

I just tried out your approach in adding one variable at a time but unfortunately, no matter which variable I add after the DV, the model always has a prob>chi2 just below 1.0000 (e.g. 0.9888). Please see examples below:

xtlogit cso ln_total_assets i.country i.year, re vce(robust) // prob>chi2: 0.9948
xtlogit cso culpable_industry i.country i.year, re vce(robust) //prob>chi2: 0.9895
xtlogit cso ln_fte i.country i.year, re vce(robust) //prob>chi2: 0.9888
xtlogit cso es_score i.country i.year, re vce(robust) // prob>chi2: 0.9831
...

Did I understand your approach correctly? What does that mean now? That all my variables are redundant?
I am really lost now...

Thanks so much for your support

Franka

[Carlo Lazzaro]

Frank:
first, no panic please.
I meant something like:

xtlogit cso ln_total_assets i.country i.year, re vce(robust)
xtlogit cso ln_total_assets culpable_industry i.country i.year, re vce(robust)
xtlogit cso ln_total_assets culpable_industry ln_fte i.country i.year, re vce(robust)

and so on.

[Franka Gutzmer]

Hi Carlo,

Just tried it that way and still no satisfying results... Each time I get a prob>chi2 from 0.9xxx. I tried it both ways: By leaving the ones out that increased the score from one step to another and by also still including them when adding the new one.

Any further idea?

Thanks,
Franka

[Carlo Lazzaro]

Franka:
try a more parsimonious model (that is, one with a lower number of regressors).