Xtlogit with random or fixed effects

[Jordi Imbrechts]

Dear all,

For my thesis I have to investigate the causes of layoffs for (big) Belgian firms. Data is panel data (unbalanced), period 2011-2020 (but with gaps).

Currently I'm stuck deciding wether to use FE or RE for my xtlogit model.

When I run the following commands:

xtlogit Collectiefontslag DalingProductiviteit1J DalingROA1J StandAlone DUO L.Lnleeftijd_w5 L.Lngrootte_w5 L.Schuldgraad_w1 L.MVAratio_w5, fe
estimates store fixed_effects
xtlogit Collectiefontslag DalingProductiviteit1J DalingROA1J StandAlone DUO L.Lnleeftijd_w5 L.Lngrootte_w5 Schuldgraad_w1 MVAratio_w5, re
hausman fixed_effects .

Result:

Prob>chi2 =      0.0000

Conclusion: I have to use FE

Problem:
When I use xtlogit FE model, Stata tells me the following:

note: multiple positive outcomes within groups encountered.
note: 9,489 groups (57,529 obs) dropped because of all positive or
      all negative outcomes.
note: StandAlone omitted because of no within-group variance.
note: DUO omitted because of no within-group variance.

More than half of my observations have been dropped (only 40,712 remain) & I can't use both StandAlone and DUO independent variables (both binary variables). Personally I find it quite strange that more than half of my observations have been dropped and that I can't use 2 of my 4 independent variables! As a solution I thought to proceed with RE model, but this is methodologically incorrect? Does anyone know what could be the best solution here?

Kind regards,
Jordi

[Carlo Lazzaro]

Jordi:
the issue you're facing is frequent with the logistic regression machinery.
If the outcome does not change within the panels, the culprit observations are dropped; otherwise, MLE cannot maximize.
There's nothing wrong with living with the resulting dataset, as data are what they are.
Eventually, please note that (conditional) fixed effect estimator wipes out time-invariant predictors and suffers from limited within-panel variation.
That said, thise above are not good reasons to switch to the -re- specification.

[Jordi Imbrechts]

Carlo,

Thanks for your advice. Although I do not completely understand why 2 of my independent variables become omitted (both are binary variables; DUO indicates = 1 when a firm has a Domestic Ultimate Owner (so no Global), when a firm has a mother company; StandAlone indicates = 1 when a firm is not a part of a group (= 0 when it is part of a businessgroup).
To be able to give a conclusion in my thesis about the 2 hypotheses that come with the indepent variables, I'm thinking that I defined these 2 variables wrong orsomething that they become omitted...

Could it be perhaps because of the fact that there is somewhat correlation between these 2 dummy variables (I tried running the model with just 1 of the 2 dummy variables and the problem stays the same), or because of the fact that the value of this dummy does not change over the period of the data?

Kind regards,
Jordi

[Jordi Imbrechts]

After some research myself I think that:

Due to the fact that there is no variation across time for a given firm for both DUO and StandAlone independent dummy variables, I can't use either DUO or StandAlone using FE model. During one brief course unit of Stata at universitiy I learned that with this kind of research (I'm in my master Finance) RE is almost always no option to use (due to the requirement that correlation between disturbance term and explanatory variable = 0). Therefor FE model should be the alternative, but then I come back to my main problem that 2 independent variables become omitted.

Is there anyway to solve the no variation across time problem for a given firm for DUO/StandAlone, or should I continue by using RE model? Although this seems rather odd to me.

Kind regards,
Jordi

EDIT: After more research ( https://www.statalist.org/forums/for...not-xtlogit-fe ) and taking into account that DUO and StandAlone are important explanatory variables for my research, I think my best option is to proceed with RE model.
Altought

That said, thise above are not good reasons to switch to the -re- specification.

makes me doubt this decision a lot...

[Carlo Lazzaro]

Jordi:
the answer was already given by Stata:

note: StandAlone omitted because of no within-group variance. note: DUO omitted because of no within-group variance.

As expected, no within-panel variation=no coefficient to estimate in the -fe- estimator parliance.
As an aside, the usual caveat appllies: if -fe- is the way to go, -re- estimator will give back inconsistent (ie, unreliable) estimates; if -re- is the way to go, -fe- will give back still consistent (althougn inefficient) estimates (these are the pillars supporting the -hausman- test).

[Jordi Imbrechts]

Carlo,

Thanks for the reply. I misunderstood the note given by Stata.
Could it be possible to test for the other 2 independent variables with -fe- model, but use -re- model for DUO & StandAlone? I know this is rather an odd methodology, but in all honesty I do not know how I could otherwise interpret DUO & StandAlone.
- Or could I perhaps compare the results for my other 2 independent variables of -fe- model and compare this with -re- model, in case both give the same direction (+ or -) and significance I could argument to use -re- model but where I clearly explain that this is one of the constraints of my research?

Kind regards,
Jordi

[Carlo Lazzaro]

Jordi:
I would simply go -fe- as per the -xtlogit- outcome and explain why two of the potential predictors were wiped out by the -fe- estimator.
All in all, if yous data comes from an empirical research, there's nothing you can do but living with the data as they are.

[Jordi Imbrechts]

Thank you very much Carlo. I hope that was the last (dumb) question

[Carlo Lazzaro]

Jordi:
no dumb question at all.
Going -fe- or -re- is not always that clear, especially if you have to defend your approach with supervisors/editors/reviewers and the like.

[Jordi Imbrechts]

Carlo,

That is very true. Just one last question, until yesterday I thought that year & sector fixed effects (i.Year & i.Sector) were only possible to use with -fe- model, but this can also be used with -re- model I read somewhere. Is this true?

Thanks again.

[Carlo Lazzaro]

Jordi:
you should -xtset- your dataset this way regardless of -fe- or -re-:

xtset panelvar timevar

keeping in mind that -panelvar- only is mandatory, whereas -timevar- is necessary if you plan to use time-series operators, such as lags and leads.
That said, regardless of -fe- or -re- specification, you should not include -i.panelvar- in the right-hand side of your regression equation, whereas you can plug in -i.timevar- even if not included in -xtset-.

[Jordi Imbrechts]

Carlo,

panelvar = ID
timevar = Jaar ( = year)

Sorry I explained my question wrong. I know that -.ID is not allowed in the right-hand side of the regression equation. But controlling for i.Sector is allowed, besides controlling for i.Year aswell?

[Carlo Lazzaro]

Jordi:
usually, -i.sector- is a time-invariant predictor.
Therefore, it will be wiped out by the -fe- machinery.

[Jordi Imbrechts]

Thank you Carlo.