Incidental Parameters Problem - Ways to Circumvent?

[Carsten Preuss]

Dear community,

I am conducting an analysis where my dependent variable is of an ordinal nature. Since my sample is a panel and consists of observations from multiple industries, countries, and size classes, I was confident that including some fixed effects would capture unobserved heterogeneity. However, now I came across the Incidental Parameters Problems, saying that incidental parameters are inconsistently estimated in a ML panel estimation, as N → ∞, since only T observations are used to estimate each parameter (Cameron & Trivedi, 2005).

So far so good, after reading myself around the standard literature, I could not find anything helpful but that econometricians should be cautious using fixed effects in a ML panel estimation. For, example, Lancaster (2000) also states that it is remarkable that after 50 years that problem got published by Neymann and Scott (1948), there is still no solution (p. 409).

Does this mean, that one cannot run a Non-linear model with fixed effects? What should one do instead? I have seen at least a hundreds of research papers that made use of logic or profit models with fixed effects and were not even mentioning this problem. Can anybody suggest a solution or does have any ideas how to circumvent the issue?

Thanks in advance!

Carsten

[Carlo Lazzaro]

Carsten:
the fix is to perform a conditional fixed effect -xtlogit- (-xtlogit, fe-).

[Carsten Preuss]

Hi Carlo,

Thanks a lot for your answer! I would kindly like to ask, if you could provide any further readings on this or if you could shortly explain, in particular, what the difference between -xtlogit, fe- and logit with, let's say time-fixed effects is.
I know that in linear models, running -xtreg, fe- and -reg- with time-fixed effects is the same. However, I get different results for-xtlogit, fe- and logit with time-fixed effects.

Thanks a lot in advance!

[Richard Williams]

Paul Allison's book is very good:

https://www.amazon.com/Effects-Regre.../dp/0761924973

I summarize some highlights at

https://www3.nd.edu/~rwilliam/stats3...xedEffects.pdf

https://www3.nd.edu/~rwilliam/stats3...edVsRandom.pdf

[Carsten Preuss]

Thanks a lot for your replies!
One follow-up question: I assumed initially that my data was a panel. However it is super unbalanced, meaning that although I have a total time span of 18 periods, each individual appear max in 3 consecutive periods. Hence, I decided to treat the data rather as s repeated cross section. That said, does including time, country, and, let's say size and industry fixed effects still impose the incidental parameter problem to my non-linear (ologit) model?

Thank you very much in advance!

Carsten

[Carsten Preuss]

Dear community,

I very kindly wanted to place a reminder to my last question, just in case the post has been overseen by people who would have been able to answer.

Thanks a lot in advance!

[Carlo Lazzaro]

Carsten:
I do not see any advantage in treating your data as (repeated) cross-sectional instead of going -xtologit- .
Is fixed effect your concern (as -xtologit- allows -re- specification only)?

[Carsten Preuss]

Thanks, Carlo, for picking up on my post!

Yes indeed, I think the fixed effects are my concern. I am generally unsure when exactly the incidental parameters become a problem to a model. If I understood correctly, by using individual fixed effects (within estimator) the problem is that in a short panel (fixed T) - which would be the case, as entities appear maximum in three consecutive periods - the number of groups (i.id) increases with n, so the incidental parameters cause the estimates to be biased. In order to circumvent, it is advised to use the fixed effects estimator (conditional fixed effects), because then the individual fixed effects will get absorbed and will not cause a problem anymore. Is that correct?

However, if I went for only fixed effects dummies for, let's say industry, country and time, the incidental parameters problem should not pose a problem, because fixed effects are not increasing with n. I am I also right here?

So, since I have only a very short time series per entity and there is no fixed effects estimator available for an ordered logit model (as you said, -xtologit- allows -re- specification only), I was wondering, if it would be OK to treat the sample as a repeated cross section and ignore the individual time-fixed effects, ie. just go with -ologit- and control for time industry and country fixed effects.

I hope I was clear enough to understand the trade off I am thinking about.

Thank you very much for your help!

Carsten

[Carlo Lazzaro]

Carsten:
however, I think that an issue still stands out: due to the panel structure of your data, you cannot consider your observations as independent; hence, you should invoke clustered standard errors on -panelid-.

[Carsten Preuss]

Thanks for the quick reply!

Yes, of course, I have clustered the standard errors on the panel id. However, I do not control for individual fixed effects. I hope that is not completely wrong in my case.

[Carlo Lazzaro]

Carsten:
individual fixed effect (i.panelid) would be omitted due to collinearity, as I experienced in the following toy-example:

use http://www.stata-press.com/data/r15/fullauto
g year=1
expand 2
bysort model: replace year=2 if _n==2
ologit rep77 i.foreign i.year i.model, vce(cluster model)
note: 5000.model omitted because of collinearity
*as expected, the model does not converge*