robust vs cluster s.e. in FE or RE models

[Vaggelis Ktenas]

I would like to ask something that has been discussed but i'm still not sure. In a model with panel data that exists heterogeneity among panels and autocorrelation of errors, should i use cluster st. errors in panel variable, whereas when i have only the absence of homogeneity in variance the most appropriate is to use robust? Moreover, the use of clustering standard errors has to do with the experimental design and if the "treatment" is assigned to groups rather than to persons i should also cluster the errors in panel variable. Is that right? Are there some models that these two options are equals? My model has all these "problems" with assumptions of linear regression in panel analysis.

Thank you in advance

[Clyde Schechter]

In a fixed-effects model the non-cluster robust variance estimator is not valid and should not be used. Actually, in Stata, it cannot be used. If you specify -xtreg, fe robust-, Stata will automatically, and without even telling you, use vce(cluster panel_variable) instead. (This is true since version 13.)

With random effects models, the non-cluster robust estimator is usable. But given autocorrelation and group assignment of treatment, you should not use it.

[Vaggelis Ktenas]

i indeed use version 13. Thank you very much!

[Joro Kolev]

Hi Vaggelis,

You should give an example of what you have in mind, as it is not very clear now what you re wondering about. There are at least 3 issues which you might be wondering about in your question:

1. What Clyde explained is that even without autocorrelation (or any correlation ) within panels, the standard fixed effect variance estimator is not consistent, and one should use the clustered estimator (e.g. Stock, J.H. and Watson, M.W., 2008. Heteroskedasticity‐robust standard errors for fixed effects panel data regression. Econometrica, 76(1), pp.155-174.)

2. What Clyde also mentioned is that it makes perfect sense to use random effects panel regression, and still to cluster at the panel level if you think that the random effect structure is not picking up all the correlation (e.g., Kolev, G.I., 2012. Underperformance by female CEOs: A more powerful test. Economics Letters, 117(2), pp.436-440. Or all the huge literature on Generalised Estimating Equations, in this literature the random effects would be called the "working correlation structure", which you might think is a best guess, but you might still want to guard against misspecification of this structure.). You might have come across this issue if you were digging into old threads on Stata. In the old days of Stata (say Stata 7), Stata would not allow you to use robust or cluster options after random effects panel regression, because it was thought that "this does not make sense". Stata 13 allows the use of robust and cluster options after random effect panel regression, so this issue is gone now.

3. And the most nasty issue (because one's significance stars tend to disappear when one does this properly) which you seem to be mentioning in your question is the following:
Say you have panel data with whatever correlation structure within your panels. But your main variable of interest varies only at a higher level. Example of this is also a randomised treatment which is however randomised at the higher level, not at the panel level. Say you have panel data of people which are nested within states in the US. And your main variable of interest varies only at the state level. Or your randomisation was done at the state level. In this case you need to cluster at the state level (not at the panel level). Because regression errors of people from the same state would be correlated if they share the same regressor, or the same treatment. So you cluster at the highest level of aggregation at which you suspect correlated regression errors.

[Vaggelis Ktenas]

thank you very much Joro for all information! Well, issues 1 & 3 are clear and i 'm ok. I have clustered at the highest level of aggregation and i can understand what you and Clyde said about the case in FE model. I believe that my appropriate model is RE and due to treatment assignment, heteroskedacity and autocorrelation i used cluster. I also have big number of N and small of T so i 'll not have problem with the assumptions of the model, by using cluster, is that right? However, in issue 2 you refer that usually the RE structure solves the problem of correlation? that's because we control for everything (within and between)? I just used the command -xtserial.. Anyway thank you, i'll study what you proposed.