# Assumptions about fixed effects and random effects model

I would really appreciate if someone can clarify the following things for me (either say that's correct or why not):

• FE: control for time-variant differences, less ommited variable bias than for RE (for FE, the omitted variable bias only comes from time-variant variables, right?)
• FE caluculates deciation from mean
• RE: quantifies impact of time-invariant variables (FE does not)
• assumption of RE: covariance between error term and predictors is zero, i.e. no correlation (how about FE?)
• what are the limitations to FE and what to RE models?
• when would I prefer RE over FE, when the other way round?

Thanks for your help!

• I think it's a typo but you should write "FE: control for time-INvariant differences" – VCG Sep 11 '16 at 13:21
• oh yeah, that was a typo, should have been invariant. thanks for the heads up! – Ann-Katrin Sep 11 '16 at 13:31

So you are somewhere there. I will rewrite each of your statements:

FE: controls for time-invariant differences between groups. It likely has less OVB than RE because it removes any of the omitted variation due to time-constant factors. Then the remaining OVB in an FE estimation method can only come from time-varying factors.

FE: The FE estimation method has 2 identical methods: Demean each variable from its group average across time. Or, add a dummy variable for each group.

RE: As RE does not remove the time-invariant variation, you can estimate time-constant variables in an RE model. FE eliminates that variation from estimation.

assumption of RE: the time-invariant heterogeneity between groups is uncorrelated with the error term. FE does not make this assumption and thus we remove that variation. BOTH of these models assume that the error term is uncorrelated with the observable predictors to be consistently estimatable (not sure if that's a word).

what are the limitations to FE and what to RE models? - FE controls for a lot of potential OVB, but by doing so it limits what you can estimate. For example you cannot estimate the effect of gender on something in an FE model. RE models are more relaxed in that you can do that, and they are more efficient (smaller SEs) but they risk more OVB.

when would I prefer RE over FE, when the other way round? - Generally, FE is a safer method and you should only prefer RE if you are confident that the assumptions hold. Some people think a Hausman test can help in determining which you should use.

Last note: Modeling with an FE estimation method does NOT eliminate all OVB. Any time-varying factors you do not adequately control for can affect your results. So while FE is safer than RE, if you care about the consistency of your coefficients, be careful with any estimation method that is not quasi-experimental like 2SLS.

• Thank you for the clarifiation VCG! With regards to FE models, is it okay to say to include time dummies in the regression to control for year variation of the dependent variable? – Ann-Katrin Sep 11 '16 at 13:34
• Yes - and you probably should! You can include time dummies and thus remove the time-varying factors that affect everybody. You can also include a time-trend to remove the variation due simply to the passage of time. Also, if you like this answer, confirming it would be nice. – VCG Sep 11 '16 at 13:37
• How would a time trend variable look like? And I just confirmed your answer - I'm fairly new, I also upvoted your answer but I have less than 15 reputation, so it wont show it publicly :/ – Ann-Katrin Sep 11 '16 at 13:38
• You would generate a variable that simply increasing 1 per time unit (2006,2007,2008) and then include it. – VCG Sep 11 '16 at 13:38